ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„¢ļ…„ļ„˜ļ„®ļ„§ļ…„ļ„“ļ…† ļ„Æļ…„ļ„¹ļ„® ļ„Æļ…žļ„Ŗļ„µ-2024
ļ„±ļ…„ļ„— ļ„Æļ…œļ„¢ļ„ø ļ„ ļ„ŗļ„³ļ…‰ļ„ŗļ„„ļ„µ
ļ„³ ļ„Ŗļ„µ ļ„Ŗļ„³ļ„› ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„
(ļ„³ ļ„Ŗļ„µ ļ„Ŗļ„³ļ„› ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„-V)
ļ„ŗļ„³ ļ„: ļ…ƒļ„Ŗļ…œļ„® ļ„žļ…œļ„„ļ…‡ ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„‘ļ…œļ„›:100
ļ„®ļ…‹ļ„„: ļ„»ļ„µļ…‡ļ„› ļ„² ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„“ļ…žļ„› ļ„Æļ…„ļ„¹ļ„® ļ„ ļ……ļ„© ļ„›ļ…‡, ļ„›ļ……ļ…žļ„¶ ļ„Æļ…œļ„¢ ļ„Æļ…„ļ„¹ļ„® ļ„ ļ„¬ļ…„ ļ„›ļ…‹ļ…ƒļ„¹ļ„¹ ļ„›ļ„µļ…‹ī„” ļ„Æļ…œļ„¢ļ„ø ļ„ ļ„Æļ…„ļ„¹ļ„®
ļ…ƒļ„›ļ„ŗļ…‡ ļ„øļ…„ ļ„² ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„›ļ…„ļ„Ŗ ļ„¢ ļ„ŗļ„›ļ„¬ ļ„»ļ…‰ī„” ļ„ŗ ļ„µļ…‡ ļ„Æļ…„ļ„¹ļ„® ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„› ļ„±ļ„µ ļ„±ļ„µ ļ„»ļ„®ī„”
ļ„² ļ„-ļ„—
1. ļ„»ļ…‡ļ„¦ ļ…ƒļ„¶ļ„œļ…‡ ļ„¹ļ„±ļ„¬ ļ„ ļ„¬ļ…„ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’ ļ„›ļ„µļ…‹:
(i) ļ„“ļ…žļ„› ļ„Æļ…†ļ„” ļ„ø ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„¬ļ…‹ ļ„Æļ…†ļ„” ļ„ø ļ„¶ļ…‡ ļ„„ļ…‰ļ„ŗļ„„
(ii) ļ„® ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ
(iii) ļ…ƒļ„›ļ„ŗļ„³ 1 ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„
2. (ļ…”) ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„² ļ„øļ„® ļ„‘ļ„®ļ……ļ„³ ļ„® (MLE) ļ…ƒļ„øļ„­ļ…„ ļ„Ŗļ…Œ ļ„Ŗļ……ļ„» ļ„§ ļ„›ļ…„ ļ„² ļ„ø ļ„»ļ…‰? ļ„“ļ„» ļ„’ļ„³ ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„øļ„µļ„
(OLS) ļ…ƒļ„øļ„­ļ…„ ļ„Ŗļ…Œ ļ…ƒļ„›ļ„ŗ ļ„‘ļ„µļ„« ļ…ƒļ„øļ…žļ„  ļ„øļ…žļ„œļ„µ ļ„»ļ…‰? ļ…ƒļ„øļ„ŗļ„« ļ„µ ļ…ƒļ„øļ…žļ„  ļ„ ļ„µļ„  ļ„›ļ„µļ…‹ī„”
(ļ„‘) ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ ļ„® ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„›ļ„µļ„Ŗ ļ…ƒļ„øļ…žļ„  ļ„‘ļ…œļ„Ŗļ„µ ļ„¬ļ…žļ„ŗļ…‹ī„” ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‡ ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„›ļ„µļ„Ŗ ļ„¬ļ…‡ ļ„ļ……ļ„© ļ„
ļ„± ļ„µļ…‡ ļ„øļ…„ ļ„ ļ„µļ„  ļ„›ļ„µļ…‹ī„”
ļ„² ļ„-ļ„±ļ…„
3. xĀ² (ļ„ ļ…„-ļ„øļ„µļ„) ļ„øļ…œļ„§ ļ„Ŗļ…Œ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„›ļ…„ ļ„ŗļ„³ļ„£ļ„¬ļ…‡ ļ„»ļ…‹? ļ„“ļ„ŗļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„ļ……ļ„© ļ„ ļ„®ļ…†ļ…œ ļ„Æļ…„ ļ„Æļ„Ŗ ļ„›ļ„µļ…‹ī„”
4. ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„¬ļ…‡ ļ„„ļ…„-ļ„ŗļ„„ļ…‰ļ…ƒļ„„ļ„ŗļ…ƒļ„„ļ„› ļ„®ļ…†ļ…œ ļ„Æļ…ƒļ„µļ„² ļ…ƒļ„¹ļ„Ŗ ļ„›ļ„µļ…‹ ļ„‘ļ„Ŗļ…‡ ļ„“ļ„ŗļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„ļ……ļ„© ļ„Æļ…„ ļ„Æļ„Ŗ ļ„›ļ„µļ…‹ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„² ļ„-ļ„ŗļ…„
5. (ļ…”) 500 ļ…ƒļ„øļ„‘ļ„›ļ„Ŗļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ…ƒļ„øļ…žļ„ , 280 ļ„ ļ…ļ„¶ ļ„œ ļ„© ļ„ø ļ„¶ļ…‡ ļ„Æ ļ„— ļ„ļ„— ļ„»ļ„® ļ„‘ļ„Ŗļ…‡ ļ„± ļ„›ļ…„ ļ„›ļ„©ļ„› ļ„œ ļ„©
ļ„ø ļ„¶ļ…‡ ļ„»ļ„®ī„” ļ„›ļ…„ ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ„» ļ„³ļ…œļ„® ļ„ŗļ„›ļ„¬ļ…‡ ļ„» ļ„ ļ…ƒļ„› ļ„¬ļ…‹ļ„øļ…ˆ ļ„ ļ…„ļ„¾ ļ„ ļ„±ļ„µ ļ„±ļ„µ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ„®?
(ļ„‘) Z ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„•ļ„Æļ„“ļ…‹ļ„ ļ„ ļ„± ļ„µļ…‡ ļ„ ļ„µļ„  ļ„›ļ„µļ…‹ī„”
6. ļ„“ļ…žļ„› ļ„Æļ…„ļ„“ļ…‹ļ„ļ„¹ ļ„¶ ļ„Æļ…„ļ„“ļ…‹ļ„ ļ…ƒļ„øļ…žļ„ , ļ„¬ļ…‹ ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ ļ„®ļ…‡ ļ„»ļ…‡ļ„¦ ļ…ƒļ„¶ļ„œļ…‡ ļ„®ļ„Ŗļ…„ļ„¢ļ…‡ ļ…ƒļ„¬ļ…žļ„Ŗļ…‡:
ļ„®ļ„³ļ…†ļ„®
ļ„’ļ„› ļ„µ
ļ„ŗļ„­ ļ„µļ„® ļ„šļ„ŗļ„Ŗ
ļ„šļ„ŗļ„Ŗ ļ„Ŗļ…Œ ļ„²ļ„„ļ„›ļ„© ļ„ ļ„¬ļ…‡
ļ„øļ„µļ„ ļ„ ļ„¬ ļ„¢ļ…‹ļ„æ
1
10
15
90
2
12
14
108
5% ļ„³ļ„»ļ…žļ„Ŗļ„Ŗ ļ„¬ļ…‡ ļ„Æļ…žļ„­ļ„µ 'ļ„Ŗļ…‡ ļ„®ļ„³ļ…†ļ„® ļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„ø ļ„ ļ„¬ļ…„ ļ„ŗļ„³ ļ„®ļ„Ŗ ļ„¬ļ…„ ļ„¢ ļ„ļ„  ļ„›ļ„µļ…‹ī„”
ļ„ŗļ…‰ļ„›ļ„¹ļ„®-ļ„§ļ…„
7. ļ„“ļ…žļ„› ļ„„ļ„µļ…žļ…ƒļ„›ļ…œļ„ ļ„›ļ…œļ„Æļ„®ļ…„ ļ„  ļ„µ ļ„±ļ…„ ļ„ļ„§ ļ„ ļ„¬ļ…‡ ļ„„ ļ„“ļ„µ ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„»ļ„µļ…‡ļ„› ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„•ļ„³ļ„µ ļ„¬ļ…„ ļ„¢ ļ„ļ„  ļ„›ļ„µļ„® ļ„  ļ„»ļ……ļ…œļ„¬ļ…„
ļ„»ļ…‰ī„” ļ„›ļ…œļ„Æļ„®ļ…„ ļ„ŗ ļ„µļ…‡ ļ„±ļ…„ ļ„ļ„§ ļ„ ļ„®ļ…†ļ…œ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„±ļ…‡ ļ„ ļ……ļ„©ļ…‡ ļ„»ļ…‹ļ„— ļ„„ļ„µļ…žļ„› ļ„ 'ļ„Ŗļ…‡ ļ„øļ„µļ„Ŗļ„¬ļ…„ ļ„»ļ…‰ī„” ļ…ƒļ„¾ļ…œļ„¬ļ„ļ…„ļ„’ļ„ (ļ„»ļ„¾ ļ„µ ļ„ ļ„³ļ…„ļ„¶)
ļ„¬ļ„µļ„ŗ ļ„•ļ„© ļ„ø ļ„¶ļ…‡ ļ…ƒļ„µļ„› ļ„µļ„§ ļ„»ļ…‡ļ„¦ ļ„ ļ…ƒļ„¬ļ…žļ„Ŗļ…„ ļ„ŗ ļ„µļ„©ļ…„ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„¬ļ…žļ„Ŗļ…‡ ļ„ļ„— ļ„»ļ„®:
ļ„±ļ…„ ļ„ļ„§ 1
ļ„±ļ…„ ļ„ļ„§ 2
ļ„±ļ…„ ļ„ļ„§ 3
ļ„±ļ…„ ļ„ļ„§ 4
20
19
21
15
23
15
19
17
18
17
20
16
17
20
17
18
16
16
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„“ļ„ŗ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® ļ„¬ļ…„ ļ„¢ ļ„ļ„  ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„»ļ„µļ…‡ļ„› ļ„±ļ…„ ļ„ļ„§ ļ„¬ļ…‡ ļ„„ ļ„“ļ„µ ļ„ ļ„¬ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…„ļ„øļ„® ļ„“ļ…žļ„›ļ…‹ ļ…ƒļ„¢ļ„» ļ„»ļ……ļ…œļ„¬ ļ„»ļ…‰ī„”
8. ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„¬ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„›ļ…„ ļ„»ļ…‰? ļ„“ļ„ŗ ļ„¬ļ…„ļ„’ļ„ ļ„³ļ……ļ…žļ„œ ļ„­ ļ„µļ„® ļ„ø ļ„ 'ļ„Ŗļ…‡ ļ„ ļ„µļ„  ļ„›ļ„µļ…‹ī„” ļ„“ļ…žļ„› ļ„Æ ļ„ŗļ…‡
ļ„‘ļ„Ŗļ…‡ ļ„¬ļ…‹ ļ„Æ ļ„ŗļ…‡ ANOVA ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„ ļ…ƒļ„øļ…žļ„  ļ„øļ…„ ļ„‘ļ…œļ„Ŗļ„µ ļ„›ļ„µļ…‹ī„”
ļ„¢ļ…„ļ„˜ļ„®ļ„§ļ…„ļ„“ļ…† ļ„•ļ…žļ„Ŗļ„µ ļ„Æļ…žļ„Ŗļ„µ-2024
ļ„±ļ…„ļ„— ļ„Æļ…œļ„¢ļ„ø ļ„ ļ„ŗļ„³ļ…‰ļ„ŗļ„„ļ„µ
ļ„³ ļ„Ŗļ„µ ļ„Ŗļ„³ļ„› ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„
(ļ„³ ļ„Ŗļ„µ ļ„Ŗļ„³ļ„› ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„-V)
ļ„ŗļ„³ ļ„: ļ…ƒļ„Ŗļ…œļ„® ļ„žļ…œļ„„ļ…‡ ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„‘ļ…œļ„›:100
ļ„®ļ…‹ļ„„: ļ„»ļ„µļ…‡ļ„› ļ„² ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„“ļ…žļ„› ļ„Æļ…„ļ„¹ļ„® ļ„ ļ……ļ„© ļ„›ļ…‡, ļ„›ļ……ļ…žļ„¶ ļ„Æļ…œļ„¢ ļ„Æļ…„ļ„¹ļ„® ļ„ ļ„¬ļ…„ ļ„›ļ…‹ļ…ƒļ„¹ļ„¹ ļ„›ļ„µļ…‹ī„” ļ„Æļ…œļ„¢ļ„ø ļ„ ļ„Æļ…„ļ„¹ļ„®
ļ…ƒļ„›ļ„ŗļ…‡ ļ„øļ…„ ļ„² ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„›ļ…„ļ„Ŗ ļ„¢ ļ„ŗļ„›ļ„¬ ļ„»ļ…‰ī„” ļ„ŗ ļ„µļ…‡ ļ„Æļ…„ļ„¹ļ„® ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„› ļ„±ļ„µ ļ„±ļ„µ ļ„»ļ„®ī„”
ļ„² ļ„-ļ„—
1. ļ„»ļ…‡ļ„¦ ļ…ƒļ„¶ļ„œļ…‡ ļ„¹ļ„±ļ„¬ ļ„ ļ„¬ļ…„ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’ ļ„›ļ„µļ…‹:
(i) ļ„“ļ…žļ„› ļ„Æļ…†ļ„” ļ„ø ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„¬ļ…‹ ļ„Æļ…†ļ„” ļ„ø ļ„¶ļ…‡ ļ„„ļ…‰ļ„ŗļ„„
(ii) ļ„® ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ
(iii) ļ…ƒļ„›ļ„ŗļ„³ 1 ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„
ļ„•ļ…žļ„Ŗļ„µ:ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® ļ„„ļ…‰ļ„ŗļ…ƒļ„„ļ…œļ„ ļ…ƒļ„øļ…žļ„  ļ„³ļ……ļ…žļ„œ ļ„ŗļ…œļ„›ļ„¶ļ„Æ ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„© : ļ„“ļ…žļ„› ļ„ŗļ„­ ļ„µļ„® ļ„›ļ„» ļ„©ļ…„
ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗ ļ„»ļ…‹ ļ„¢ļ…‹ ļ„“ļ…žļ„› ļ„µļ„»ļ…žļ„ŗ ļ„®ļ…†ļ…œ ļ„ŗļ……ļ„¶ļ„£ļ…‚ļ„•ļ„© ļ„¬ļ…„ ļ„›ļ…‹ļ…ƒļ„¹ļ„¹ ļ„›ļ„µ ļ…ƒļ„µļ„»ļ…‚ ļ„»ļ…‰ī„” ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„ŗļ…‚ļ„»ļ„³ļ„©ļ…‡
ļ„“ļ…žļ„› ļ„±ļ…œļ„¬ ļ„§ļ…žļ„±ļ…‚ ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ„‘ļ…œļ„¬ļ„µ ļ„›ļ…„ ļ„»ļ…‰ ļ„±ļ…‚ļ„µļ…‡ ļ„¹ļ…žļ„› ļ„»ļ…‰ī„” ļ„Æļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„Ŗļ……ļ„µļ…œļ„Ŗ ļ„®ļ„»ļ…„
ļ„
ļ„œļ…‹ļ„¶ļ…§ ļ„ŗļ„›ļ„¬ļ…‡; ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ
ļ„ŗļ……ļ„µļ…‚ļ„ļ…‚ļ„, ļ…ƒļ„®ļ„µļ…„ļ„œļ„©ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„±ļ…†ļ„Ŗļ…‚ļ„ 'ļ„Ŗļ…‡ ļ„²ļ„µļ…‹ļ„ŗļ…‚ ļ„›ļ„µļ„®ļ…‚ ļ„Æļ…Šļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„“ļ„» ļ…ƒļ„±ļ„¶ļ„›ļ……ļ„¶ ļ„•ļ„»ļ…„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ…ƒļ„øļ…ƒļ„ļ„’ļ„®ļ…„ ļ„‘ļ„Ŗļ…‡ ļ„‘ļ…œļ„›ļ„æļ…‚
ļ…ƒļ„øļ…ƒļ„ļ„’ļ„®ļ…„ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„® ļ„¢ļ„¬ļ…Œ ļ„•ļ„» ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„•ļ„» ļ„»ļ„³ļ…‡ļ„¹ļ…‚ ļ„ŗļ…žļ„  ļ„®ļ…†ļ…œ ļ…ƒļ„ŗļ…žļ„­ļ…‡ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ "ļ„®ļ„»ļ…„
ļ„
ļ„¬ļ…‡ļ„œ" ļ„ŗļ„›ļ„¬ļ…‡, ļ„Æļ„µ ļ„•ļ„» ļ„°ļ…‰ļ„ŗļ„¶ļ…‡ ļ„¶ļ…‰ļ„© ļ„¶ļ„” ļ„§ļ…‡ļ„„ļ…‚, ļ…ƒļ„®ļ„“ļ„³ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„Ŗļ„µļ„› ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„“ļ„ŗ ļ„›ļ„»ļ…‚ļ„©ļ…„ ļ…ƒļ„øļ…žļ„ ,
ļ„‘ļ„ŗļ…„
ļ„
ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„„ļ…‰ļ„ŗļ…ƒļ„„ļ…œļ„ ļ…ƒļ„øļ…žļ„  ļ„ ļ…‚ļ„µ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„ŗļ…œļ„›ļ„¶ļ„Æļ…‚ļ„ ļ„¬ļ…„ ļ„Æļ„æļ„ ļ…‹ļ„¶ ļ„›ļ„µļ…‚ļ„ļ„ļ…‡: ļ„“ļ…žļ„›-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‡ ļ„‘ļ„Ŗļ…‡ ļ„¬ļ…‹-
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‡ ļ„„ļ…‰ļ„ŗļ„„, ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ, ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„›ļ„ŗļ„³ I ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ī„” ļ„‘ļ…œļ„Ŗ ļ„Ŗļ…žļ„›, ļ„“ļ„» ļ„¹ļ„±ļ„¬ ļ„“ļ…žļ„› ļ„±ļ……ļ„£ļ…‚ļ„µļ„Ŗ ļ„®ļ…†ļ…œ
ļ„»ļ…žļ„¶ ļ„›ļ„µļ„® ļ„øļ…‚ļ„ļ„ ļ„‘ļ„®ļ……ļ„²ļ„øļ…„ ļ„³ļ…ƒļ„»ļ„ŗļ…†ļ„ŗ ļ„»ļ…‹ļ„©ļ„ļ…‡ī„”
(i) ļ„“ļ…žļ„›-ļ„Æļ…†ļ„” ļ„ø ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„¬ļ…‹-ļ„Æļ…†ļ„” ļ„ø ļ„¶ ļ„„ļ…‰ļ„ŗļ„„: ļ…ƒļ„›ļ…žļ„«ļ…‡ ļ„¬ļ…‡ļ„œļ„© ļ„»ļ…‰ ļ„“ļ„» ļ„ ļ……ļ„©ļ„®
ļ„’ļ„™ ļ„’ļ„Æļ„©ļ…„ ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗļ…„ ļ„ŗļ„³ļ…‚ļ„®ļ„Ŗļ…‚ ļ„®ļ…‚ļ„¶ ļ„‘ļ…žļ„ļ…‡ ļ„øļ„­ļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„” ļ„³ļ…œļ„® ļ„¶ļ„™ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µ ļ„µļ„»ļ…‡ ļ„»ļ…‹ ļ…ƒļ„› ļ„›ļ…„ ļ„›ļ…‹ļ„” ļ„®ļ„øļ…„
ļ„
ļ„¬ļ„øļ…‚ļ„” ļ„³ļ„µļ…„ļ„¾ļ…‚ļ„ ļ„¬ļ…„ ļ…ƒļ„µļ„›ļ„øļ„µļ…„ ļ„¬ļ„µ ļ„®ļ…†ļ…œ ļ„øļ„­ļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ī„” ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…„ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„“ļ„» ļ„»ļ…‰ ļ…ƒļ„› ļ„“ļ„» ļ„¬ļ„øļ…‚ļ„” ļ…ƒļ„³ļ„’ļ„µļ…„
ļ„“ļ„¶ļ…‚ļ„¢ ļ„®ļ…‚ļ„¶ļ…Œ ļ„øļ…žļ„­ ļ„³ļ„¬ļ„¬ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ī„” ļ„›ļ……ļ„¬ļ„µļ„Ŗļ…„ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡, ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ…ƒļ„ŗļ„µļ„° ļ„Ŗļ…‚ļ„ ļ„»ļ…„ ļ…ƒļ„¬ļ„¶ļ„ ļ„ŗļ„Æļ…„ ļ„µļ…žļ„œļ„¬ļ…‡ ļ„»ļ…‹ ļ„¢ļ…‡ļ„›ļ„µ ļ„“ļ„»
ļ…ƒļ„µļ„›ļ„øļ„µļ…„ ļ„®ļ…†ļ…œ ļ„øļ„­ļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ - ļ„®ļ…‚ ļ…ƒļ„› ļ„¢ļ…‡ļ„›ļ„µ ļ„“ļ„» ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„žļ„„ļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ī„” ļ„“ļ…žļ„«ļ…‡, ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„’ļ„Æļ„©ļ…‚ ļ…ƒļ„­ļ„’ļ„® ļ„“ļ…žļ„› ļ…ƒļ„¬ļ„¹ļ…‚ ļ…ƒļ„øļ…žļ„ 
ļ„›ļ…ˆļ„¬ļ…ƒļ„µļ„Ŗ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ - ļ„•ļ…žļ„Æļ„µ ļ„øļ…žļ„¶, ļ„ŗļ……ļ„­ļ…‚ļ„µ ļ„¬ļ…„ ļ„²ļ…‚ļ„¶ ļ…ƒļ„øļ…žļ„ ī„” ļ„“ļ„» ļ„“ļ…žļ„›-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‡ ļ„„ļ…‰ļ„ŗļ„„ ļ„¬ļ…‚ ļ„ŗļ…‚ļ„µ ļ„»ļ…‰ī„”
ļ„“ļ…žļ„›-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‚ ļ„„ļ…‰ļ„ŗļ„„ ļ„“ļ„» ļ„¢ļ…‚ļ„ļ„ ļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ„“ļ…žļ„› ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µ (ļ…ƒļ„¢ļ„øļ…ˆ ļ…ƒļ„› ļ„šļ„ŗļ„Ŗ ļ…ƒļ„µļ„›ļ„øļ„µļ…„ ļ„¬ļ„µ) ļ„“ļ…žļ„› ļ„œļ…‚ļ„ŗ ļ„³ļ……ļ…žļ„¶ ļ„Ŗļ…Œ
ļ„øļ…žļ„­ ļ„»ļ…‰ ļ„¢ļ…‚ļ„ ļ„žļ…žļ„„ ļ„»ļ…‰, ļ„Æļ„µ ļ„¬ļ…‹ļ„øļ…ˆ ļ„®ļ„»ļ…„
ļ„
ī„” "ļ„Æļ…†ļ„”" ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„‘ļ…ƒļ„Ŗļ„‘ļ…œļ„Ŗ ļ„‘ļ…œļ„Ŗ ļ„®ļ…†ļ…œ ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚
ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ…ƒļ„ļ„’ ļ„§ļ…‡ļ„„ļ…‚ ļ„“ļ„ŗ ļ„Æļ…†ļ„” ļ…ƒļ„øļ…žļ„  ļ„’ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„›ļ…‹ļ„¶ ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ (ļ…ƒļ„§ļ„°ļ…‚ļ„¶ļ„„ ļ„­ļ…‚ļ„µļ„®ļ…‚ ļ…ƒļ„›
ļ„¬ļ„øļ…‚ļ„” ļ„¬ļ…‚ ļ„›ļ…‹ļ„” ļ„Æļ…„ļ„²ļ…‚ļ„ø ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‰) ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µļ„® ļ„¶ļ„” ļ„›ļ…‚ļ…€ļ…„ ļ„ŗļ„±ļ…†ļ„Ŗ ļ„»ļ„®ī„”
ļ„»ļ……ļ„©, ļ„“ļ…žļ„› ļ„»ļ…‹ļ„µ ļ…ƒļ„¬ļ…„ļ„¹ ļ„¬ļ…„ ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ī„” ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„®ļ„»ļ…„
ļ„
ļ„¢ļ…‚ļ„©ļ„¬ļ…‡ ļ…ƒļ„› ļ„¬ļ„øļ…‚ļ„” ļ„³ļ„µļ…„ļ„¾ļ…‚ļ„ ļ„¬ļ…„ ļ„³ļ„¬ļ„¬ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ ļ„¢ļ…‚ļ„ ļ„®ļ……ļ„›ļ„ŗļ…‚ļ„®
ļ„Æļ„»ļ……ļ…œļ„ ļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰; ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ…ƒļ„ŗļ„µļ…€ ļ„“ļ„» ļ„¬ļ…‡ļ„œļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ…‹ ļ…ƒļ„› ļ„“ļ„» ļ„›ļ…‹ļ„” ļ…€ļ„µļ„› ļ„Æļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰, ļ„¢ļ…‚ļ„ ļ„Ŗļ…‚ļ„ ļ„ŗļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„› ļ„¢ļ…‚ļ„
ļ„®ļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„›ī„” ļ„“ļ…žļ„«ļ…‡, ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ„¬ļ…‹ļ„øļ…‚ļ„ ļ…ƒļ„¬ļ„¹ļ…‚ļ„øļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„¬ļ…‡ļ„œļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‚ ļ„»ļ…‰ - ļ„›ļ…„ ļ…ƒļ„µļ„›ļ„øļ„µļ…„ ļ…ƒļ„øļ…žļ„  ļ„ŗļ……ļ„­ļ…‚ļ„µ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ…‚ļ„
ļ…ƒļ„øļ„ļ„æļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„¬ļ…‹-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‚ ļ„„ļ…‰ļ„ŗļ„„ ļ…ƒļ„›ļ„»ļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„¬ļ…‹-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‡ ļ„„ļ…‰ļ„ŗļ„„ ļ…ƒļ„øļ…žļ„ , ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„øļ…œļ„§
ļ„¬ļ…‡ ļ„¬ļ…‹ ļ…ƒļ„ŗļ…ƒļ„µļ„’ļ„ (ļ„Æļ…†ļ„”ļ…‚ļ„) ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„øļ…œļ…ƒļ„§ļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ…ƒļ„ŗļ„µļ…€ ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„§ļ…‡ļ„„ļ…‚ ļ„¬ļ…‹ļ„øļ…‚ļ„ ļ„Æļ…†ļ„”ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„’ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ ļ„Ŗļ…‚ļ„
ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ī„”
ļ„ŗļ…œļ„œļ…‡ļ„Æ ļ…ƒļ„øļ…žļ„ :
ā€¢ ļ„“ļ…žļ„›-ļ„Æļ…†ļ„” ļ„ø ļ„¶ ļ„„ļ…‰ļ„ŗļ„„:ļ„“ļ…žļ„› ļ„œļ…‚ļ„ŗ ļ…ƒļ„¬ļ„¹ļ…‚ (ļ„øļ„­ļ„©ļ…‚ ļ„¢ļ…‚ļ„ ļ„žļ„„ļ…‚ļ„•ļ„©ļ…‚) 'ļ„Ŗļ…‡ ļ…ƒļ„­ļ„’ļ„® ļ„›ļ…ˆļ„¬ļ…ƒļ„µļ„Ŗ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„¬ļ…‹-ļ„Æļ…†ļ„” ļ„ø ļ„¶ ļ„„ļ…‰ļ„ŗļ„„:ļ„¬ļ…‹ļ„øļ…‚ļ„ ļ…ƒļ„¬ļ„¹ļ…‚ļ„øļ…‚ļ„ (ļ„›ļ…‹ļ„” ļ„øļ…„ ļ„‘ļ…œļ„Ŗļ„µ) 'ļ„Ŗļ…‡ ļ…ƒļ„øļ„ ļ…‚ļ„µ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„“ļ…‚ļ„¬ ļ„µļ…žļ„œļ„© ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„ŗļ…ļ„œļ…‚ ļ„Ŗļ„µļ…„ļ„›ļ…‚ ļ„»ļ…‰: ļ„“ļ…žļ„›-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‚ ļ„“ļ…žļ„› ļ„ŗļ„®ļ…‚ļ„”ļ„Æļ„µ ļ„µļ…‚ļ„”ļ„°ļ„¶ ļ„øļ„µļ„ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰, ļ„ŗļ„„ļ…„ļ„›
ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ…ƒļ„¬ļ„¹ļ…‚ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„®ļ„¹ļ…‚ļ„®ļ…‚ ļ„±ļ„©ļ…‚ļ„“ļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰; ļ„¬ļ…‹-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‚ ļ„“ļ…žļ„› ļ„øļ…‚ļ„”ļ„§-ļ„˜ļ„ļ„ļ„¶ ļ„›ļ…‰ļ„³ļ„µļ…‡ ļ„øļ„µļ„ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰,
ļ…ƒļ„›ļ„ŗļ…‡ ļ„øļ…„ ļ„Ŗļ„±ļ„¬ļ…„ļ„¶ļ…„ ļ„®ļ…†ļ…œ ļ„›ļ…‰ļ„Æļ„ ļ„µ ļ„›ļ„µļ„® ļ„¶ļ„” ļ„¬ļ…‹ļ„øļ…ˆ ļ„Æļ…‚ļ„ŗļ…‡ ļ„¬ļ…‡ļ„œļ„¬ļ…‚ ļ„»ļ…‰ī„”
(ii) ļ„® ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ: ļ„¼ļ„Ŗļ„µļ…‡ ļ„ø ļ„¶ ļ„œļ…‡ļ„Ŗļ„µ
ļ„‘ļ…žļ„ļ…‡, ļ„‘ļ„Æļ„µļ…‚ļ„­ ļ„øļ…‚ļ„¶ļ…„ ļ„«ļ…‚ļ„ ļ„±ļ…‚ļ„µļ…‡ ļ„¬ļ……ļ„±ļ…‚ļ„µļ…‚ ļ„ŗļ…‹ļ„ ļ…‹ī„” ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„›ļ…‹ļ„” ļ„œļ…‚ļ„ŗ ļ„œļ…‡ļ„Ŗļ„µ ļ„»ļ…‰ ļ…ƒļ„¢ļ…žļ„«ļ…‡, ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ„ŗļ„±ļ…†ļ„Ŗ
ļ…ƒļ„³ļ„¶ļ„¬ļ…‡ ļ„»ļ„®, ļ„Ŗļ…‚ļ„ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ…ƒļ„øļ„¹ļ„øļ…‚ļ„ŗ ļ„®ļ…‚ļ„¶ ļ„›ļ…ƒļ„» ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‹, "ļ„’ļ„»ļ…‚! ļ„“ļ„» ļ„¹ļ…žļ„›ļ…„ ļ„¬ļ…„ ļ„¹ļ„³ļ…†ļ„¶ļ…„ļ„‘ļ„Ŗ ļ„®ļ…†ļ…œ ļ„ŗļ…‚ļ„±ļ„Ŗ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”"
ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ…ƒļ„øļ…žļ„ , ļ„“ļ„ŗ ļ„œļ…‡ļ„Ŗļ„µ ļ„®ļ…†ļ…œ ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ ļ…ƒļ„›ļ„»ļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ ļ„“ļ…žļ„› ļ„„ļ…‰ļ„ŗļ„„ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ„¬ļ…‡ ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„¬ļ…‚ ļ„ŗļ„³ļ…†ļ„» ļ„»ļ…‰ ļ„¢ļ…‹ ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µļ„® ļ„øļ…žļ„¶ ļ„¶ļ…‰ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„“ļ„» ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„‘ļ…ƒļ„Ŗļ„‘ļ…œļ„Ŗ ļ„®ļ„Ŗļ…„ļ…ƒļ„¢ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„¬ļ…‡ ļ„ŗļ…žļ„  ļ„»ļ…‹ļ„© 'ļ„Ŗļ…‡ ļ„»ļ…‹ļ„© ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ„»ļ…„
ļ„
ļ„µļ…žļ„œļ„¬ļ…‡ī„”
ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„© ļ„øļ„¢ļ…Œ, ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ļ„’ļ„ ļ„¶ļ„” ļ„„ļ…‰ļ„ŗļ„„ ļ„ŗļ„›ļ…‹ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ„“ļ…žļ„› ļ„’ļ„³ ļ„øļ…œļ„§ 'ļ„Ŗļ…‡ ļ…ƒļ„øļ„ ļ…‚ļ„µ ļ„›ļ„µļ…‹ī„” ļ„¢ļ…‡ļ„›ļ„µ ļ„®ļ„¶
ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„¬ļ…‡ ļ„Ŗļ…ƒļ„»ļ„Ŗ ļ„šļ„ŗļ„Ŗ ļ„ŗļ„›ļ…‹ļ„µ 50 ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„³ļ„»ļ…žļ„Ŗļ„ø ļ„Æļ…žļ„­ļ„µ (Ī±) 5% ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„œļ…‡ļ„Ŗļ„µ
ļ„“ļ„» ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰:
ā€¢ ļ„“ļ…žļ„›-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‡ ļ„„ļ…‰ļ„ŗļ„„ (ļ„•ļ…žļ„  ļ„ŗļ„›ļ…‹ļ„µ ļ„¬ļ…„ ļ„²ļ…‚ļ„¶ ļ…ƒļ„øļ…žļ„ ) ļ„¶ļ„”, 60 ļ„Ŗļ…Œ ļ„•ļ…žļ„Æļ„µ ļ„¬ļ…‡ ļ„ŗļ„›ļ…‹ļ„µ ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ ļ…ƒļ„øļ…žļ„  ļ„’
ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„¬ļ…‹-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‡ ļ„„ļ…‰ļ„ŗļ„„ ļ„¶ļ„” (ļ…ƒļ„›ļ„ŗļ…‡ ļ„øļ…„ ļ„²ļ„„ļ„›ļ„©ļ…‚ ļ„¬ļ…„ ļ„²ļ…‚ļ„¶ ļ…ƒļ„øļ…žļ„ ), 40 ļ„Ŗļ…Œ ļ„žļ…žļ„„ ļ„¢ļ…‚ļ„ 60 ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ„›ļ…‹ļ„µ ļ„®ļ…‚ļ„¾ļ……ļ„›
ļ„œļ…‡ļ„Ŗļ„µ ļ…ƒļ„øļ…žļ„  ļ„’ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ…ƒļ„ļ„’ ļ„§ļ…‡ļ„„ļ…‚ ļ„“ļ„ŗ "ļ„¼ļ„Ŗļ„µļ…‡ ļ„øļ…‚ļ„¶ļ…‡ ļ„œļ…‡ļ„Ŗļ„µ" ļ…ƒļ„øļ…žļ„  ļ„’ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ ļ„“ļ„» ļ„ŗļ…œļ„›ļ…‡ļ„Ŗ ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ……ļ„£
ļ„‘ļ„ŗļ…‚ļ„­ļ…‚ļ„µļ„® ļ„øļ…‚ļ„Æļ…ƒļ„µļ„’ ļ„»ļ…‰, ļ…ƒļ„¢ļ„ŗ ļ„®ļ…‚ļ„¶ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‹ī„”
ļ„“ļ„ŗ ļ„¶ļ„”, ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ ļ„‘ļ„ŗļ„¶ ļ…ƒļ„øļ…žļ„  ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„¶ļ…‚ļ„¶ ļ„£ļ…œļ„§ļ…‚ ļ„»ļ…‰ - ļ„“ļ…žļ„› ļ„ŗļ„Æļ…žļ„¹ļ„„ ļ„ŗļ…œļ„›ļ…‡ļ„Ŗ ļ„»ļ…‰ ļ…ƒļ„› ļ„ŗļ„±ļ…†ļ„Ŗ
ļ„›ļ…‚ļ„µļ„øļ…‚ļ„” ļ„›ļ„µļ„® ļ„¶ļ„” ļ„›ļ…‚ļ…€ļ…„ ļ„³ļ„¾ļ„±ļ…†ļ„Ŗ ļ„»ļ„®ī„”
(iii) ļ…ƒļ„›ļ„ŗļ„³ I ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„: ļ„¢ļ„¬ļ…Œ ļ„¢ ļ„ŗļ…†ļ„ŗ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®
ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ„­ļ…„ļ„’ ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗ ļ„øļ…„ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„„ļ…‰ļ„ŗļ…ƒļ„„ļ…œļ„ ļ…ƒļ„øļ…žļ„ , ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„“ļ„ŗ ļ„¶ļ„”
ļ„»ļ……ļ…œļ„¬ļ…„ļ„’ļ„ ļ„»ļ„® ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„°ļ…‰ļ„ŗļ„¶ļ…‡ ļ„Æļ…†ļ„µļ…„ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ ļ„±ļ„¢ļ…‚ļ„— ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ 'ļ„Ŗļ…‡ ļ„‘ļ„­ļ…‚ļ„µļ„Ŗ ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„¬ļ…‹ ļ„Ŗļ„µļ…§ļ…‚ļ„ ļ„¬ļ…„ļ„’ļ„
ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„»ļ„®: ļ„„ļ…‚ļ„”ļ„Æ I ļ„ļ„¶ļ„Ŗļ…„ ļ„‘ļ„Ŗļ…‡ ļ„„ļ…‚ļ„”ļ„Æ II ļ„ļ„¶ļ„Ŗļ…„ī„”
ļ…ƒļ„›ļ„ŗļ„³ I ļ„ļ„¶ļ„Ŗļ…„: ļ„ļ„¶ļ„Ŗ ļ„‘ļ„¶ ļ„µļ„³
ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ…ƒļ„›ļ„ŗļ…‡ ļ„‘ļ„Æļ„µļ…‚ļ„­ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µ ļ„µļ„»ļ…‡ ļ„»ļ…‹, ļ„‘ļ„Ŗļ…‡ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„Æļ„µļ„”ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‡ļ„œļ„¬ļ…‡ ļ„»ļ…‹ ļ„‘ļ„Ŗļ…‡ ļ„Ŗļ……ļ„µļ…œļ„Ŗ ļ…ƒļ„›ļ„ŗļ…‡
'ļ„Ŗļ…‡ ļ„¬ļ…‹ļ„¹ ļ„¶ļ„ļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ…‹, ļ„Æļ„µ ļ„±ļ…‚ļ„‘ļ„¬ ļ…ƒļ„øļ…žļ„  ļ„Æļ„Ŗļ…‚ ļ„¶ļ…žļ„ļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„“ļ„» ļ„“ļ…žļ„› ļ„®ļ……ļ„›ļ„ŗļ…‚ļ„® ļ„µļ…ƒļ„»ļ„Ŗ ļ„µļ…‚ļ„»ļ„ļ…„ļ„µ ļ„ŗļ…„ī„” ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„
ļ…ƒļ„øļ…žļ„ , ļ„“ļ„» ļ„“ļ…žļ„› ļ…ƒļ„›ļ„ŗļ„³ I ļ„ļ„¶ļ„Ŗļ…„ ļ„»ļ…‰ī„” ļ„“ļ„» ļ„•ļ„¬ļ…Œ ļ„øļ…‚ļ„Æļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ„¬ļ…Œ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ ļ„²ļ…‚ļ„øļ…ˆ
ļ„“ļ„» ļ„‘ļ„ŗļ„¶ ļ…ƒļ„øļ…žļ„  ļ„ŗļ…žļ„  ļ„»ļ…‰ī„”
ļ„ŗļ…‚ļ„§ļ…„ ļ„¬ļ„øļ…‚ļ„” ļ„¬ļ…„ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„© ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ļ„—: ļ„¢ļ…‡ļ„›ļ„µ ļ„¬ļ„øļ…‚ļ„” ļ„¬ļ…‚ ļ„‘ļ„ŗļ„¶ ļ…ƒļ„øļ…žļ„  ļ„›ļ…‹ļ„” ļ„Æļ…„ļ„²ļ…‚ļ„ø ļ„®ļ„»ļ…„
ļ„
ļ„»ļ……ļ…œļ„¬ļ…‚, ļ„Æļ„µ
ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„„ļ…‰ļ„ŗļ„„ ļ„“ļ„» ļ…ƒļ„ŗļ…žļ„„ļ…‚ ļ„›ļ…žļ„Øļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„“ļ„» ļ„›ļ…œļ„³ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ…ƒļ„›ļ„ŗļ„³ I ļ„ļ„¶ļ„Ŗļ…„ ļ„›ļ…„ļ„Ŗļ…„ ļ„»ļ…‰ī„” ļ„“ļ„ŗ ļ„¶ļ„”
ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„³ļ„»ļ…žļ„Ŗļ„Ŗļ…‚ ļ„Æļ…žļ„­ļ„µ (Ī±) ļ„ŗļ…‰ļ…žļ„„ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‚ļ„, ļ„‘ļ„›ļ„ŗļ„µ 0.05 ļ„¢ļ…‚ļ„ 5%ī™€ ļ„“ļ„» ļ„Æļ…žļ„­ļ„µ ļ„“ļ…žļ„› ļ…ƒļ„›ļ„ŗļ„³ I ļ„ļ„¶ļ„Ŗļ…„ ļ„›ļ„µļ„®
ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„¬ļ…†ļ„¢ļ…‡ ļ„¹ļ„±ļ„¬ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ , ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„ļ„¶ļ„Ŗ ļ„‘ļ„¶ļ…‚ļ„µļ„³ ļ„¬ļ…„ 5% ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„ŗļ„øļ…„ļ„›ļ…‚ļ„µ
ļ„›ļ„µļ„® ļ„¶ļ„” ļ…ƒļ„Ŗļ„’ļ„µ ļ„»ļ…‹ī„”
ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„: ļ„œļ……ļ…œļ…ƒļ„£ļ„’ ļ„³ļ…ļ„›
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„»ļ……ļ„© ļ„•ļ„¶ļ„„ ļ…ƒļ„¬ļ…„ļ„¹ ļ„¬ļ…„ ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ī„” ļ„“ļ…žļ„› ļ„¹ļ…žļ„›ļ…„ ļ„ŗļ…žļ„ ļ„³ļ……ļ…žļ„  ļ„¬ļ…‹ļ„¹ļ…„ ļ„»ļ…‰, ļ„Æļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„•ļ„ŗļ„®ļ…†ļ…œ ļ„°ļ„æļ„® ļ…ƒļ„øļ…žļ„  ļ„‘ļ„ŗļ„°ļ„¶ ļ„µļ…ƒļ„»ļ…œļ„¬ļ…‡ ļ„»ļ…‹
ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„ŗļ„±ļ…†ļ„Ŗ ļ„ŗļ…†ļ„œļ„³ ļ„ŗļ„®ī„” ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ…ƒļ„øļ…žļ„ , ļ„“ļ„» ļ„“ļ…žļ„› ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„ ļ„»ļ…‰ī„” ļ„“ļ„» ļ„•ļ„¬ļ…Œ ļ„øļ…‚ļ„Æļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ„¬ļ…Œ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µļ„® ļ…ƒļ„øļ…žļ„  ļ„‘ļ„ŗļ„°ļ„¶ ļ„µļ…ƒļ„»ļ…œļ„¬ļ…‡ ļ„»ļ…‹ ļ„²ļ…‚ļ„øļ…ˆ ļ„“ļ„» ļ„ļ„¶ļ„Ŗ ļ„»ļ…‰ī„”
ļ„¬ļ„øļ…‚ļ„” ļ„¬ļ…‡ ļ„³ļ…‚ļ„³ļ„¶ļ…‡ ļ…ƒļ„øļ…žļ„ , ļ„¢ļ…‡ļ„›ļ„µ ļ„¬ļ„øļ…‚ļ„” ļ„‘ļ„ŗļ„¶ ļ…ƒļ„øļ…žļ„  ļ„³ļ„µļ…„ļ„¾ļ…‚ļ„ ļ„¬ļ…„ ļ„³ļ„¬ļ„¬ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰, ļ„Æļ„µ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„„ļ…‰ļ„ŗļ„„ ļ„“ļ„» ļ…ƒļ„ŗļ…žļ„„ļ…‚
ļ„›ļ…žļ„Øļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„“ļ„» ļ„®ļ„»ļ…„
ļ„
ļ„›ļ„µļ„¬ļ…„, ļ„Ŗļ…‚ļ„ ļ„“ļ„» ļ„“ļ…žļ„› ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„ ļ„»ļ…‰ī„” ļ„“ļ„ŗ ļ„ļ„¶ļ„Ŗļ…„ ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ Ī² ļ„¬ļ……ļ„’ļ„µļ…‚
ļ„¬ļ„µļ„ŗļ…‚ļ„” ļ„ļ„” ļ„»ļ…‰ī„” ļ„“ļ…žļ„› ļ„•ļ…žļ„  Ī² ļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± ļ„»ļ…‰ ļ…ƒļ„› ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„‘ļ„ŗļ„¶ ļ„Æļ…„ļ„²ļ…‚ļ„øļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ļ……ļ„’ļ„•ļ„© ļ„¬ļ…„ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚
ļ„µļ…žļ„œļ„¬ļ…‡ ļ„»ļ…‹, ļ„“ļ„ŗ ļ„¶ļ„” ļ„œļ…‹ļ„¢ļ„›ļ„µļ„Ŗļ…‚ ļ„„ļ…‚ļ„”ļ„Æ I ļ„ļ„¶ļ„Ŗļ…„ ļ„®ļ…†ļ…œ ļ„ŗļ…œļ„Ŗļ……ļ…ƒļ„¶ļ„Ŗ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ļ„— ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„Ŗļ…Œ ļ„žļ…žļ„„ ļ„›ļ„µļ„® ļ„¬ļ…‚ ļ„„ļ…„ļ„ ļ…‚
ļ„µļ…žļ„œļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ„® ļ„¶ļ„”:
ā€¢ ļ…ƒļ„›ļ„ŗļ„³ I ļ„ļ„¶ļ„Ŗļ…„ (Ī±):ļ„¢ļ„¬ļ…Œ ļ„“ļ„» ļ„®ļ„»ļ…„
ļ„
ļ„›ļ„µļ„¬ļ…‚ ļ„Ŗļ…‚ļ„ "ļ„»ļ…‚ļ„, ļ„“ļ„» ļ„›ļ…œļ„³ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰!" ļ„›ļ…ƒļ„»ļ„©ļ…‚ī„” ļ„“ļ…žļ„› ļ„ļ„¶ļ„Ŗ
ļ„ŗļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„›ī„”
ā€¢ ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„ (Ī²):"ļ„®ļ„»ļ…„
ļ„
, ļ„“ļ„» ļ„›ļ…œļ„³ ļ„®ļ„»ļ…„
ļ„
ļ„›ļ„µļ„¬ļ…‚!" ļ„›ļ…ƒļ„»ļ„©ļ…‚ ļ„¢ļ„¬ļ…Œ ļ„“ļ„» ļ„‘ļ„ŗļ„¶ ļ…ƒļ„øļ…žļ„  ļ„›ļ…œļ„³ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„“ļ…žļ„› ļ„ļ„¶ļ„Ŗ ļ„®ļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„›ī„”
ļ„“ļ„»ļ„®ļ…‚ļ„ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„ŗļ…œļ„Ŗļ……ļ„¶ļ„® ļ„¶ļ…žļ„²ļ„©ļ…‚ ļ„“ļ…žļ„› ļ„µļ…žļ„ŗļ…„ 'ļ„Ŗļ…‡ ļ„Ŗļ……ļ„µļ„® ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰ī„” Ī± ļ„®ļ…†ļ…œ ļ„žļ„„ļ…‚ļ„•ļ„©ļ…‚ (ļ„„ļ…‰ļ„ŗļ„„ ļ„®ļ…†ļ…œ ļ„ŗļ„¼ļ„Ŗ
ļ„±ļ„©ļ…‚ļ„•ļ„©ļ…‚) ļ„£ļ…†ļ„¦ļ…‡ ļ„‘ļ„¶ļ…‚ļ„µļ„³ ļ„®ļ…†ļ…œ ļ„žļ„„ļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ ļ„Æļ„µ ļ„‘ļ„ŗļ„¶ ļ„Æļ…„ļ„²ļ…‚ļ„øļ…‚ļ„ (ļ„„ļ…‚ļ„”ļ„Æ II ļ„ļ„¶ļ„Ŗļ…„) ļ„®ļ…†ļ…œ ļ„ļ……ļ„’ļ„•ļ„© ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ…†ļ…œ
ļ„øļ„­ļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ī„” Ī± ļ„®ļ…†ļ…œ ļ„øļ„­ļ…‚ļ„•ļ„© ļ„®ļ…‚ļ„¶ ļ„ŗļ…žļ„ ļ…‡ ļ„Æļ…„ļ„²ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‚ ļ„Æļ„Ŗļ…‚ ļ„¶ļ„ļ…‚ļ„•ļ„©ļ…‚ ļ„’ļ„ŗļ…‚ļ„® ļ„»ļ…‹ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ ļ„Æļ„µ ļ„»ļ…‹ļ„µ ļ„£ļ…†ļ„¦ļ…‡ ļ„‘ļ„¶ļ…‚ļ„µļ„³
ļ„¬ļ…‚ ļ„¢ļ…‹ļ„œļ„³ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„ŗļ…œļ„›ļ„¶ļ„Æ ļ„ ļ„®ļ…†ļ…œ ļ„¢ļ…‹ļ„æļ„®
ļ„“ļ„» ļ„ŗļ…‚ļ„µļ…‡ ļ„ŗļ…œļ„›ļ„¶ļ„Æā€”ļ„“ļ…žļ„›-ļ„Æļ…†ļ„”ļ„¶/ļ„¬ļ…‹-ļ„Æļ…†ļ„”ļ„¶ ļ„„ļ…‰ļ„ŗļ„„, ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ, ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„›ļ„ŗļ„³ I/II ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ā€”ļ„“ļ…žļ„› ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗļ…„
ļ„„ļ…†ļ„¶ļ…ƒļ„›ļ…žļ„„ ļ„¬ļ…‡ ļ„„ļ……ļ„›ļ…ƒļ„æļ„’ļ„ ļ„øļ…‚ļ„ļ„ ļ„¢ļ……ļ„æļ…‡ ļ„»ļ…‹ļ„— ļ„»ļ„®ī„”
1. ļ„Æļ…†ļ„” ļ„¬ ļ„°ļ…‰ļ„ŗļ„¶ ļ„›ļ„µļ…‹:ļ„›ļ…„ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ…ƒļ„¬ļ„¹ļ…‚ (ļ„“ļ…žļ„› ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‡) ļ„øļ…žļ„¶ ļ„¬ļ…‡ļ„œ ļ„µļ„»ļ…‡ ļ„»ļ…‹ ļ„¢ļ…‚ļ„ ļ„¬ļ…‹ļ„øļ…ˆ ļ…ƒļ„¬ļ„¹ļ…‚ļ„øļ…‚ļ„ (ļ„¬ļ…‹ ļ„Æļ…†ļ„”
ļ„øļ…‚ļ„¶ļ…‡) ļ„øļ…žļ„¶?
2. ļ„¼ļ„Ŗļ„µļ…‡ ļ„¬ ļ„œļ…‡ļ„Ŗļ„µ ļ…ƒļ„®ļ„µļ„­ ļ„µļ„Ŗ ļ„›ļ„µļ…‹:ļ„•ļ„ŗ ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µ ļ„®ļ…†ļ…œ ļ„Æļ…ƒļ„µļ„²ļ…‚ļ…ƒļ„¹ļ„Ŗ ļ„›ļ„µļ…‹ ļ…ƒļ„¢ļ…žļ„«ļ…‡ ļ„ŗļ„±ļ…†ļ„Ŗ ļ„“ļ…œļ„®ļ…‡ ļ„³ļ„¾ļ„±ļ…†ļ„Ŗ ļ„»ļ„®
ļ…ƒļ„› ļ„•ļ„» ļ„®ļ„¶ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µ ļ„ŗļ„›ļ„©ī„”
3. ļ„ŗļ…œļ„Ŗļ……ļ„¶ļ„® ļ„¢ļ…‹ļ„œļ„³:ļ„ŗļ„³ļ„£ļ…‹ ļ…ƒļ„› ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…„ļ„’ļ„ ļ„»ļ„® (ļ„„ļ…‚ļ„”ļ„Æ I ļ„¢ļ…‚ļ„ ļ„„ļ…‚ļ„”ļ„Æ II ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„) ļ„‘ļ„Ŗļ…‡ ļ„•ļ„ŗ
ļ„‘ļ„®ļ……ļ„ŗļ…‚ļ„µ ļ„’ļ„Æļ„©ļ…‡ ļ„³ļ„»ļ…žļ„Ŗļ„ø ļ„¬ļ…‡ ļ„Æļ…žļ„­ļ„µ ļ„¬ļ…„ ļ„“ļ…‹ļ„¢ļ„®ļ…‚ ļ„±ļ„©ļ…‚ļ„™ī„”
ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„“ļ…žļ„› ļ„Æļ…„ļ„“ļ…‹ļ„ ļ„›ļ„µļ„®ļ…‚ ļ„“ļ…žļ„› ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶ ļ„¢ļ…‚ļ„ļ„  ļ„¬ļ…„ ļ„“ļ…‹ļ„¢ļ„®ļ…‚ ļ„±ļ„©ļ…‚ļ„•ļ„© ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰ī„” ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„’ļ„Æļ„©ļ…‚
ļ„Ŗļ„µļ…„ļ„›ļ…‚ ļ„ ļ……ļ„©ļ„¬ļ…‡ ļ„»ļ…‹, ļ„›ļ…‚ļ„µļ„øļ…‚ļ„” ļ„¶ļ„” ļ„’ļ„Æļ„©ļ…‡ ļ„³ļ…‚ļ„Æļ„¬ļ…œļ„§ ļ„Æļ…ƒļ„µļ„²ļ…‚ļ…ƒļ„¹ļ„Ŗ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹, ļ„‘ļ„Ŗļ…‡ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ…†ļ…œ
ļ„ŗļ„øļ…„ļ„›ļ…‚ļ„µ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ī„” ļ„“ļ„ŗ ļ„Ŗļ„µļ…§ļ…‚ļ„, ļ„°ļ…‰ļ„ŗļ„¶ļ…‡ ļ„“ļ…‹ļ„¢ļ„®ļ…‚ļ„±ļ…žļ„­, ļ„Ŗļ„µļ„›ļ„Æļ…†ļ„µļ„® ļ„‘ļ„Ŗļ…‡ ļ„±ļ„ ļ…‚ļ„‘ļ„“ļ…‹ļ„ ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ…ƒļ„ŗļ…žļ„„
ļ„ŗļ…œļ„œļ…‡ļ„Æ ļ…ƒļ„øļ…žļ„ , ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ…ƒļ„ŗļ„µļ…€ ļ„“ļ…žļ„› ļ„Æļ…œļ„®ļ…‡ 'ļ„Ŗļ…‡ ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ„® - ļ„“ļ„» ļ„•ļ„Ŗļ„ŗļ……ļ„›ļ„Ŗļ…‚, ļ„Ŗļ„µļ„› ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„­ļ„’ļ„®
ļ„®ļ…‚ļ„¶ ļ…ƒļ„®ļ„µļ„©ļ…‡ ļ„¬ļ…„ ļ„›ļ„»ļ…‚ļ„©ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ…žļ„›-ļ„Æļ…†ļ„” ļ„ø ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„¬ļ…‹-ļ„Æļ…†ļ„” ļ„ø ļ„¶ ļ„„ļ…‰ļ„ŗļ„„ļ„“ļ„» ļ…ƒļ„®ļ„µļ„­ļ…‚ļ„µļ„Ŗ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„ŗļ„±ļ…†ļ„Ŗ ļ…ƒļ„›ļ…žļ„«ļ…‡ ļ„¶ļ…žļ„²ļ„©ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„® ļ„¾ļ……ļ„› ļ„œļ…‡ļ„Ŗļ„µļ„¼ļ„Ŗļ„µļ…‡ ļ„øļ…‚ļ„¶ļ…‡ ļ„œļ…‡ļ„Ŗļ„µ ļ„®ļ…†ļ…œ ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„¢ļ…žļ„«ļ…‡ ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ„›ļ…‚ļ„µļ„øļ…‚ļ„” ļ„›ļ„µļ„®ļ…„ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ…ƒļ„›ļ„ŗļ„³ I ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„›ļ„ŗļ„³ II ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„“ļ…‚ļ„¬ ļ…ƒļ„¬ļ„øļ…‚ļ„™ ļ…ƒļ„› ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„ŗļ…œļ„²ļ„ø ļ„»ļ„®, ļ„‘ļ„Ŗļ…‡ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„¢ļ…‹ļ„œļ„³ļ…‚ļ„ ļ„®ļ…†ļ…œ
ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶ ļ„ŗļ…œļ„Ŗļ……ļ…ƒļ„¶ļ„Ŗ ļ„›ļ„µļ„®ļ…‚ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„“ļ„»ļ„®ļ…‚ļ„ ļ„ŗļ…œļ„›ļ„¶ļ„Æļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„©ļ…‚ ļ„“ļ…žļ„› ļ„»ļ……ļ„®ļ„µļ„³ļ…œļ„¬ ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗ ļ„±ļ„©ļ„® ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰ā€”ļ…ƒļ„®ļ„ļ„µļ…‚ļ„®ļ…„ ļ„›ļ„µļ„® ļ„øļ…‚ļ„¶ļ…‚, ļ„ŗļ…‚ļ„øļ„­ļ…‚ļ„®, ļ„‘ļ„Ŗļ…‡
ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ļ„øļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„ŗļ…„ļ„³ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‹ļ„øļ…‚ļ„ ļ„Ŗļ…Œ ļ„¢ļ…‚ļ„©ļ…†ī„” ļ„“ļ„ŗ ļ„³ļ…‚ļ„®ļ…ƒļ„ŗļ„›ļ„Ŗļ…‚ ļ„®ļ…‚ļ„¶, ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„®ļ…‚ ļ…ƒļ„ŗļ„µļ…€ ļ„„ļ…‰ļ„ŗļ„„ ļ„ŗļ„»ļ…„ ļ„Øļ…œļ„ ļ„®ļ…‚ļ„¶ ļ„›ļ„µļ„¬ļ…‡
ļ„»ļ…‹ ļ„±ļ„¶ļ…ƒļ„› ļ„»ļ„µ ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„°ļ…‰ļ„ŗļ„¶ļ…‡ ļ„¬ļ…‡ ļ…ƒļ„Æļ…žļ„”ļ…‡ ļ„›ļ„¶ļ…‚ ļ„‘ļ„Ŗļ…‡ ļ„Ŗļ„µļ„› ļ„¬ļ…„ ļ„øļ…„ ļ„›ļ„¬ļ„µ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ī„”
2. (ļ…”) ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„² ļ„øļ„® ļ„‘ļ„®ļ……ļ„³ ļ„® (MLE) ļ…ƒļ„øļ„­ļ…„ ļ„Ŗļ…Œ ļ„Ŗļ……ļ„» ļ„§ ļ„›ļ…„ ļ„² ļ„ø ļ„»ļ…‰? ļ„“ļ„» ļ„’ļ„³ ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„øļ„µļ„
(OLS) ļ…ƒļ„øļ„­ļ…„ ļ„Ŗļ…Œ ļ…ƒļ„›ļ„ŗ ļ„‘ļ„µļ„« ļ…ƒļ„øļ…žļ„  ļ„øļ…žļ„œļ„µ ļ„»ļ…‰? ļ…ƒļ„øļ„ŗļ„« ļ„µ ļ…ƒļ„øļ…žļ„  ļ„ ļ„µļ„  ļ„›ļ„µļ…‹ī„”
(ļ„‘) ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ ļ„® ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„›ļ„µļ„Ŗ ļ…ƒļ„øļ…žļ„  ļ„‘ļ…œļ„Ŗļ„µ ļ„¬ļ…žļ„ŗļ…‹ī„” ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‡ ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„›ļ„µļ„Ŗ ļ„¬ļ…‡ ļ„ļ……ļ„© ļ„
ļ„± ļ„µļ…‡ ļ„øļ…„ ļ„ ļ„µļ„  ļ„›ļ„µļ…‹ī„”
ļ„•ļ…žļ„Ŗļ„µ:ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗ ļ„»ļ…‹ ļ„¢ļ…‹ ļ„“ļ…žļ„› ļ„µļ„»ļ…žļ„ŗ ļ„®ļ…†ļ…œ ļ„ŗļ……ļ„¶ļ„£ļ…‚ļ„•ļ„© ļ„¬ļ…„ ļ„›ļ…‹ļ…ƒļ„¹ļ„¹ ļ„›ļ„µ ļ…ƒļ„µļ„»ļ…‚ ļ„»ļ…‰ī„” ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„›ļ…‹ļ„¶
ļ„ŗļ……ļ„µļ…‚ļ„ļ…‚ļ„ (ļ„§ļ…‡ļ„„ļ…‚ ļ„Æļ……ļ„’ļ„“ļ…œļ„„) ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„ŗļ„³ļ…†ļ„» ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„›ļ…œļ„³ ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„¬ļ…‡ ļ…ƒļ„Æļ…žļ„”ļ…‡ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„²ļ…‚ļ…ƒļ„øļ„Ŗ ļ„›ļ„»ļ…‚ļ„©ļ…„ ļ„¬ļ…‚
ļ„Æļ„Ŗļ…‚ ļ„¶ļ„ļ…‚ļ„•ļ„©ļ…‚ ļ„»ļ…‰ī„” ļ„›ļ„” ļ„øļ…‚ļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„ŗļ……ļ„µļ…‚ļ„ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„’ļ„Æļ„©ļ…„ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’ ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ "ļ„¬ļ…†ļ„µļ…„" ļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„›ļ„µļ„® ļ„¬ļ…„
ļ„›ļ…‹ļ…ƒļ„¹ļ„¹ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ (ļ„¢ļ…‹ ļ…ƒļ„› ļ„’ļ„³ ļ„žļ…žļ„„ļ…‹ ļ„žļ…žļ„„ ļ„øļ„µļ„ļ…‚ļ„ ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰)ī™€ ļ„»ļ…‹ļ„µ ļ„øļ…‚ļ„µ, ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„Æļ……ļ…žļ„”ļ„¬ļ…‡ ļ„»ļ…‹: "ļ„“ļ„»ļ„®ļ…‚ļ„ ļ„ŗļ……ļ„µļ…‚ļ„ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¬ļ…‡ļ„œļ„¬ļ…‡
ļ„»ļ…‹ļ„—, ļ…ƒļ„›ļ„»ļ„æļ…„ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’ ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„²ļ…‚ļ…ƒļ„øļ„Ŗ ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰?" (ļ„¢ļ…‹ ļ…ƒļ„› ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®
ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰)ī™€ ļ„¬ļ…‹ļ„øļ…ˆ ļ„Ŗļ„µļ…„ļ„›ļ…‡ ļ„ŗļ…žļ„ ļ…‚ļ„” ļ„®ļ…†ļ…œ ļ„•ļ„¢ļ…‚ļ„ļ„µ ļ„›ļ„µļ„® ļ„¬ļ…‚ ļ„•ļ„¬ļ…‡ļ„¹ ļ„µļ…žļ„œļ„¬ļ…‡ ļ„»ļ„®, ļ„Æļ„µ ļ„•ļ„» ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„µļ„©ļ„®ļ…„ļ„Ŗļ…„ļ„’ļ„ ļ„¬ļ…„
ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„»ļ……ļ„© ļ„’ļ„™ ļ„“ļ„ŗ ļ…ƒļ„øļ„¹ļ…‡ ļ„®ļ…†ļ…œ ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶ ļ„¬ļ…‹ ļ…ƒļ„»ļ…žļ…ƒļ„ŗļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„•ļ„¢ļ…‚ļ„ļ„µ ļ„›ļ„µļ…„ļ„—: (a) ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®
(MLE) ļ„‘ļ„Ŗļ…‡ ļ„“ļ„» ļ„’ļ„³ ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„øļ„µļ„ (OLS) ļ„Ŗļ…Œ ļ…ƒļ„›ļ„øļ…ˆ ļ„øļ…žļ„œļ„µļ…‚ ļ„»ļ…‰ī„” (b) ļ„“ļ…žļ„› ļ„‘ļ…œļ„¬ļ…‚ļ„¾ļ…‡ ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ…ƒļ„øļ…žļ„ 
ļ„‘ļ…œļ„Ŗļ„µ, ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‡ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„¬ļ…‡ ļ„ļ……ļ„©ļ…‚ļ„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ī„”
󷊆󷊇ļ„² ļ„ (a): ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„² ļ„øļ„® ļ„‘ļ„®ļ……ļ„³ ļ„® (MLE) ļ„‘ļ„Ŗļ…‡ OLS ļ„Ŗļ…Œ ļ„“ļ„ŗļ„¬ ļ„‘ļ…œļ„Ŗļ„µ
1. ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„² ļ„øļ„® ļ„‘ļ„®ļ……ļ„³ ļ„® (MLE) ļ„›ļ…„ ļ„»ļ…‰?
ā€¢ MLE ļ„“ļ…žļ„› ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„³ļ…‚ļ„§ļ„¶ ļ„¬ļ…‡ ļ„³ļ…‚ļ„Æļ„¬ļ…œļ„§ļ…‚ļ„ ļ„¬ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„¶ļ„ļ…‚ļ„•ļ„© ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„Ŗļ„µļ…„ļ„›ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„» ļ…ƒļ„øļ„ ļ…‚ļ„µ ļ„ŗļ„µļ„¶ ļ„»ļ…‰: ļ„•ļ„» ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µ ļ„³ļ……ļ…žļ„¶ ļ„ ļ……ļ„©ļ…‹ ļ„¢ļ…‹ ļ„¬ļ…‡ļ„œļ…‡ ļ„ļ„— ļ„§ļ…‡ļ„„ļ…‚ ļ„®ļ…†ļ…œ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ…žļ„­ "ļ„ŗļ…œļ„²ļ…‚ļ…ƒļ„øļ„Ŗ" ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…‡
ļ„»ļ„®ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ā€¢ ļ„¬ļ…†ļ„¢ļ…‡ ļ„¹ļ„±ļ„¬ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ , MLE ļ„Æļ……ļ…žļ„”ļ„¬ļ…‚ ļ„»ļ…‰: "ļ„¢ļ…‡ļ„›ļ„µ ļ„“ļ„» ļ„•ļ„» ļ„§ļ…‡ļ„„ļ…‚ ļ„Æļ……ļ„’ļ„“ļ…œļ„„ ļ„»ļ„® ļ„¢ļ…‹ ļ„³ļ…Š ļ„¬ļ…‡ļ„œļ„¬ļ…‚ ļ„»ļ…‚ļ„, ļ„Ŗļ…‚ļ„ ļ…ƒļ„›ļ„»ļ„æļ…‡
ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µ ļ„³ļ……ļ…žļ„¶ ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¬ļ…‡ļ„œļ„© ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®?"
ļ„›ļ„¬ļ„³-ļ„¬ļ„µ-ļ„›ļ„¬ļ„³ ļ„‘ļ„®ļ……ļ„²ļ„ø:
1. ļ„³ļ…œļ„® ļ„¶ļ„™ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ…ƒļ„ŗļ…žļ„›ļ…‚ 10 ļ„øļ…‚ļ„µ ļ„•ļ„”ļ…‚ļ…ƒļ„¶ļ„’ ļ„‘ļ„Ŗļ…‡ 7 ļ…ƒļ„ŗļ„µ ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ…„ļ„Ŗļ…‡ī„”
2. ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„»ļ…‰ļ…žļ„§ļ„ŗ (p) ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„¬ļ…‚ ļ„‘ļ…œļ„¬ļ…‚ļ„¾ļ…‚ ļ„¶ļ„ļ…‚ļ„•ļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ…‹ī„”
3. 10 ļ…ƒļ„øļ…žļ„ ļ…Œ 7 ļ…ƒļ„ŗļ„µļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¬ļ…‡ļ„œļ„© ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„±ļ…‚ļ„“ļ„®ļ…‹ļ„³ļ…„ļ„‘ļ„¶ ļ„°ļ…‚ļ„µļ„³ļ…†ļ„¶ļ…‡ ļ„¬ļ……ļ„’ļ„µļ…‚ ļ…ƒļ„¬ļ…žļ„Ŗļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ī„”
4. MLE ļ„›ļ…ƒļ„»ļ…œļ„¬ļ…‚ ļ„»ļ…‰: p ļ„¬ļ…‚ ļ„³ļ……ļ…žļ„¶ ļ„ ļ……ļ„©ļ…‹ ļ„¢ļ…‹ ļ„“ļ„ŗ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
5. ļ„“ļ„ŗ ļ„³ļ…‚ļ„³ļ„¶ļ…‡ ļ…ƒļ„øļ…žļ„ , p = 0.7 MLE ļ„»ļ…‰ī„”
ļ„“ļ„ŗ ļ„¶ļ„”, MLE ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„³ļ…‚ļ„§ļ„¶ ļ„®ļ…†ļ…œ ļ„•ļ„¬ļ…Œ ļ„Ŗļ…žļ„› ļ…ƒļ„„ļ„–ļ„® ļ„›ļ„µļ„® ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰ ļ„¢ļ„¬ļ…Œ ļ„Ŗļ…žļ„› ļ„“ļ„» ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„¬ļ……ļ„’ļ„µļ…‚ ļ„‘ļ„ŗļ„¶ ļ…ƒļ„øļ…žļ„ 
ļ„¬ļ…‡ļ„œļ…‡ ļ„ļ„— ļ„§ļ…‡ļ„„ļ…‚ ļ„®ļ…†ļ…œ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ„»ļ…„
ļ„
ļ…ƒļ„¬ļ…œļ„¬ļ…‚ī„”
2. ļ„’ļ„µļ„§ļ…„ļ„®ļ„µļ…„ ļ„¶ļ…„ļ„ŗļ„„ ļ„ŗļ„›ļ……ļ„—ļ„‘ļ„µ (OLS) ļ„›ļ…„ ļ„»ļ…‰?
ā€¢ OLS ļ„“ļ…žļ„› ļ…ƒļ„øļ„­ļ…„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„³ļ……ļ…žļ„œ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ…ƒļ„µļ„ļ„µļ…‰ļ„¹ļ„® ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ…ƒļ„øļ…žļ„  ļ„øļ„µļ„Ŗļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„» ļ…ƒļ„®ļ„µļ…„ļ„œļ„© ļ„›ļ…„ļ„Ŗļ…‡ ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ…ƒļ„®ļ„Ŗ ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„øļ„µļ„ ļ„‘ļ…œļ„Ŗļ„µļ…‚ļ„ ļ„¬ļ…‡ ļ„¢ļ…‹ļ„æ ļ„®ļ…†ļ…œ ļ„žļ„„ļ…‚ ļ„›ļ…‡
ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µļ…‚ļ„ ļ„¬ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„¶ļ„ļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„ŗļ„­ļ…‚ļ„µļ„® ļ„µļ…‡ļ…ƒļ„œļ„› ļ…ƒļ„µļ„ļ„µļ…‰ļ„¹ļ„® ļ…ƒļ„øļ…žļ„ , OLS ļ„•ļ„» ļ„¶ļ…‚ļ„”ļ„® ļ„¶ļ…žļ„²ļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„§ļ…‡ļ„„ļ…‚ ļ„Æļ……ļ„’ļ„“ļ…œļ„„ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„¶ļ…‚ļ„”ļ„® ļ„¬ļ…‡
ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„øļ„µļ„ ļ„¶ļ…œļ„±ļ„›ļ…‚ļ„µļ…„ ļ„¬ļ…†ļ„µļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„Ŗļ…Œ ļ„žļ…žļ„„ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„•ļ„¬ ļ„»ļ„µļ„®:ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„Æļ„æļ…§ļ…‚ļ„” ļ„¬ļ…‡ ļ„žļ…œļ…ƒļ„„ļ„’ļ„ ļ„Ŗļ…Œ ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„›ļ…‚ļ„ ļ„¬ļ…„ ļ„²ļ…ƒļ„øļ…žļ„œļ„±ļ…‚ļ„©ļ…„ ļ„›ļ„µļ„® ļ„¶ļ„” ļ„“ļ…žļ„›
ļ„¶ļ…‚ļ„”ļ„® ļ…ƒļ„°ļ…žļ„„ ļ„›ļ„µ ļ„µļ„»ļ…‡ ļ„»ļ…‹, ļ„Ŗļ…‚ļ„ OLS ļ„Øļ„¶ļ…‚ļ„© ļ„‘ļ„Ŗļ…‡ ļ„“ļ…œļ„„ļ„µļ„ŗļ…‰ļ„Æļ„„ ļ„¬ļ…„ ļ„ ļ…‹ļ„© ļ„›ļ„µļ…‡ļ„ļ…‚ ļ„¢ļ…‹ ļ„‘ļ„ŗļ„¶ ļ„‘ļ…œļ„›ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ…ƒļ„®ļ„Ŗ
ļ„‘ļ…œļ„›ļ…‚ļ„ ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„øļ„µļ„ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„Ŗļ…Œ ļ„žļ…žļ„„ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
3. MLE ļ„‘ļ„Ŗļ…‡ OLS ļ…ƒļ„øļ„ ļ„› ļ„µ ļ„³ļ……ļ…žļ„œ ļ„‘ļ…œļ„Ŗļ„µ
ļ„Æļ…ƒļ„»ļ„¶ļ…†
ļ„’ļ„³ ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„øļ„µļ„ (OLS)
ļ„¬ļ„µļ„¹ļ„®
ļ„‘ļ…ƒļ„¢ļ„»ļ…‡ ļ„³ļ…‚ļ„Æļ„¬ļ…œļ„§ ļ„ ļ……ļ„©ļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„øļ„µļ„
ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„¢ļ…‹ļ„æ ļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„Ŗļ…Œ ļ„žļ…žļ„„ ļ„›ļ„µļ„¬ļ…‡
ļ„»ļ„®ī„”
ļ„¶ ļ„ļ…† ļ„»ļ…‹ļ„© ļ„¬ļ…„
ļ„“ļ…‹ļ„ļ„Ŗ
ļ„³ļ……ļ…žļ„œ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„¶ļ…„ļ„®ļ…„ļ„‘ļ„µ ļ…ƒļ„µļ„ļ„µļ…‰ļ„¹ļ„® ļ„³ļ…‚ļ„§ļ„¶ļ…‚ļ„
ļ„¶ļ„” ļ„øļ„µļ…ƒļ„Ŗļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„­ ļ„µļ„® ļ„ø ļ„
ļ„³ļ…œļ„® ļ„¶ļ„™ ļ…ƒļ„› ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„’ļ„³ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡
ļ„ŗļ…ƒļ„«ļ„µ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„®ļ…‚ļ„¶ ļ„øļ…œļ„§ļ…„ļ„’ļ„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ļ„’ļ„
ļ„»ļ„®ī„”
ļ„’ļ„•ļ„„ļ„Æļ……ļ…žļ„„
ļ„ļ…ļ„ŗ-ļ„³ļ…‚ļ„µļ„›ļ…‹ļ„ø ļ„­ļ…‚ļ„µļ„®ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‡ ļ„Ŗļ…ƒļ„»ļ„Ŗ ļ„ŗļ„² ļ„Ŗļ…Œ
ļ„øļ„­ļ…„ļ„’ ļ„µļ…‡ļ…ƒļ„œļ„› ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ…ƒļ„Ŗļ„’ļ„µ
ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„Æļ…ƒļ„»ļ„¶ļ…†
ļ„’ļ„³ ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„øļ„µļ„ (OLS)
ļ„¶ļ„ ļ„›ļ„Ŗ
ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„ŗļ…ƒļ„«ļ„Ŗļ…„ļ„’ļ„ ļ„Ŗļ…žļ„› ļ„ŗļ…„ļ…ƒļ„³ļ„Ŗ ļ…ƒļ„¢ļ…žļ„«ļ…‡ ļ„øļ„µļ„
ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„Ŗļ…Œ ļ„žļ…žļ„„ ļ„›ļ„µļ„®ļ…‚
ļ„ŗļ„³ļ„£ļ„¬ļ…‚ļ„µļ…„ ļ„µļ…žļ„œļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’
"ļ„øļ„µļ„ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„›ļ„µļ„›ļ…‡ ļ…ƒļ„›ļ„»ļ„æļ…„
ļ„¶ļ…‚ļ„”ļ„® ļ„§ļ…‡ļ„„ļ…‚ ļ„®ļ…†ļ…œ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ„­ļ…„ļ„’ ļ„Øļ…œļ„ ļ„®ļ…‚ļ„¶
ļ…ƒļ„°ļ…žļ„„ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰?"
4. MLE ļ„‘ļ„Ŗļ…‡ OLS ļ…ƒļ„øļ„ ļ„› ļ„µ ļ„›ļ„®ļ…‰ļ„›ļ„¹ļ„®
ļ…ƒļ„¬ļ„¶ļ„ ļ„ŗļ„Æ ļ„ļ…žļ„¶ ļ„“ļ„» ļ„»ļ…‰ ļ…ƒļ„›, ļ„’ļ„³ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„øļ…œļ„§ļ…„ļ„’ļ„ ļ„ļ„”ļ„’ļ„ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„øļ…‚ļ„¶ļ…‡ ļ„µļ…‡ļ…ƒļ„œļ„› ļ…ƒļ„µļ„ļ„µļ…‰ļ„¹ļ„® ļ„¬ļ…‡ ļ„³ļ…‚ļ„³ļ„¶ļ…‡ ļ…ƒļ„øļ…žļ„ ,
OLS ļ„‘ļ„Ŗļ…‡ MLE ļ„“ļ…žļ„›ļ…‹ ļ…ƒļ„¢ļ„»ļ…‡ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ…ƒļ„¬ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„“ļ„» ļ„“ļ„ŗ ļ„¶ļ„” ļ„»ļ…‰ ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„øļ„µļ„ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„›ļ„µļ„®ļ…‚
ļ„ļ…ƒļ„©ļ…ƒļ„Ŗļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„’ļ„³ļ„Ŗļ…‚ ļ„¬ļ…‡ ļ„‘ļ„­ļ…„ļ„® ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„›ļ„µļ„® ļ„¬ļ…‡ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„»ļ…‰ī„”
ļ„“ļ„ŗ ļ„¶ļ„”, OLS ļ„®ļ…†ļ…œ MLE ļ„¬ļ…‡ ļ„“ļ…žļ„› ļ…ƒļ„øļ„¹ļ…‡ļ„¹ ļ„³ļ…‚ļ„³ļ„¶ļ…‡ ļ„øļ„¢ļ…Œ ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ„¢ļ…‚ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ī„”
󷈷ó·ˆø󷈹ó·ˆŗ󷈻󷈼ļ„² ļ„ (ļ„‘): ļ„‘ļ„®ļ……ļ„³ ļ„® ļ„±ļ„® ļ„³ ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„› ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‡ ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„› ļ„¬ļ…‡ ļ„ļ……ļ„©
1. ļ„‘ļ„®ļ……ļ„³ ļ„® ļ„±ļ„® ļ„³ ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„›
ā€¢ ļ„‘ļ„®ļ……ļ„³ ļ„® ļ„¶ļ„ ļ„•ļ„© ļ„ø ļ„¶ :
o ļ„§ļ…‡ļ„„ļ…‚ ļ„Ŗļ…Œ ļ…ƒļ„›ļ„ŗļ…‡ ļ„‘ļ„©ļ„¢ļ…‚ļ„© ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µ ļ„¬ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„¶ļ„” ļ„øļ„µļ…ƒļ„Ŗļ„’ ļ„¢ļ…‚ļ„© ļ„øļ…‚ļ„¶ļ…‚ ļ„“ļ…žļ„›
ļ…ƒļ„®ļ„“ļ„³, ļ„°ļ…‚ļ„µļ„³ļ…†ļ„¶ļ…‚, ļ„¢ļ…‚ļ„ ļ„Ŗļ„µļ…„ļ„›ļ…‚ī„”
o ļ„“ļ„» ļ„“ļ…žļ„› ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ ļ„»ļ…‰ ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„“ļ„» ļ„®ļ„³ļ…†ļ„®ļ…‡ 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„µļ„²ļ„µ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
o ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„šļ„ŗļ„Ŗ xĖ‰\bar{x} ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ Ī¼ ļ„¬ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„»ļ…‰ī„”
ā€¢ ļ„‘ļ…œļ„¬ ļ„¾ :
o ļ„¢ļ„¬ļ…Œ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„®ļ…†ļ…œ ļ…ƒļ„›ļ„ŗļ…‡ ļ„œļ…‚ļ„ŗ ļ„®ļ„³ļ…†ļ„®ļ…‡ 'ļ„Ŗļ…‡ ļ„¶ļ…‚ļ„ļ…† ļ„›ļ…„ļ„Ŗļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ ļ„Ŗļ…‚ļ„ ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ…„ļ„Ŗļ…‚ ļ„‘ļ„ŗļ„¶
ļ„ŗļ…œļ…ƒļ„œļ„’ļ„Ŗļ„³ļ„› ļ„³ļ……ļ…žļ„¶ī„”
o ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± xĖ‰=52\bar{x} = 52 ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ 52 Ī¼ ļ„¬ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®
ļ„»ļ…‰ī„”
ļ„ŗļ„³ ļ„®ļ„Ŗ :ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„®ļ…†ļ…œ ļ„“ļ…žļ„› ļ…ƒļ„øļ„‘ļ…œļ„¢ļ„® ļ„ŗļ„³ļ„£ļ…‹, ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„®ļ…†ļ…œ ļ„•ļ„» ļ„Æļ„›ļ„øļ…‚ļ„® ļ„ŗļ„³ļ„£ļ…‹ ļ„¢ļ…‹ ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ
ļ„‘ļ„ŗļ„¶ ļ„ŗļ„³ļ…žļ„ļ„µļ…„ (ļ„§ļ…‡ļ„„ļ…‚) ļ„®ļ…‚ļ„¶ ļ…ƒļ„øļ„‘ļ…œļ„¢ļ„® ļ„¬ļ…„ ļ„Æļ…‚ļ„¶ļ„©ļ…‚ ļ„›ļ„µļ„® 'ļ„Ŗļ…‡ ļ…ƒļ„³ļ„¶ļ„¬ļ…‚ ļ„»ļ…‰ī„”
2. ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‡ ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„› ļ„¬ļ…‡ ļ„ļ……ļ„©
ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‡ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„›ļ…‹ļ„¶ ļ„›ļ……ļ„£ ļ„¶ļ…‹ļ„æļ…„
ļ„
ļ„¬ļ…‡ ļ„ļ……ļ„© ļ„»ļ…‹ļ„©ļ…‡ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„’ļ„™ ļ„•ļ„®ļ…§ļ…‚ļ„ ļ„¬ļ…„ ļ„Æļ„æļ„ ļ…‹ļ„¶ ļ„›ļ„µļ…„ļ„—:
(ļ…”) ļ…ƒļ„®ļ„µļ„Æļ…žļ„œļ„Ŗ
ā€¢ ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ…‡ļ„›ļ„µ ļ„“ļ„ŗļ„¬ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ…ƒļ„®ļ„Ŗ ļ„³ļ……ļ…žļ„¶ ļ„ŗļ…žļ„ ļ…‡ ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µ ļ„¬ļ…‡ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„šļ„ŗļ„Ŗ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„»ļ…‰ī„”
ā€¢ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ…ƒļ„›ļ„•
ļ„
? ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„šļ„ŗļ„Ŗļ„®, ļ„“ļ„» ļ…ƒļ„®ļ„¹ļ…‚ļ„®ļ…‡ 'ļ„Ŗļ…‡ ļ„Æļ„»ļ……ļ…œļ„ ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
(ļ„‘) ļ„“ļ„›ļ„ŗ ļ„µļ„Ŗ
ā€¢ ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„“ļ„›ļ„ŗļ…‚ļ„µ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ…‡ļ„›ļ„µ, ļ…ƒļ„¢ļ„øļ…ˆ-ļ…ƒļ„¢ļ„øļ…ˆ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¬ļ…‚ ļ„’ļ„›ļ…‚ļ„µ ļ„øļ„­ļ„¬ļ…‚ ļ„»ļ…‰, ļ„“ļ„» ļ„ŗļ…žļ„ ļ…‡
ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µ ļ…ƒļ„øļ…žļ„  ļ„›ļ„®ļ„øļ„µļ„¢ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ…ƒļ„ŗļ…žļ„›ļ…‡ ļ„•ļ„”ļ…‚ļ„¶ļ„© ļ„®ļ…‚ļ„¶, ļ…ƒļ„ŗļ„µļ…‚ļ„ ļ„¬ļ…‚ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„ŗļ…žļ„ ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„¬ļ…‡ ļ„®ļ…‡ļ„æļ…‡
ļ„Æļ„»ļ……ļ…œļ„ ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ…ƒļ„›ļ„•
ļ„
ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„®? ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„›ļ…‚ļ…€ļ…„ ļ„§ļ…‡ļ„„ļ…‚ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶, ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› 'ļ„Ŗļ…‡ ļ„²ļ„µļ…‹ļ„ŗļ…‚ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‹ī„”
(c) ļ„›ļ……ļ„¹ļ„¶ļ„Ŗ
ā€¢ ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„¶ļ„ļ…‚ļ„•ļ„© ļ„øļ…‚ļ…ƒļ„¶ļ„’ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ, ļ„ŗļ„² ļ„Ŗļ…Œ ļ„”ļ…‹ļ„„ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„øļ…‚ļ„¶ļ…‚ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„›ļ……ļ„¹ļ„¶ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„¢ļ…‡ļ„›ļ„µ ļ„¬ļ…‹ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ ļ„»ļ„®, ļ„Æļ„µ ļ„“ļ…žļ„› ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„žļ…žļ„„ ļ„•ļ„Ŗļ„µļ…‚ļ„‘-ļ„ ļ„æļ…§ļ…‚ļ„‘ ļ„›ļ„µļ„¬ļ…‚
ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„Ŗļ„µļ„¢ļ…„ļ„» ļ…ƒļ„¬ļ…žļ„Ŗļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ…ƒļ„›ļ„•
ļ„
ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„»ļ…‰? ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„“ļ„» ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„ŗļ„„ļ…„ļ„› ļ„‘ļ…œļ„¬ļ…‚ļ„¾ļ…‡ ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
(ļ„ŗ) ļ„›ļ……ļ„¹ļ„¶ļ„Ŗ
ā€¢ ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„›ļ…‚ļ…€ļ…„ ļ„»ļ…‰ ļ„¢ļ…‡ļ„›ļ„µ ļ„“ļ„» ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µ ļ„±ļ…‚ļ„µļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ…ƒļ„øļ…žļ„  ļ„ŗļ…‚ļ„µļ…„ ļ„¢ļ…‚ļ„©ļ„›ļ…‚ļ„µļ…„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‚
ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„“ļ…žļ„› ļ„’ļ„³ ļ„øļ…œļ„§ ļ…ƒļ„øļ…žļ„  ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„¶ļ„” ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„šļ„ŗļ„Ŗ ļ„›ļ…‚ļ…€ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ…ƒļ„›ļ„•
ļ„
ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„®? ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„›ļ…‹ļ„” ļ„øļ…„ ļ„¢ļ…‚ļ„©ļ„›ļ…‚ļ„µļ…„ ļ„±ļ„µļ„±ļ…‚ļ„¬ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ……ļ…œļ„¬ļ…„ī„”
(e) ļ„ŗ ļ„¬ļ„ļ…„ (ļ…ƒļ„øļ„» ļ„µļ„›ļ„Ŗ )
ā€¢ ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„³ļ„£ļ„© ļ…ƒļ„øļ…žļ„  ļ„’ļ„ŗļ…‚ļ„® ļ„»ļ…‹ļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ…ƒļ„›ļ„•
ļ„
? ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„±ļ„»ļ……ļ„Ŗ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ„ļ……ļ…œļ„£ļ„¶ļ„¬ļ…‚ļ„µ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ„‘ļ„ŗļ„¶ ļ„¬ļ……ļ„®ļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ…ƒļ„øļ…žļ„ 
ļ…ƒļ„øļ„»ļ…‚ļ„µļ„› ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…‡ī„”
ó¼©ŗ󼩻ļ„‘ļ„®ļ……ļ„³ ļ„® ļ„¶ļ„ ļ„•ļ„© ļ„ø ļ…ƒļ„¶ļ„’ļ„ ļ„¶ļ„” ļ„›ļ„» ļ„©ļ…„ ļ„ŗļ„³ ļ„®ļ„Ŗ
ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„Ŗļ…„ļ„µļ„‘ļ…œļ„¬ļ…‚ļ„¾ ļ„»ļ…‹ ļ„¢ļ…‹ ļ„“ļ…žļ„› ļ…ƒļ„®ļ„¹ļ…‚ļ„®ļ…‡ 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„¹ļ…‚ļ„®ļ…‚ ļ„¶ļ„ļ…‚ ļ…ƒļ„µļ„»ļ…‚ ļ„»ļ…‰:
ā€¢ ļ…ƒļ„®ļ„µļ„Æļ…žļ„œļ„Ŗ :ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„Ŗļ…„ļ„µ, ļ„šļ„ŗļ„Ŗļ„®, ļ„±ļ……ļ…žļ„¶'ļ„ŗļ…„ 'ļ„Ŗļ…‡ ļ„¶ļ…žļ„ļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„“ļ„›ļ„ŗ ļ„µļ„Ŗ :ļ…ƒļ„¢ļ…œļ„®ļ…‡ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ„Ŗļ…„ļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„ ļ„¶ļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ…‹, ļ„•ļ„» ļ„±ļ……ļ…žļ„¶'ļ„ŗļ…„ ļ„¬ļ…‡ ļ„¬ļ……ļ„’ļ„¶ļ…‡ ļ„™ļ„®ļ…‡ ļ„»ļ…„ ļ„®ļ…‡ļ„æļ…‡ ļ„“ļ„›ļ…žļ„¦ļ…‡ ļ„»ļ……ļ…œļ„¬ļ…‡
ļ„¢ļ…‚ļ„ļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„›ļ……ļ„¹ļ„¶ļ„Ŗ :ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„Ŗļ…„ļ„µ ļ…ƒļ„œļ…œļ„§ļ…‡ ļ„»ļ…‹ļ„— ļ„®ļ„»ļ…„
ļ„
, ļ„ŗļ„ļ…Œ ļ„“ļ…žļ„›ļ„¦ļ…‡ ļ„»ļ…‹ļ„— ļ„»ļ„®ī„”
ā€¢ ļ„›ļ……ļ„¹ļ„¶ļ„Ŗ :ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ…ƒļ„®ļ„¹ļ…‚ļ„®ļ…‡ ļ„¬ļ…„ ļ„ŗļ…ƒļ„«ļ„Ŗļ…„ ļ„±ļ…‚ļ„µļ…‡ ļ„•ļ„Æļ„¶ļ„±ļ„­ ļ„ŗļ…‚ļ„µļ…„ ļ„¢ļ…‚ļ„©ļ„›ļ…‚ļ„µļ…„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ī„”
ā€¢ ļ„ŗ ļ„¬ļ„ļ…„:ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„­ļ„®ļ……ļ„¹ ļ„ŗļ…œļ„²ļ…‚ļ„¶ļ„©ļ…‚ ļ„’ļ„ŗļ…‚ļ„® ļ„»ļ…‰, ļ„±ļ„»ļ……ļ„Ŗ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ„ļ……ļ…œļ„£ļ„¶ļ„¬ļ…‚ļ„µ ļ„®ļ„»ļ…„
ļ„
ī„”
ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„¶ļ„ļ…‚ļ„•ļ„© ļ„øļ…‚ļ„¶ļ…‚ ļ„“ļ…žļ„› ļ„»ļ……ļ„®ļ„µļ„³ļ…œļ„¬ ļ„Ŗļ…„ļ„µļ„‘ļ…œļ„¬ļ…‚ļ„¾ ļ„øļ…‚ļ„ļ„ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ā€”ļ„ŗļ„»ļ…„, ļ„ŗļ„„ļ…„ļ„›, ļ„²ļ„µļ…‹ļ„ŗļ…‡ļ„³ļ…œļ„¬, ļ„‘ļ„Ŗļ…‡
ļ„›ļ……ļ„¹ļ„¶ī„”
󹶓󹶔󹶕󹶖󹶗󹶘ļ…ƒļ„ŗļ…žļ„„
ļ„’ļ„™ ļ„“ļ„» ļ„ŗļ„² ļ„“ļ„›ļ…žļ„¦ļ…‡ ļ„±ļ…œļ„®ļ…§ļ…„ļ„—:
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ā€¢ ļ„øļ…žļ„­ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„² ļ„øļ„® ļ„‘ļ„®ļ……ļ„³ ļ„® (MLE)ļ„“ļ…žļ„› ļ„’ļ„³ ļ…ƒļ„øļ„­ļ…„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µ ļ„ ļ……ļ„©ļ„¬ļ…„ ļ„»ļ…‰ ļ…ƒļ„¢ļ„ŗ ļ„®ļ…‚ļ„¶ ļ„¬ļ…‡ļ„œļ…‡
ļ„ļ„— ļ„§ļ…‡ļ„„ļ…‚ ļ„®ļ…†ļ…œ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ…œļ„²ļ…‚ļ…ƒļ„øļ„Ŗ ļ„±ļ„©ļ…‚ļ„“ļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„’ļ„³ ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„øļ„µļ„ (OLS)ļ„“ļ…žļ„› ļ„œļ…‚ļ„ŗ ļ…ƒļ„øļ„­ļ…„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„øļ„µļ„ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„žļ…žļ„„ ļ„Ŗļ…Œ ļ„žļ…žļ„„ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡
ļ„’ļ„³ ļ„ļ„¶ļ„Ŗļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„³ļ…‚ļ„³ļ„¶ļ…‡ ļ…ƒļ„øļ…žļ„ , ļ„“ļ„» MLE ļ„®ļ…‚ļ„¶ ļ„³ļ…‡ļ„¶ ļ„œļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„› ļ„±ļ„® ļ„³ ļ„‘ļ„®ļ……ļ„³ ļ„®:ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„› ļ…ƒļ„®ļ„“ļ„³ ļ„¢ļ…‚ļ„ ļ„°ļ…‚ļ„µļ„³ļ…†ļ„¶ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰; ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„‘ļ„ŗļ„¶
ļ„ŗļ…œļ…ƒļ„œļ„’ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„§ļ…‡ļ„„ļ…‚ ļ„Ŗļ…Œ ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ī„”
ā€¢ ļ„ ļ…œļ„ļ…‡ ļ„‘ļ„®ļ……ļ„³ ļ„®ļ„›:ļ„•ļ„» ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ, ļ„“ļ„›ļ„ŗļ…‚ļ„µ, ļ„›ļ……ļ„¹ļ„¶, ļ„›ļ…‚ļ…€ļ…„ ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„µļ„¶ ļ„»ļ…‹ļ„©ļ…‡ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„‘ļ…œļ„Ŗ ļ…ƒļ„øļ…žļ„ , MLE ļ„‘ļ„Ŗļ…‡ OLS ļ„¬ļ…‹ļ„øļ…ˆ ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„µļ„©ļ„®ļ…„ļ„Ŗļ…„ļ„’ļ„ ļ„®ļ…‚ļ„¶ ļ„µļ„»ļ…žļ„ŗļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„»ļ…žļ„¶ ļ„›ļ„µļ„® ļ„øļ…‚ļ„¶ļ…‡ ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗļ…‚ļ„ ļ„øļ…‚ļ„ļ„ ļ„»ļ„®, ļ„¢ļ„¬ļ…Œ
ļ…ƒļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„¶ļ„ļ…‚ļ„•ļ„© ļ„øļ…‚ļ„¶ļ…‡ ļ„•ļ„» ļ„ŗļ…‚ļ„­ļ„® ļ„»ļ„® ļ„¢ļ…‹ ļ„•ļ„» ļ„øļ„µļ„Ŗļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„¶ļ„ļ…‚ļ„•ļ„© ļ„øļ…‚ļ„¶ļ…‚ ļ„•ļ„»
ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„¶ļ„ļ…‚ļ„Ŗļ…‚ļ„µ ļ„ŗļ…žļ„ ļ…‚ļ„” ļ„øļ…žļ„¶ ļ„“ļ„¹ļ…‚ļ„µļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰, ļ…ƒļ„¢ļ„øļ…ˆ ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‚ ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗ ļ„¶ļ„ļ…‚ļ„Ŗļ…‚ļ„µ ļ„ŗļ„»ļ…„ ļ„¬ļ…‹ļ„¹ļ…„ ļ„®ļ…†ļ…œ
ļ„•ļ„¢ļ…‚ļ„ļ„µ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„² ļ„-ļ„±ļ…„
3. xĀ² (ļ„ ļ…„-ļ„øļ„µļ„) ļ„øļ…œļ„§ ļ„Ŗļ…Œ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„›ļ…„ ļ„ŗļ„³ļ„£ļ„¬ļ…‡ ļ„»ļ…‹? ļ„“ļ„ŗļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„ļ……ļ„© ļ„ ļ„®ļ…†ļ…œ ļ„Æļ…„ ļ„Æļ„Ŗ ļ„›ļ„µļ…‹ī„”
ļ„•ļ…žļ„Ŗļ„µ:ļ„ ļ…„-ļ„ŗļ„›ļ……ļ„—ļ„‘ļ„µ (Ļ‡Ā²) ļ„øļ…œļ„§ ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„©
ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„•ļ„Ŗļ„ŗļ……ļ„› ļ„œļ…‹ļ„¢ļ…„ ļ„»ļ…‹ ļ„¢ļ…‹ ļ„ŗļ…œļ…ƒļ„œļ„’ļ„øļ…‚ļ„ ļ„¬ļ…‡ ļ„ŗļ„³ļ……ļ…œļ„¬ļ„µ ļ…ƒļ„øļ…žļ„  ļ„¶ļ……ļ„›ļ…‡ ļ„»ļ…‹ļ„— ļ„Æļ…‰ļ„„ļ„µļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„© ļ„¬ļ…„
ļ„›ļ…‹ļ…ƒļ„¹ļ„¹ ļ„›ļ„µ ļ…ƒļ„µļ„»ļ…‚ ļ„»ļ…‰ī„” ļ„»ļ„µ ļ„ŗļ…œļ…ƒļ„œļ„’ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„¢ļ…‚ļ„Æļ„¬ļ…„ ļ„»ļ…‰, ļ„Æļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„¢ļ…‚ļ„©ļ„¬ļ…‡ ļ„»ļ…‹ ļ…ƒļ„› ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„¬ļ…‡ ļ„Æļ…„ļ„±ļ…œļ„­ ļ…ƒļ„Æļ…žļ„”ļ…‡ ļ„“ļ…žļ„›
ļ„ļ……ļ„Æļ„Ŗ ļ„Ŗļ„µļ„› ļ„»ļ…‰ī„” ļ„‘ļ…œļ„›ļ„æļ…‚ ļ…ƒļ„øļ…ƒļ„ļ„’ļ„®ļ…„ ļ„§ļ…‡ļ„„ļ…‚ ļ„Ŗļ…žļ„› ļ…ƒļ„±ļ„¶ļ„›ļ……ļ„¶ ļ„“ļ„ŗ ļ„Ŗļ„µļ…§ļ…‚ļ„ ļ„Æļ„»ļ……ļ…œļ„ ļ„¬ļ…‡ ļ„»ļ„®: ļ„•ļ„» ļ„Æļ…‰ļ„„ļ„µļ„® ļ„¶ļ…žļ„²ļ„©ļ…‚,
ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ„³ļ…‚ļ„Æļ„©ļ…‚ ļ„‘ļ„Ŗļ…‡ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„®ļ…‚ ļ„ ļ…‚ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„“ļ„ŗ ļ„“ļ…‚ļ„Ŗļ„µļ…‚ ļ…ƒļ„øļ…žļ„  ļ„ŗļ„² ļ„Ŗļ…Œ
ļ„¹ļ„›ļ„Ŗļ…„ļ„¹ļ…‚ļ„¶ļ…„ ļ„ŗļ…‚ļ„­ļ„®ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„“ļ…žļ„› ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ„»ļ…‰, ļ…ƒļ„¢ļ„ŗļ„®ļ…†ļ…œ ļ„‘ļ„›ļ„ŗļ„µ Ļ‡Ā² (ļ„ ļ…„-ļ„øļ„µļ„) ļ„¬ļ……ļ„’ļ„µļ…‚ ļ„¬ļ„µļ„ŗļ…‚ļ„“ļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚
ļ„»ļ…‰ī„”
ļ„“ļ„ŗļ„¬ļ…‡ ļ„³ļ…†ļ„¶ ļ„µļ…†ļ„Æ ļ…ƒļ„øļ…žļ„ , ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ„“ļ„» ļ„³ļ…‚ļ„Æļ„© ļ„±ļ…‚ļ„µļ…‡ ļ„»ļ…‰ ļ…ƒļ„› ļ…ƒļ„®ļ„µļ…„ļ„œļ„© ļ„‘ļ„®ļ……ļ„³ļ…‚ļ…ƒļ„®ļ„Ŗ ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„Ŗļ…Œ ļ…ƒļ„›ļ…œļ„®ļ…„ ļ„¬ļ…†ļ„µ ļ„²ļ„„ļ„›ļ„¬ļ…‡
ļ„»ļ„®ī„” ļ„Æļ„µ ļ„»ļ„µļ…‡ļ„› ļ„²ļ„„ļ„›ļ…‚ļ„‘ ļ„®ļ…†ļ…œ ļ„‘ļ„¶ļ…žļ„-ļ„«ļ„¶ļ…žļ„ ļ…ƒļ„øļ…žļ„  ļ„¬ļ…‡ļ„œļ„© ļ„¬ļ…„ ļ„±ļ„¢ļ…‚ļ„—, ļ„“ļ„» ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„“ļ…žļ„› ļ…ƒļ„ŗļ…œļ„ļ„¶ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„
ļ…ƒļ„øļ…žļ„  ļ„¢ļ…‹ļ„æļ„¬ļ…‚ ļ„»ļ…‰, ļ„²ļ„„ļ„›ļ…‚ļ„‘ ļ„®ļ…†ļ…œ ļ„øļ„µļ„ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ„Ŗļ…‚ļ„ ļ„¢ļ…‹ ļ„“ļ„» ļ„“ļ„›ļ…„ļ„®ļ…„ ļ„±ļ„©ļ…‚ļ„“ļ„’ ļ„¢ļ…‚ ļ„ŗļ„›ļ…‡ ļ…ƒļ„› ļ„ŗļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„› ļ„‘ļ„Ŗļ…‡
ļ„®ļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„› ļ„¬ļ…‹ļ„øļ…ˆ ļ„‘ļ…œļ„Ŗļ„µ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„“ļ…‹ļ„ļ„¬ļ…‚ļ„® ļ„Æļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„“ļ„» ļ„Æļ„»ļ……ļ…œļ„  ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„‘ļ„µļ„«ļ„Æļ…†ļ„µļ„® ļ„³ļ…‚ļ„Æ
ļ…ƒļ„¬ļ…œļ„¬ļ…„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„øļ„’ļ„Æļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„øļ„µļ„Ŗļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰, ļ„„ļ…‡ļ„±ļ„¶ ļ…ƒļ„øļ…žļ„  ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µļ„Ŗļ…‚ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„Ŗļ…Œ ļ„¶ļ…‰ ļ„›ļ…‡
ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„¶ļ„ļ…‚ļ„•ļ„© ļ„Ŗļ…žļ„›ī„”
ļ„³ļ…†ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„ŗļ…œļ„›ļ„¶ļ„Æ
ļ„’ļ„™ ļ„“ļ…žļ„› ļ„Æļ„¶ ļ„¶ļ„” ļ„ŗļ„³ļ…ˆ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„Æļ…žļ„”ļ…‡ ļ„ ļ…žļ„¶ļ…„ļ„—ī„” ļ„ ļ…„-ļ„ŗļ„›ļ……ļ„—ļ„‘ļ„µ ļ„øļ…œļ„§ 20ļ„øļ…„
ļ„
ļ„ŗļ„¬ļ…„ ļ„¬ļ…‡ ļ„¹ļ……ļ„µļ…† ļ…ƒļ„øļ…žļ„  ļ„›ļ…‚ļ„µļ„¶ ļ„Æļ…„ļ„‘ļ„µļ„ŗļ„® ļ„¬ļ…‡
ļ„›ļ…œļ„³ ļ„Ŗļ…Œ ļ„•ļ„²ļ„µļ…„ī„” ļ„•ļ„» ļ„“ļ„» ļ„¢ļ…‚ļ„ļ„ ļ„© ļ„¶ļ„” ļ„“ļ…žļ„› ļ„Ŗļ„µļ…„ļ„›ļ…‚ ļ„ ļ…‚ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„ŗļ…„ ļ…ƒļ„› ļ„›ļ…„ ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ…ƒļ„ļ„’ ļ„§ļ…‡ļ„„ļ…‚ ļ„“ļ…žļ„› ļ…ƒļ„ŗļ„­ļ…‚ļ„ļ„Ŗļ„›
ļ„Æļ…‰ļ„„ļ„µļ„® ļ„¬ļ…„ ļ„Æļ…‚ļ„¶ļ„©ļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„© ļ„øļ„¢ļ…Œ, ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ ļ…ƒļ„ŗļ…žļ„›ļ…‡ ļ„®ļ…†ļ…œ 100 ļ„øļ…‚ļ„µ ļ„•ļ„¶ļ„„ļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ…‹, ļ„Ŗļ…‚ļ„
ļ„Ŗļ……ļ„ŗļ…„
ļ„
50 ļ…ƒļ„ŗļ„µ ļ„‘ļ„Ŗļ…‡ 50 ļ„Æļ…†ļ„”ļ…‚ļ„ ļ„¬ļ…„ ļ„•ļ„³ļ…„ļ„¬ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ī„” ļ„Æļ„µ ļ„‘ļ„ŗļ„¶ ļ…ƒļ„øļ…žļ„ , ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ 47 ļ…ƒļ„ŗļ„µ ļ„‘ļ„Ŗļ…‡ 53 ļ„Æļ…†ļ„”ļ…‚ļ„ ļ…ƒļ„³ļ„¶
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„ŗļ„›ļ„¬ļ…„ļ„’ļ„ ļ„»ļ„®ī„” ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ…ƒļ„›ļ„øļ…ˆ ļ„¢ļ…‚ļ„©ļ„¬ļ…‡ ļ„»ļ…‹ ļ…ƒļ„› ļ„“ļ„» ļ„²ļ„„ļ„›ļ„©ļ…‚ ļ…ƒļ„ŗļ„µļ…€ ļ„ŗļ…œļ„¢ļ…‹ļ„ ļ„®ļ…‚ļ„¶ ļ„»ļ…‰, ļ„¢ļ…‚ļ„ ļ…ƒļ„ŗļ…žļ„›ļ…‡ ļ…ƒļ„øļ…žļ„  ļ„›ļ……ļ„£ ļ„ļ„¶ļ„Ŗ ļ„»ļ…‰?
ļ„›ļ…‚ļ„µļ„¶ ļ„Æļ…„ļ„‘ļ„µļ„ŗļ„® ļ„®ļ…‡ ļ„‘ļ…ƒļ„¢ļ„»ļ…‡ ļ„ŗļ„øļ…‚ļ„¶ļ…‚ļ„ ļ„¬ļ…‡ ļ„¢ļ„øļ…‚ļ„± ļ„¬ļ…‡ļ„© ļ„¶ļ„” ļ„ ļ…„-ļ„ŗļ„›ļ……ļ„—ļ„‘ļ„µ ļ„„ļ…‰ļ„ŗļ„„ ļ…ƒļ„Ŗļ„’ļ„µ ļ„›ļ…„ļ„Ŗļ…‚ī„”
ļ„ļ…ƒļ„©ļ…ƒļ„Ŗļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡, Ļ‡Ā² ļ„øļ…œļ„§ ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„’ļ„³ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ļ…‚ļ„ ļ„¬ļ…‡ ļ„øļ„µļ„ļ…‚ļ„ ļ„¬ļ…‡ ļ„¢ļ…‹ļ„æ ļ„Ŗļ…Œ ļ„Æļ…‰ļ„¬ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„’ļ„™ ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„›ļ„¬ļ„³ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„ŗļ„³ļ„£ļ…„ļ„—:
1. ļ„ŗļ„„ļ…Šļ„§ļ„µļ„§ ļ„ŗļ„­ ļ„µļ„® ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶: Zā‚, Zā‚‚, ..., Zā‚™ ļ„øļ„µļ„ļ…‡ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ļ…‚ļ„ ļ„¬ļ…„ ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ„¢ļ…‹ ļ„“ļ…žļ„› ļ…ƒļ„³ļ„’ļ„µļ…„
ļ„’ļ„³ ļ„øļ…œļ„§ (ļ„šļ„ŗļ„Ŗ 0, ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® 1) ļ„¬ļ…„ ļ„Æļ…‚ļ„¶ļ„©ļ…‚ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„“ļ„» ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„±ļ„Ŗļ…‚ ļ„¬ļ…‡ "ļ…ƒļ„±ļ„¶ļ…ƒļ„§ļ…œļ„
ļ„±ļ„¶ļ…‚ļ„›" ļ„»ļ„®ī„”
2. ļ„øļ„µļ„ļ…„ļ„›ļ„µļ„® ļ„‘ļ„Ŗļ…‡ ļ„ŗļ…œļ„œļ…‡ļ„Æ: ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ„»ļ„®ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„»ļ„µļ…‡ļ„› ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ ļ„¬ļ…‚ ļ„øļ„µļ„ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ ļ„‘ļ„Ŗļ…‡ ļ„•ļ„»ļ„®ļ…‚ļ„
ļ„®ļ…†ļ…œ ļ„“ļ„›ļ…žļ„¦ļ…‡ ļ„¢ļ…‹ļ„æļ„¬ļ…‡ ļ„»ļ…‹, ļ„Ŗļ…‚ļ„ ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ„“ļ…žļ„› ļ„®ļ„øļ…‚ļ„ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ ļ…ƒļ„³ļ„¶ļ„¬ļ…‚ ļ„»ļ…‰:
ļ„“ļ„» ļ„®ļ„øļ…‚ļ„ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶, Ļ‡Ā², n ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ (df) ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ„¬ļ…„ ļ„Æļ…‚ļ„¶ļ„©ļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„’ļ„³ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„ļ„©ļ„®ļ…‚ ļ…ƒļ„øļ…žļ„  ļ„øļ„µļ„Ŗļ…‡ ļ„ļ„— ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„¢ļ…‚ļ„©ļ„›ļ…‚ļ„µļ…„ ļ„¬ļ…‡ ļ„„ļ……ļ„›ļ…ƒļ„æļ„’ļ„ ļ„¬ļ…„ ļ„ŗļ…œļ…ƒļ„œļ„’
ļ„®ļ…‚ļ„¶ ļ„³ļ…‡ļ„¶ ļ„œļ…‚ļ„ļ„¬ļ…„ļ„’ļ„ ļ„»ļ„®ī„”
ļ„“ļ„ŗ ļ„¶ļ„”, ļ„ŗļ…œļ„œļ…‡ļ„Æ ļ…ƒļ„øļ…žļ„ , Ļ‡Ā² ļ„“ļ…žļ„› ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„Ŗļ„µļ…„ļ„›ļ…‡ ļ„®ļ…‚ļ„¶ ļ„šļ„ŗļ„Ŗ ļ„Ŗļ…Œ ļ„øļ„µļ„ ļ„²ļ„„ļ„›ļ„©ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¢ļ…‹ļ„æļ„® ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„Ŗļ„µļ…„ļ„›ļ…‚ ļ„»ļ…‰ī„”
ļ„ ļ…„-ļ„ŗļ„›ļ……ļ„—ļ„‘ļ„µ ļ„øļ…œļ„§ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„øļ„¹ļ…‡ļ„¹ļ„Ŗ ļ„ø ļ„
ļ„»ļ……ļ„©, ļ„’ļ„™ ļ„ ļ…„-ļ„ŗļ„›ļ……ļ„—ļ„‘ļ„µ ļ…ƒļ„§ļ„ŗļ„„ļ…„ļ…„ļ…ƒļ„±ļ„–ļ„¹ļ„® ļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„ļ……ļ„©ļ…‚ļ„ ļ„¬ļ…„ ļ„Æļ„æļ„ ļ…‹ļ„¶ ļ„›ļ„µļ…„ļ„—, ļ„“ļ…žļ„›-ļ„“ļ…žļ„› ļ„›ļ„µļ„›ļ…‡, ļ„“ļ…žļ„› ļ„ŗļ…‚ļ„»ļ„³ļ„©ļ…‡
ļ„’ ļ„µļ„»ļ…„ ļ„›ļ„»ļ…‚ļ„©ļ…„ ļ„¬ļ…‡ ļ„‘ļ…ƒļ„­ļ„’ļ„øļ…‚ļ„ ļ„øļ…‚ļ„ļ„:
1. ļ„øļ…œļ„§ ļ„¬ļ…„ ļ…ƒļ„›ļ„ŗļ„³ ļ„‘ļ„Ŗļ…‡ ļ„’ļ„› ļ„µ
ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ„ŗļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ…ƒļ„Ŗļ„µļ„”ļ…„ (ļ„ŗļ…žļ„¢ļ…‡-ļ…ƒļ„Ŗļ„µļ„”ļ…„) ļ„»ļ…‰ ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„ŗļ„µļ„° ļ„ļ…‰ļ„µ-ļ„®ļ…‰ļ„ļ…‡ļ…ƒļ„„ļ„ø ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ (Ļ‡Ā² ā‰„ 0) ļ„¶ļ„”
ļ„Æļ…ƒļ„µļ„²ļ…‚ļ…ƒļ„¹ļ„Ŗ ļ„›ļ…„ļ„Ŗļ…„ ļ„ļ„” ļ„»ļ…‰ī„” ļ„“ļ„» ļ„ŗļ…ƒļ„»ļ„¢ ļ„µļ…†ļ„Æ ļ…ƒļ„øļ…žļ„  ļ„ŗļ„³ļ„£ ļ„’ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰: ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„“ļ„» ļ„øļ„µļ„ļ…‚ļ„ ļ„¬ļ…‚ ļ„¢ļ…‹ļ„æ ļ„»ļ…‰, ļ„“ļ„» ļ„›ļ„¬ļ…‡
ļ„øļ…„ ļ„®ļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„› ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…‚ī„”
ā€¢ ļ„”ļ…‹ļ„„ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ (df) ļ„¶ļ„”, ļ„øļ…œļ„§ ļ„±ļ„»ļ……ļ„Ŗ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ…ƒļ„øļ„ļ„æļ…„ ļ„»ļ…‹ļ„” ļ„»ļ…‰ī„”
ā€¢ ļ…ƒļ„¢ļ„øļ…ˆ-ļ…ƒļ„¢ļ„øļ…ˆ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„øļ„­ļ„¬ļ…„ļ„’ļ„ ļ„»ļ„®, ļ„øļ…œļ„§ ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„ŗļ„³ļ„µļ…†ļ„Æ ļ„»ļ…‹ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ„’ļ„³
ļ„øļ…œļ„§ ļ„øļ„µļ„ļ…„ ļ„¶ļ…žļ„ļ„© ļ„¶ļ…žļ„ ļ„Æļ…Šļ„¬ļ…„ ļ„»ļ…‰ī„”
2. ļ„’ļ„¾ ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„
Ī½ ļ„¬ļ……ļ„’ļ„µļ…‚ ļ„¬ļ„µļ„ŗļ…‚ļ„”ļ„’ļ„ ļ„ļ„”ļ„’ļ„ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ (df), ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ„¶ļ„” ļ„›ļ…ˆļ„¬ļ„µļ…„ ļ„»ļ„®ī„” ļ„“ļ„» ļ„’ļ„³
ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„’ļ„³ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ļ…‚ļ„ ļ„¬ļ…„ ļ„ŗļ…œļ…ƒļ„œļ„’ ļ„®ļ…†ļ…œ ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ„® ļ…ƒļ„¢ļ„®ļ…§ļ…‚ļ„ ļ„¬ļ…‚ ļ„øļ„µļ„ ļ„‘ļ„Ŗļ…‡ ļ„¢ļ…‹ļ„æ ļ„›ļ…„ļ„Ŗļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚
ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„® ļ„¶ļ„”, ļ„¢ļ…‡ļ„›ļ„µ Ļ‡Ā² 5 ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„øļ„µļ„ ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„®ļ…‚ļ„µļ„³ļ„¶ļ…‚ļ„ 'ļ„Ŗļ…‡ ļ„‘ļ„­ļ…‚ļ„µļ„Ŗ ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ df = 5ī™€
ā€¢ ļ…ƒļ„øļ„»ļ…‚ļ„µļ„› ļ„•ļ„Æļ„“ļ…‹ļ„ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ , ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„§ļ…‡ļ„„ļ…‚ ļ…ƒļ„øļ…žļ„  ļ„µļ……ļ„›ļ…‚ļ„øļ„„ļ…‚ļ„ ļ„¶ļ„” ļ„‘ļ„®ļ……ļ„›ļ…†ļ„¶ ļ„»ļ……ļ…œļ„¬ļ…„ļ„’ļ„ ļ„»ļ„®,
ļ…ƒļ„¢ļ„øļ…ˆ ļ…ƒļ„› ļ„Æļ…‰ļ„µļ…‚ļ„³ļ…„ļ„„ļ„µļ…‚ļ„ ļ„¬ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„¶ļ„ļ…‚ļ„•ļ„©ļ…‚ī„”
3. ļ„³ļ…žļ„­ļ„³ ļ„® ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„²ļ…œļ„®ļ„Ŗ
ļ„“ļ…žļ„› Ļ‡Ā² ļ„øļ…œļ„§ ļ„¬ļ…‚ ļ„³ļ…žļ„­ļ„³ļ…‚ļ„® ļ„“ļ„ŗļ„¬ļ…„ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰:
ļ„“ļ„» ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„Ŗļ…Œ ļ„¬ļ……ļ…žļ„ļ„©ļ…„ ļ„»ļ…‰:
ļ„“ļ„» ļ…ƒļ„øļ„¹ļ…‡ļ„¹ļ„Ŗļ…‚ ļ„œļ…‚ļ„ŗ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„¹ļ…‚ļ„®ļ„¬ļ…‚ļ„µ ļ„»ļ…‰ ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„“ļ„» ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ ļ…ƒļ„› ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ļ…‚ļ„ ļ„¬ļ…„ ļ…ƒļ„ļ„©ļ„Ŗļ…„ ļ„¬ļ…‡
ļ„®ļ…‚ļ„¶ ļ„øļ…œļ„§ ļ„¬ļ…‚ ļ„°ļ…‰ļ„¶ļ…‚ļ„‘ ļ…ƒļ„›ļ„øļ…ˆ ļ„øļ„­ļ„¬ļ…‚ ļ„»ļ…‰ī„”
4. ļ„˜ļ„§ļ…„ļ…ƒļ„„ļ…ƒļ„øļ„„ļ…„ ļ…ƒļ„øļ„¹ļ…‡ļ„¹ļ„Ŗ
ļ„ ļ…„-ļ„ŗļ„›ļ„øļ…‡ļ„‘ļ„µ ļ…ƒļ„§ļ„ŗļ„„ļ…„ļ…„ļ…ƒļ„±ļ„–ļ„¹ļ„® ļ„¬ļ…‡ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„ŗļ……ļ…œļ„¬ļ„µ ļ„Æļ…ƒļ„»ļ„¶ļ…†ļ„’ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„“ļ…žļ„› ļ„“ļ„ŗļ„¬ļ…„ ļ„˜ļ„§ļ…„ļ…ƒļ„„ļ…ƒļ„øļ„„ļ…„ ļ„»ļ…‰:
ā€¢ ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„›ļ…‹ļ„¶ ļ„¬ļ…‹ ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ ļ„»ļ„®, Ļ‡Ā²ā‚ Ī½ā‚ df ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ ļ„‘ļ„Ŗļ…‡ Ļ‡Ā²ā‚‚ Ī½ā‚‚ df ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶, ļ„Ŗļ…‚ļ„
ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„¬ļ…‚ ļ„¢ļ…‹ļ„æ ļ„øļ…„ ļ„ ļ…„-ļ„øļ„µļ„ ļ„®ļ…†ļ…œ Ī½ā‚ + Ī½ā‚‚ df ļ„®ļ…‚ļ„¶ ļ„øļ…œļ…ƒļ„§ļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰:
ļ„“ļ„» ļ…ƒļ„øļ„¹ļ…‡ļ„¹ļ„Ŗļ…‚ ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„ŗļ„µļ…‹ļ„Ŗļ…‚ļ„ ļ„Ŗļ…Œ ļ„¢ļ…‚ļ„©ļ„›ļ…‚ļ„µļ…„ ļ„®ļ…†ļ…œ ļ„¢ļ…‹ļ„æļ„® ļ…ƒļ„øļ…žļ„  ļ„±ļ„»ļ……ļ„Ŗ ļ„•ļ„Æļ„“ļ…‹ļ„ļ…„ ļ„»ļ…‰ī„”
5. ļ„Æļ„¶-ļ„¢ļ„®ļ„µļ…‡ļ…ƒļ„„ļ…œļ„ ļ„°ļ…œļ„›ļ„¹ļ„® (MGF)
ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„› ļ„Æļ„¶-ļ„¢ļ„®ļ„µļ…‡ļ…ƒļ„„ļ…œļ„ ļ„°ļ…œļ„›ļ„¹ļ„® (MGF) ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰, ļ„¢ļ…‹ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ…ƒļ„øļ…ƒļ„ļ„’ļ„®ļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„’ļ„ŗļ…‚ļ„®ļ…„ ļ„®ļ…‚ļ„¶
ļ„•ļ„³ļ…„ļ„¬ ļ„›ļ…„ļ„Ŗļ…‡ ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„•ļ…žļ„  ļ„Æļ„¶ļ…‚ļ„ ļ„¬ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„¬ļ…„ ļ„’ļ…ƒļ„ļ„’ ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„” Ī½ df ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ Ļ‡Ā² ļ„¬ļ…‚ MGF ļ„»ļ…‰:
ļ„“ļ„» ļ„¹ļ…‚ļ„®ļ„¬ļ…‚ļ„µ ļ„°ļ…œļ„›ļ„¹ļ„® ļ„ļ…ƒļ„©ļ…ƒļ„Ŗļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„³ļ…žļ„­ļ„³ļ…‚ļ„®, ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„‘ļ„Ŗļ…‡ ļ„»ļ…‹ļ„µ ļ…ƒļ„øļ„¹ļ…‡ļ„¹ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ„µļ„® ļ…ƒļ„øļ…žļ„ 
ļ„³ļ„¬ļ„¬ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
6. ļ„ŗļ…ƒļ„›ļ„–ļ„®ļ…‰ļ…ž ļ„ŗ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„µļ„„ļ…‹ļ…ƒļ„ŗļ„ŗ
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ā€¢ ļ…ƒļ„Ŗļ„µļ„”ļ…„: ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ„ŗļ…žļ„¢ļ…‡ ļ„Æļ…‚ļ„ŗļ…‡ ļ…ƒļ„Ŗļ„µļ„”ļ…„ ļ„»ļ…‰, ļ…ƒļ„¢ļ„ŗ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„Ŗļ„µļ„”ļ…„ = āˆš(8/Ī½) ļ„»ļ…‰ī„” ļ…ƒļ„¢ļ„øļ…ˆ-ļ…ƒļ„¢ļ„øļ…ˆ Ī½ ļ„øļ„­ļ„¬ļ…‚ ļ„»ļ…‰,
ļ…ƒļ„Ŗļ„µļ„”ļ…„ ļ„žļ„„ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„›ļ……ļ„µļ„„ļ…‹ļ…ƒļ„ŗļ„ŗ: ļ„›ļ……ļ„µļ„„ļ…‹ļ…ƒļ„ŗļ„ŗ "ļ„Æļ…„ļ„›ļ„§ļ„®ļ…‡ļ„ŗ" ļ„®ļ…†ļ…œ ļ„³ļ…‚ļ„Æļ„¬ļ…‚ ļ„»ļ…‰ī„” Ļ‡Ā² ļ„øļ…œļ„§ ļ„¶ļ„”, ļ„›ļ……ļ„µļ„„ļ…‹ļ…ƒļ„ŗļ„ŗ = 12/Ī½ī™€ ļ„¬ļ……ļ„±ļ…‚ļ„µļ…‚, ļ…ƒļ„¢ļ„øļ…ˆ-
ļ…ƒļ„¢ļ„øļ…ˆ df ļ„øļ„­ļ„¬ļ…‚ ļ„»ļ…‰, ļ„øļ…œļ„§ ļ„ŗļ„³ļ„Ŗļ„¶ ļ„»ļ…‹ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ„’ļ„³ ļ„øļ„›ļ„µ ļ„øļ„µļ„ļ…„ ļ…ƒļ„¬ļ„œļ…‚ļ„” ļ…ƒļ„¬ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„˜ļ„Æļ„¶ļ…„ļ„›ļ…‡ļ„¹ļ„® ļ„‘ļ„Ŗļ…‡ ļ„‘ļ„®ļ……ļ„²ļ„ø
ļ„’ļ„™ ļ„“ļ„ŗ ļ„ŗļ…œļ„œļ…‡ļ„Æ ļ„­ļ…‚ļ„µļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„»ļ„›ļ…„ļ„›ļ„Ŗ ļ…ƒļ„øļ…žļ„  ļ„øļ…‚ļ„Æļ„ŗ ļ…ƒļ„¶ļ„’ļ„”ļ„—ī„” ļ„“ļ…žļ„› ļ„›ļ„¶ļ…‚ļ„ŗļ„µļ…†ļ„³ ļ„¬ļ…„ ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„¢ļ…žļ„«ļ…‡ ļ„“ļ…žļ„›
ļ„‘ļ…ƒļ„­ļ„’ļ„Æļ„› ļ„“ļ„» ļ„¬ļ…‡ļ„œļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ļ„’ļ„ ļ„¬ļ…‚ ļ„Æļ…„ļ„¬ļ„µļ„¹ļ„® ļ„•ļ„³ļ…„ļ„¬ ļ„›ļ…„ļ„Ŗļ…‡ ļ„Æļ…žļ„­ļ„µļ…‚ļ„ ļ„®ļ…‚ļ„¶ ļ„³ļ…‡ļ„¶ ļ„œļ…‚ļ„ļ„¬ļ…‚
ļ„»ļ…‰ī„” ļ„‘ļ…ƒļ„­ļ„’ļ„Æļ„› 20 ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„ļ…„ļ…‡ļ„§ A, 30 ļ„ļ…„ļ…‡ļ„§ B, ļ„‘ļ„Ŗļ…‡ 50 ļ„ļ…„ļ…‡ļ„§ C ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ„µļ„® ļ„¬ļ…„ ļ„•ļ„³ļ…„ļ„¬ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„Æļ…„ļ…„ļ…ƒļ„œļ„’ ļ„Ŗļ…Œ ļ„±ļ…‚ļ„‘ļ„¬, ļ„‘ļ„ŗļ„¶ ļ„ŗļ…œļ…ƒļ„œļ„’ļ„øļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„«ļ…‹ļ„æļ…§ļ…‚ ļ…€ļ„µļ„› ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„ ļ…„-ļ„ŗļ„›ļ……ļ„—ļ„‘ļ„µ ļ„„ļ…‰ļ„ŗļ„„ ļ„¶ļ…‚ļ„ļ…† ļ„›ļ„µļ„›ļ…‡, ļ„‘ļ…ƒļ„­ļ„’ļ„Æļ„›
ļ„³ļ…‚ļ„Æ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ„¬ļ…‡ļ„œļ…‡ ļ„ļ„— ļ„‘ļ…œļ„Ŗļ„µ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„»ļ„® ļ„¢ļ…‚ļ„ ļ…ƒļ„ŗļ„µļ…€ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„³ļ…ļ„›ļ…‡ ļ„¬ļ…‡ ļ„›ļ…‚ļ„µļ„® ļ„»ļ„®ī„”
ļ„“ļ„ŗļ…‡ ļ„Ŗļ„µļ…§ļ…‚ļ„, Ļ‡Ā² ļ„øļ…œļ„§ ļ„“ļ„»ļ„®ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„»ļ…‰:
1. ļ„Ŗļ…œļ„¬ļ„µļ……ļ„ŗļ„Ŗļ…„ ļ„¬ļ…‡ ļ„„ļ…‰ļ„ŗļ„„- ļ„“ļ„» ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„®ļ…‚ ļ…ƒļ„› ļ„›ļ…„ ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ…ƒļ„ļ„’ ļ„§ļ…‡ļ„„ļ…‚ ļ„“ļ…žļ„› ļ…ƒļ„ŗļ„­ļ…‚ļ„ļ„Ŗļ„› ļ„øļ…œļ„§ ļ„¬ļ…„ ļ„Æļ…‚ļ„¶ļ„©ļ…‚
ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
2. ļ„’ļ„¾ ļ„¬ļ…„ ļ„¬ļ…„ ļ„Æļ„µļ…„ļ…ƒļ„œļ„’- ļ„“ļ„» ļ„¬ļ…‡ļ„œļ„© ļ„¶ļ„” ļ…ƒļ„› ļ„›ļ…„ ļ„¬ļ…‹ ļ„¹ļ…„ļ…‡ļ„©ļ…„ļ„±ļ…žļ„­ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ ļ„ŗļ„±ļ…œļ„­ļ„Ŗ ļ„»ļ„®, ļ„ŗļ…œļ„›ļ„„ļ„›ļ…‚ļ„¶ļ…„ļ„®
ļ„ŗļ…‚ļ„µļ„©ļ…„ļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„øļ„µļ…ƒļ„Ŗļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
3. ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„¶ļ„” ļ…ƒļ„øļ„¹ļ„ø ļ„ŗ ļ„‘ļ…œļ„Ŗļ„µ ļ„¶- ļ„’ļ„³ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ…ƒļ„øļ…žļ„ , Ļ‡Ā² ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„Ŗļ…Œ ļ„’ļ„±ļ…‚ļ„¬ļ…„
ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„¬ļ…‚ ļ„‘ļ…œļ„¬ļ…‚ļ„¾ļ…‚ ļ„¶ļ„ļ…‚ļ„•ļ„© ļ…ƒļ„øļ…žļ„  ļ„³ļ„¬ļ„¬ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„›ļ„» ļ„©ļ…„ ļ„ŗļ„³ ļ„®ļ„Ŗ
ļ„»ļ„µļ…‡ļ„› ļ„ŗļ„„ļ…Šļ„§ļ„µļ„§ ļ„ŗļ„­ļ…‚ļ„µļ„® ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ ļ„®ļ…†ļ…œ ļ„“ļ…žļ„› ļ„’ļ„µļ„›ļ…‰ļ„ŗļ„„ļ„µļ…‚ ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„› ļ„ŗļ…œļ„ļ…„ļ„Ŗļ„›ļ…‚ļ„µ ļ„¬ļ…‡ ļ„µļ…†ļ„Æ ļ…ƒļ„øļ…žļ„  ļ„ŗļ…‹ļ„ ļ…‹ī„”
ļ…ƒļ„øļ„‘ļ„›ļ„Ŗļ…„ļ„ļ„Ŗ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡, ļ„»ļ„µ ļ„“ļ…žļ„› ļ„’ļ„Æļ„©ļ…„ ļ„­ļ……ļ„® ļ„øļ„¢ļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ (ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„±, ļ„šļ„ŗļ„Ŗ ļ„¾ļ…„ļ„µļ…‹ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶)ī™€ ļ„»ļ„µļ…‡ļ„› ļ„­ļ……ļ„® ļ„®ļ…†ļ…œ
ļ„øļ„µļ„ ļ„›ļ„µļ„® ļ„®ļ…‚ļ„¶ ļ„Ŗļ…‚ļ„›ļ„Ŗ ļ„øļ„­ļ„¬ļ…„ ļ„»ļ…‰ (ļ„®ļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„› ļ„®ļ…‹ļ„„ļ„ŗ ļ„®ļ…†ļ…œ ļ„»ļ„„ļ…‚ ļ„›ļ…‡) ļ„‘ļ„Ŗļ…‡ ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¢ļ…‹ļ„æļ„® ļ„®ļ…‚ļ„¶ ļ„“ļ…žļ„›
ļ„¹ļ„›ļ„Ŗļ…„ļ„¹ļ…‚ļ„¶ļ…„ ļ„ŗļ„³ļ…†ļ…ƒļ„»ļ„› ļ„­ļ……ļ„®ļ…„ ļ„±ļ„©ļ„¬ļ…„ ļ„»ļ…‰ - ļ„“ļ„» Ļ‡Ā² ļ„»ļ…‰ī„” ļ„ŗļ…œļ„ļ…„ļ„Ŗļ„›ļ…‚ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ…ƒļ„ļ„©ļ„Ŗļ…„ (ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„) 'ļ„Ŗļ…‡
ļ…ƒļ„®ļ„µļ„²ļ„µ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ļ„—, ļ…ƒļ„ŗļ…œļ„°ļ„®ļ…„ ļ„ŗļ„­ļ…‚ļ„µļ„®, ļ…ƒļ„Ŗļ„µļ„”ļ…„, ļ„¢ļ…‚ļ„ ļ„‘ļ„³ļ…„ļ„µ ļ„‘ļ„Ŗļ…‡ ļ„ŗļ…œļ„Ŗļ……ļ…ƒļ„¶ļ„Ŗ ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…„ ļ„»ļ…‰ī„” ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„¢ļ„øļ…ˆ ļ„“ļ…žļ„› ļ…ƒļ„ŗļ…œļ„°ļ„®ļ…„
ļ„›ļ„” ļ„²ļ…‚ļ„ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¢ļ…‹ļ„æ ļ„ŗļ„›ļ„¬ļ…„ ļ„»ļ…‰, ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„¢ļ…‚ļ„©ļ„›ļ…‚ļ„µļ…„ ļ„¬ļ…‡ ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„ŗļ„µļ…‹ļ„Ŗļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„“ļ…žļ„› ļ„‘ļ„µļ„«ļ„Æļ…†ļ„µļ„® ļ„³ļ…‚ļ„Æ ļ…ƒļ„øļ…žļ„ 
ļ„¢ļ…‹ļ„æļ„® ļ„¬ļ…„ ļ„’ļ…ƒļ„ļ„’ ļ…ƒļ„¬ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ…ƒļ„ŗļ…žļ„„
ļ„ŗļ…œļ„œļ…‡ļ„Æ ļ…ƒļ„øļ…žļ„ , ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ…ƒļ„ŗļ„µļ…€ ļ„“ļ…žļ„› ļ„°ļ…‚ļ„µļ„³ļ…†ļ„¶ļ…‡ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„»ļ…‰ī„” ļ„“ļ„» ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„±ļ„Ŗļ…‚, ļ„²ļ„„ļ„›ļ„©ļ…‚, ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„³ļ…†ļ…ƒļ„»ļ„› ļ„³ļ…‚ļ„Æ
ļ„¬ļ…„ ļ„›ļ„»ļ…‚ļ„©ļ…„ ļ„»ļ…‰ī„” ļ„øļ„µļ„ ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„’ļ„³ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¢ļ…‹ļ„æ ļ„›ļ…‡, ļ„“ļ„» ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„¬ļ…‡ ļ„ŗļ…‚ļ„µ ļ„®ļ…†ļ…œ ļ„»ļ…‚ļ„ŗļ„¶ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ„‘ļ„Ŗļ…‡
ļ„‘ļ…œļ„›ļ„æļ…‚ ļ…ƒļ„øļ…ƒļ„ļ„’ļ„®ļ…„ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ„‘ļ„Ŗļ…‡ ļ„Æļ…‰ļ„„ļ„µļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„© ļ„¬ļ…„ ļ„’ļ…ƒļ„ļ„’ ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„“ļ„ŗļ„¬ļ…‡
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„ļ……ļ„© - ļ„³ļ…žļ„­ļ„³ļ…‚ļ„®, ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®, ļ…ƒļ„Ŗļ„µļ„”ļ…‡ļ„Æļ„©, ļ„¢ļ…‹ļ„æļ„®, ļ„‘ļ„Ŗļ…‡ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„µļ„²ļ„µļ„Ŗļ…‚ - ļ„“ļ„ŗļ„®ļ…†ļ…œ
ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„› ļ„±ļ„»ļ……ļ„Æļ…žļ„œļ…„ ļ„‘ļ„Ŗļ…‡ ļ„¹ļ„›ļ„Ŗļ…„ļ„¹ļ…‚ļ„¶ļ…„ ļ„ŗļ…‚ļ„­ļ„® ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ„®ī„”
Ļ‡Ā² ļ„®ļ…†ļ…œ ļ„øļ„µļ„ ļ„²ļ„„ļ„›ļ„©ļ…‚ļ„ ļ„¬ļ…‡ ļ„¢ļ…‹ļ„æ ļ„øļ„¢ļ…Œ ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ„›ļ…‡ ļ„‘ļ„Ŗļ…‡ ļ„“ļ„ŗ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„øļ„¹ļ…‡ļ„¹ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ ļ„›ļ…‡, ļ„›ļ…‹ļ„” ļ„øļ…„ ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„®ļ…‚
ļ…ƒļ„ŗļ„µļ…€ ļ„‘ļ„ŗļ„¶-ļ„ŗļ…œļ„ŗļ…‚ļ„µ ļ„§ļ…‡ļ„„ļ…‚ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ…ƒļ„øļ…žļ„  ļ„¶ļ…‚ļ„ļ…† ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ ļ„±ļ„¶ļ…ƒļ„› ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„ŗļ…‹ļ„  ļ„¬ļ…„ ļ„‘ļ…œļ„Ŗļ„µļ…„ļ„ø
ļ„ŗļ……ļ…œļ„¬ļ„µļ„Ŗļ…‚ ļ„¬ļ…„ ļ„øļ…„ ļ„›ļ„¬ļ„µ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„ ļ…„-ļ„øļ„µļ„ ļ„øļ…œļ„§ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„“ļ…‚ļ„¬ ļ…ƒļ„¬ļ„øļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ ļ…ƒļ„› ļ„ŗļ…œļ…ƒļ„œļ„’ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„¬ļ……ļ„®ļ…„ļ„’ ļ…ƒļ„øļ…žļ„ , ļ„»ļ„°ļ„æļ…‚-ļ„¬ļ„°ļ„æļ…„ ļ„¬ļ…‚ ļ„øļ…„ ļ„“ļ…žļ„› ļ„Æļ…‰ļ„„ļ„µļ„® ļ„œļ…‹ļ„¢ļ…‡
ļ„¢ļ…‚ļ„© ļ„¬ļ…„ ļ„•ļ„§ļ…„ļ„› ļ…ƒļ„øļ…žļ„  ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„»ļ…„ ļ„ŗļ…‚ļ„­ļ„®ļ…‚ļ„ ļ„®ļ…‚ļ„¶, ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„”
4. ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„¬ļ…‡ ļ„„ļ…„-ļ„ŗļ„„ļ…‰ļ…ƒļ„„ļ„ŗļ…ƒļ„„ļ„› ļ„®ļ…†ļ…œ ļ„Æļ…ƒļ„µļ„² ļ…ƒļ„¹ļ„Ŗ ļ„›ļ„µļ…‹ ļ„‘ļ„Ŗļ…‡ ļ„“ļ„ŗļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„ļ……ļ„© ļ„Æļ…„ ļ„Æļ„Ŗ ļ„›ļ„µļ…‹ī„”
ļ„•ļ…žļ„Ŗļ„µ: ļ„“ļ…žļ„› ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„›ļ„¶ļ…‚ļ„ŗ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„“ļ…žļ„› ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…„ ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ī„” ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„’ļ„Æļ„©ļ…„
ļ„“ļ…†ļ„®ļ…„ļ„øļ„µļ…ƒļ„ŗļ„„ļ…„ ļ„¬ļ…‡ ļ„ŗļ…‚ļ„µļ…‡ ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„•ļ„ ļ…‚ļ„” ļ„¬ļ…‚ ļ„‘ļ…œļ„¬ļ…‚ļ„¾ļ…‚ ļ„¶ļ„ļ…‚ļ„•ļ„© ļ„¶ļ„” ļ…ƒļ„›ļ„»ļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„±ļ…‡ļ„¹ļ…žļ„›,
ļ„•ļ„» ļ„ŗļ…‚ļ…ƒļ„µļ„’ļ„ ļ„®ļ…†ļ…œ ļ„®ļ„»ļ…„
ļ„
ļ„³ļ…‚ļ„Æ ļ„ŗļ„›ļ„¬ļ…‡, ļ„“ļ„ŗ ļ„¶ļ„” ļ„•ļ„» ļ„“ļ…žļ„› ļ„”ļ…‹ļ„„ļ…‚ ļ…ƒļ„¢ļ„»ļ…‚ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„¶ļ…Šļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„»ļ……ļ„© ļ„ ļ……ļ„©ļ…ļ„Ŗļ…„ ļ„’ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰:
ļ„•ļ„» ļ…ƒļ„›ļ„øļ…ˆ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„® ļ…ƒļ„› ļ„›ļ…„ ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„¬ļ…‚ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„šļ„ŗļ„Ŗ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„²ļ„µļ…‹ļ„ŗļ…‡ļ„“ļ…‹ļ„ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„»ļ…‰,
ļ„œļ…‚ļ„ŗ ļ„›ļ„µļ„›ļ…‡ ļ„¢ļ„¬ļ…Œ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„‘ļ„©ļ„¢ļ…‚ļ„© ļ„»ļ…‰?
ļ„“ļ„» ļ…ƒļ„±ļ„¶ļ„›ļ……ļ„¶ ļ„•ļ„»ļ…„ ļ„ŗļ…ƒļ„«ļ„Ŗļ…„ ļ„»ļ…‰ ļ…ƒļ„¢ļ„ŗļ„®ļ…‡ ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„¬ļ…‡ ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„®ļ…†ļ…œ ļ„¢ļ„®ļ„³ ļ…ƒļ„¬ļ…žļ„Ŗļ…‚, ļ…ƒļ„¢ļ„ŗļ„®ļ…†ļ…œ ļ…ƒļ„øļ„¶ļ…„ļ„‘ļ„³ ļ„ŗļ…„ļ„¶ļ…„ ļ„ļ…‹ļ„ŗļ…‡ļ„„
(ļ…ƒļ„¢ļ„ŗļ„®ļ…‡ "ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„" ļ„¬ļ…‡ ļ„›ļ„¶ļ„³ļ…„ ļ„®ļ…‚ļ„³ ļ„»ļ…‡ļ„¦ ļ…ƒļ„¶ļ…ƒļ„œļ„’) ļ„¬ļ……ļ„’ļ„µļ…‚ ļ„Æļ…‡ļ„¹ ļ„›ļ…„ļ„Ŗļ…‚ ļ…ƒļ„ļ„’ ļ„ŗļ…„ī„” ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„Ŗ
ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„ŗļ„² ļ„Ŗļ…Œ ļ„¹ļ„›ļ„Ŗļ…„ļ„¹ļ…‚ļ„¶ļ…„ ļ„šļ„¾ļ…‚ļ„µļ…‚ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„“ļ…žļ„› ļ„±ļ„© ļ„ļ„—, ļ„œļ…‚ļ„ŗ ļ„›ļ„µļ„›ļ…‡ ļ„¢ļ„¬ļ…Œ ļ„”ļ…‹ļ„„ļ…‡ ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ ļ„®ļ…‚ļ„¶
ļ„®ļ…ƒļ„¢ļ…žļ„¦ļ„©ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„’ļ„™ ļ„“ļ„ŗ ļ„ŗļ…œļ„›ļ„¶ļ„Æ ļ„®ļ…†ļ…œ ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶ ļ„Æļ…„ļ„ļ„„ ļ„›ļ„µļ…„ļ„—: ļ„Æļ…ƒļ„»ļ„¶ļ…‚ļ„ ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„®ļ…†ļ…œ ļ„Æļ…ƒļ„µļ„²ļ…‚ļ…ƒļ„¹ļ„Ŗ ļ„›ļ„µļ„›ļ…‡, ļ…ƒļ„°ļ„µ ļ„“ļ„ŗļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ
ļ„ļ……ļ„©ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ„µļ„›ļ…‡, ļ„‘ļ„Ŗļ…‡ ļ„‘ļ…œļ„Ŗ ļ…ƒļ„øļ…žļ„  ļ„“ļ„» ļ„ŗļ„³ļ„£ ļ„›ļ…‡ ļ…ƒļ„› ļ„“ļ„» ļ„“ļ…œļ„®ļ…‚ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ…ƒļ„›ļ„•
ļ„
ļ„»ļ…‰ī„”
󷊆󷊇ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„¬ļ…‡ ļ„„ļ…„ļ„ŗļ„„ļ…‰ļ…ƒļ„„ļ„ŗļ…ƒļ„„ļ„› ļ„¬ļ…„ ļ„Æļ…ƒļ„µļ„² ļ„¹
ļ„³ļ…œļ„® ļ„¶ļ„™ ļ„ŗļ…‚ļ„§ļ…‡ ļ„›ļ…‹ļ„¶ ļ„“ļ…žļ„› ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„®ļ„³ļ…†ļ„®ļ…‚ X1,X2,ā€¦,Xn ļ„»ļ…‰ ļ„¢ļ…‹ ļ„“ļ…žļ„› ļ„’ļ„³ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„Ŗļ…Œ ļ…ƒļ„¶ļ„’ ļ…ƒļ„ļ„’ ļ„»ļ…‰ ļ…ƒļ„¢ļ„ŗļ„¬ļ…‚
ļ„šļ„ŗļ„Ŗ Ī¼\mu ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ Ļƒ2 ļ„»ļ…‰ī„”
ā€¢ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± ļ„“ļ„» ļ„»ļ…‰:
ā€¢ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„“ļ„» ļ„»ļ…‰:
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„»ļ……ļ„©, ļ„¢ļ…‡ļ„›ļ„µ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® Ļƒ2\sigma^2 ļ„¢ļ…‚ļ…ƒļ„©ļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚, ļ„Ŗļ…‚ļ„ ļ„‘ļ„ŗļ…„
ļ„
zstatistic ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‚ļ„:
ļ„¢ļ…‹ ļ…ƒļ„› ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„’ļ„³ ļ„øļ…œļ„§ ļ„¬ļ…„ ļ„Æļ…‚ļ„¶ļ„©ļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„Æļ„µ ļ„‘ļ„ŗļ„¶ ļ…ƒļ„¾ļ…œļ„¬ļ„ļ…„ ļ…ƒļ„øļ…žļ„ , Ļƒ2 ļ„’ļ„³ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„‘ļ„©ļ„¢ļ…‚ļ„© ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„“ļ„ŗ ļ„¶ļ„” ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„ŗļ…Šļ„Æļ„¶ ļ„øļ…‡ļ„µļ…„ļ„˜ļ„ļ„ŗ S2S^2
ļ„®ļ…‚ļ„¶ ļ„±ļ„¬ļ„¶ļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„” ļ„“ļ„» ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„¬ļ…‚ tstatistic ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰:
ļ„“ļ„» ļ„‘ļ…œļ„›ļ„æļ…‚ (n ā€“ 1) ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ ļ„“ļ…žļ„› tļ„øļ…œļ„§ ļ„¬ļ…„ ļ„Æļ…‚ļ„¶ļ„©ļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
󷈷ó·ˆø󷈹ó·ˆŗ󷈻󷈼ļ„ŗļ„„ļ…‰ļ…ƒļ„„ļ„ŗļ…ƒļ„„ļ„›ļ„ŗ ļ„¬ļ…„ ļ„¶ļ…‹ļ„æ ļ…ƒļ„›ļ„•
ļ„
ļ„»ļ…‰?
ā€¢ ļ„¢ļ„¬ļ…Œ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„¬ļ…‚ ļ„’ļ„›ļ…‚ļ„µ ļ„øļ…žļ„§ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„øļ…‡ļ„µļ…„ļ„˜ļ„ļ„ŗ S2 Ļƒ2 ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„ ļ…œļ„ļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰,
ļ„‘ļ„Ŗļ…‡ ztest ļ„øļ„­ļ…„ļ„’ ļ„›ļ…œļ„³ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„Æļ„µ ļ„¢ļ„¬ļ…Œ ļ„ŗļ…Šļ„Æļ„¶ ļ„¬ļ…‚ ļ„’ļ„›ļ…‚ļ„µ ļ„”ļ…‹ļ„„ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ Ļƒ\sigma ļ„®ļ…†ļ…œ SS ļ„®ļ…‚ļ„¶ ļ„±ļ„¬ļ„¶ļ„© ļ„®ļ…‚ļ„¶ ļ„øļ…‚ļ„­ļ…†
ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗļ…‚ ļ„’ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„ŗ ļ„øļ…‚ļ„­ļ…† ļ„‘ļ…ƒļ„®ļ„¹ļ…ƒļ„ ļ„Ŗļ„Ŗļ…‚ ļ„¶ļ„” ļ„øļ…œļ„§ ļ…ƒļ„¾ļ…œļ„³ļ…‡ļ„øļ…‚ļ„µ ļ„»ļ…‰, ļ„¢ļ…‹ ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„”ļ…‹ļ„„ļ…‡ ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ ļ„¶ļ„” ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„²ļ„µļ…‹ļ„ŗļ…‡ļ„“ļ…‹ļ„
ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„“ļ„ŗ ļ„¶ļ„”, tstatistic ļ„“ļ…žļ„› ļ„ŗļ…‚ļ„øļ„­ļ…‚ļ„® ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„ŗļ„øļ…„ļ„›ļ…‚ļ„µ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰: "ļ„³ļ…‰ļ„®ļ…†ļ…œ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…‚
ļ„Æļ„Ŗļ…‚ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‰, ļ„Æļ„µ ļ„³ļ…Š ļ„’ļ„Æļ„©ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ…‚ļ„ļ„ļ…‚ ļ„‘ļ„Ŗļ…‡ ļ„‘ļ…ƒļ„®ļ„¹ļ…ƒļ„ ļ„Ŗļ„Ŗļ…‚ ļ„¶ļ„” ļ„ŗļ„³ļ…‚ļ„“ļ…‹ļ„¢ļ„® ļ„›ļ„µļ…‚ļ„ļ„ļ…‚ī„”"
󽀼󽀽󽁀󽁁󽀾󽁂ó½€æ󽁃ļ„øļ…œļ„§ ļ„¬ļ…„ ļ„•ļ„Ŗļ„Æļ„Ŗļ…„
tstatistic ļ„¬ļ…‡ ļ„ļ……ļ„©ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„© ļ„¶ļ„”, ļ„’ļ„™ ļ„¬ļ…‡ļ„œļ…„ļ„— ļ…ƒļ„› ļ„“ļ„» ļ…ƒļ„›ļ„øļ…ˆ ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
1. ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ…ƒļ„ŗļ„­ļ…‚ļ„ļ„Ŗ ļ„Ŗļ…Œ, ļ„‘ļ„ŗļ…„
ļ„
ļ„¢ļ…‚ļ„©ļ„¬ļ…‡ ļ„»ļ…‚ļ„ ļ…ƒļ„›:
2. ļ„®ļ…‚ļ„¶ ļ„»ļ…„, ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ…ƒļ„ ļ„ŗļ„›ļ„øļ…‡ļ„‘ļ„µ ļ„øļ…œļ„§ ļ„®ļ…‚ļ„¶ ļ„ŗļ…œļ„±ļ…œļ…ƒļ„­ļ„Ŗ ļ„»ļ…‰:
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
3. ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„ļ…žļ„¶ ļ„“ļ„» ļ„»ļ…‰ ļ…ƒļ„› Z ļ„‘ļ„Ŗļ…‡ S2 ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„»ļ„®ī„”
4. ļ„“ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ…ƒļ„³ļ„¶ļ…‚ ļ„›ļ…‡, tstatistic ļ„®ļ…†ļ…œ ļ„“ļ„ŗ ļ„Ŗļ„µļ…§ļ…‚ļ„ ļ…ƒļ„¶ļ…ƒļ„œļ„’ ļ„¢ļ…‚ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰:
ļ„“ļ„» ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ (n ā€“ 1) ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„®ļ…‚ļ„¶ tļ„øļ…œļ„§ ļ„®ļ…†ļ…œ ļ„Æļ…ƒļ„µļ„²ļ…‚ļ…ƒļ„¹ļ„Ŗ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
󷇮󷇭ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„¬ļ…„ ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„ļ……ļ„©
ļ„»ļ……ļ„© ļ„’ļ„™ tstatistic ļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„ļ……ļ„©ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„“ļ„ŗļ„¬ļ…„ ļ„øļ…œļ„§ ļ„¬ļ…„ ļ„Æļ„æļ„ ļ…‹ļ„¶ ļ„›ļ„µļ…„ļ„—ī„”
1. ļ„ŗļ„³ļ„µļ…†ļ„Æļ„Ŗ
ā€¢ tļ„øļ…œļ„§ ļ„¶ļ„ļ„²ļ„ ļ„¾ļ…„ļ„µļ…‹ ļ„ŗļ„³ļ…ƒļ„³ļ„Ŗļ…„ ļ„»ļ…‰, ļ…ƒļ„±ļ„¶ļ„›ļ……ļ„¶ ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„’ļ„³ ļ„øļ…œļ„§ ļ„øļ…‚ļ„ļ„ī„”
ā€¢ ļ„“ļ„ŗļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± ļ„»ļ…‰ ļ…ƒļ„› ļ„ŗļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„› ļ„‘ļ„Ŗļ…‡ ļ„®ļ„›ļ…‚ļ„µļ…‚ļ„Ŗļ„³ļ„› ļ„²ļ„„ļ„›ļ„©ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„»ļ…‰ī„”
2. ļ„šļ„ŗļ„Ŗ
ā€¢ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ v>1 ļ„¶ļ„”, tļ„øļ…œļ„§ ļ„¬ļ…‚ ļ„³ļ…žļ„­ļ„³ļ…‚ļ„® 0 ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„» ļ„ŗļ„³ļ„£ ļ„’ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› tstatistic ļ„ŗļ…žļ„ ļ…‡ ļ„šļ„ŗļ„Ŗ Ī¼\mu ļ„¬ļ…‡ ļ„¬ļ……ļ„’ļ„¶ļ…‡ ļ„›ļ…ˆļ„¬ļ…ƒļ„µļ„Ŗ ļ„»ļ…‰ī„”
3. ļ…ƒļ„²ļ…œļ„®ļ„Ŗ
ā€¢ v>2 ļ„¶ļ„”, tļ„øļ…œļ„§ ļ„¬ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„“ļ„» ļ„»ļ…‰:
ā€¢ ļ…ƒļ„­ļ„’ļ„® ļ…ƒļ„¬ļ„™ ļ…ƒļ„› ļ„“ļ„» ļ„øļ…‡ļ„µļ…„ļ„˜ļ„ļ„ŗ 1 ļ„Ŗļ…Œ ļ„øļ…žļ„§ļ…‚ ļ„»ļ…‰, ļ„²ļ…‚ļ„ø tdistribution ļ„’ļ„³ ļ„øļ…œļ„§ ļ„®ļ…‚ļ„¶ļ…Œ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ„°ļ…‰ļ…ƒļ„¶ļ„’
ļ„»ļ…‹ļ„“ļ„’ ļ„»ļ…‰ī„”
ā€¢ vā†’āˆž ļ„¬ļ…‡ ļ„µļ…†ļ„Æ ļ…ƒļ„øļ…žļ„ , ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ 1 ļ„¬ļ…‡ ļ„®ļ…‡ļ„æļ…‡ ļ„Æļ„»ļ……ļ…œļ„ ļ„¬ļ…„ ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ tļ„øļ…œļ„§ ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„’ļ„³ ļ„øļ…œļ„§ ļ…ƒļ„øļ…žļ„  ļ„›ļ„®ļ„øļ„µļ„¢
ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
4. ļ„›ļ……ļ„µļ„„ļ…‹ļ…ƒļ„ŗļ„ŗ (ļ„Æļ…†ļ„” ļ„)
ā€¢ ļ„„ļ…„-ļ…ƒļ„§ļ„ŗļ„„ļ…„ļ…„ļ…ƒļ„±ļ„–ļ„¹ļ„® ļ…ƒļ„øļ…žļ„  ļ„’ļ„³ ļ„øļ…œļ„§ ļ„®ļ…‚ļ„¶ļ…Œ ļ„²ļ…‚ļ„µļ…„ ļ„Æļ…†ļ„”ļ…‚ļ„ ļ„»ļ……ļ…œļ„¬ļ…„ļ„’ļ„ ļ„»ļ„®ī„”
ā€¢ ļ„“ļ„ŗļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± ļ„»ļ…‰ ļ…ƒļ„› ļ„‘ļ…ƒļ„Ŗļ„‘ļ…œļ„Ŗ ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„» ļ…ƒļ„øļ„¹ļ…‡ļ„¹ļ„Ŗļ…‚ ļ„„ļ…‰ļ„ŗļ„„ ļ„®ļ…†ļ…œ ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„ŗļ…‚ļ„øļ„­ļ…‚ļ„® ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰, ļ„œļ…‚ļ„ŗ ļ„›ļ„µļ„›ļ…‡ ļ„”ļ…‹ļ„„ļ…‡ ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
5. ļ„’ļ„¾ ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ (df)
ā€¢ tļ„øļ…œļ„§ ļ„¬ļ…„ ļ„¹ļ„›ļ„¶ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ v=nāˆ’1 ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„µļ„²ļ„µ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„”ļ…‹ļ„„ļ…‡ df ļ„®ļ…‚ļ„¶, ļ„øļ…œļ„§ ļ„ ļ…‚ļ„Æļ„¶ļ…†ļ„ŗ ļ„‘ļ„Ŗļ…‡ ļ„ ļ…ļ„æļ…„ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ…ƒļ„¢ļ„øļ…ˆ-ļ…ƒļ„¢ļ„øļ…ˆ df ļ„øļ„­ļ„¬ļ…‚ ļ„»ļ…‰, ļ„“ļ„» ļ„’ļ„³ ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„®ļ…‡ļ„æļ…‡ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
6. ļ„Æļ…‰ļ„³ ļ„®ļ…‡ ļ„Ŗļ…Œ ļ„’ļ„¾ ļ„¬ļ…„
ā€¢ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„ŗļ„›ļ…‡ļ„¶-ļ„³ļ……ļ„›ļ„Ŗ ļ„»ļ…‰: ļ„“ļ„» ļ„³ļ…‚ļ„Æ ļ„¬ļ…„ļ„’ļ„ ļ„“ļ„›ļ…‚ļ„”ļ„’ļ„ 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„µļ„²ļ„µ ļ„®ļ„»ļ…„
ļ„
ļ„›ļ„µļ„¬ļ…‚ī„”
ā€¢ ļ„²ļ…‚ļ„øļ…ˆ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„•ļ„ ļ…‚ļ„” ļ„®ļ…†ļ…œ ļ„ŗļ…Šļ„„ļ…„ļ„³ļ…„ļ„„ļ„µ ļ…ƒļ„øļ…žļ„  ļ„³ļ…‚ļ„Æļ„¬ļ…‡ ļ„»ļ…‹ ļ„¢ļ…‚ļ„ ļ„“ļ…œļ„  ļ…ƒļ„øļ…žļ„ , ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„•ļ„»ļ…„ ļ„µļ…ƒļ„»ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„”
7. ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® ļ„¢ ļ„ļ„  ļ…ƒļ„øļ…žļ„  ļ„øļ„µļ„Ŗļ…Œ
ā€¢ ļ„¢ļ„¬ļ…Œ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„‘ļ„©ļ„¢ļ…‚ļ„© ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ„Ŗļ…‚ļ„ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„¬ļ…‡ ļ„ŗļ…‚ļ„­ļ„®ļ…‚ļ„ ļ„±ļ…‚ļ„µļ…‡ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ„¶ļ„”
tstatistic ļ…ƒļ„øļ„’ļ„Æļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„øļ„µļ…ƒļ„Ŗļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®ļ…‚ļ„: ļ„“ļ…žļ„› ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„„ļ…„ļ„„ļ…‰ļ„ŗļ„„, ļ„¬ļ…‹ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„„ļ…„ļ„„ļ…‰ļ„ŗļ„„, ļ„Æļ…‡ļ„‘ļ„µļ„§ ļ„„ļ…„ļ„„ļ…‰ļ„ŗļ„„ī„”
ó¼©ŗ󼩻ļ„›ļ„» ļ„©ļ…„ ļ„ŗļ„³ ļ„®ļ„Ŗ
tdistribution ļ„®ļ…†ļ…œ ļ„’ļ„³ ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„“ļ…žļ„› ļ„ŗļ…‚ļ„øļ„­ļ…‚ļ„® ļ„”ļ…‹ļ„„ļ…‡ ļ„²ļ„µļ…‚ ļ„øļ„¢ļ…Œ ļ„ŗļ…‹ļ„ ļ…‹ī„” ļ„’ļ„³ ļ„øļ…œļ„§ ļ„’ļ„Ŗļ„³ļ…ƒļ„øļ„¹ļ„øļ…‚ļ„ŗļ…„ ļ„‘ļ„Ŗļ…‡ ļ„Æļ„Ŗļ„¶ļ…„ ļ„»ļ…‰,
ļ„“ļ„» ļ„³ļ…œļ„® ļ„›ļ…‡ ļ…ƒļ„› ļ„‘ļ„ŗļ…„
ļ„
ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„±ļ…‚ļ„µļ…‡ ļ„ŗļ„² ļ„›ļ……ļ„£ ļ„¢ļ…‚ļ„©ļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„” ļ„¬ļ…†ļ„¢ļ…‡ ļ„Æļ…‚ļ„ŗļ…‡, tdistribution ļ„›ļ…ƒļ„»ļ…œļ„¬ļ…‚ ļ„»ļ…‰: "ļ„•ļ„§ļ…„ļ„›
ļ„›ļ„µļ…‹, ļ„‘ļ„ŗļ…„
ļ„
ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ…ƒļ„±ļ„¶ļ„›ļ……ļ„¶ ļ„®ļ„»ļ…„
ļ„
ļ„¢ļ…‚ļ„©ļ„¬ļ…‡, ļ„“ļ„ŗ ļ„¶ļ„” ļ„’ļ„™ ļ„»ļ…‹ļ„µ ļ„‘ļ…ƒļ„®ļ„¹ļ…ƒļ„ ļ„Ŗļ„Ŗļ…‚ ļ„¬ļ…„ ļ„’ļ…ƒļ„ļ„’ ļ„¬ļ…‡ļ„”ļ„—ī„”" ļ„“ļ„ŗ
ļ„¶ļ„” ļ„“ļ„ŗ ļ„¬ļ…„ļ„’ļ„ ļ„Æļ…†ļ„”ļ…‚ļ„ ļ„²ļ…‚ļ„µļ…„ļ„’ļ„ ļ„»ļ„® - ļ„“ļ„» ļ„ļ„¶ļ„Ŗļ…„ ļ„¶ļ„” ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„¢ļ„ļ…§ļ…‚ ļ…ƒļ„¬ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ…ƒļ„¢ļ„øļ…ˆ-ļ…ƒļ„¢ļ„øļ…ˆ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¬ļ…‚ ļ„’ļ„›ļ…‚ļ„µ ļ„øļ„­ļ„¬ļ…‚ ļ„»ļ…‰, ļ„”ļ…‹ļ„„ļ…‚ ļ„²ļ„µļ…‚ ļ„’ļ„Ŗļ„³ļ…ƒļ„øļ„¹ļ„øļ…‚ļ„ŗ ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ„‘ļ„Ŗļ…‡ ļ„‘ļ…œļ„Ŗ ļ…ƒļ„øļ…žļ„  ļ„’ļ„³ ļ„øļ…œļ„§
ļ„øļ„µļ„ļ…‚ ļ…ƒļ„¬ļ„œļ…‚ļ„” ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
󹶓󹶔󹶕󹶖󹶗󹶘ļ„‘ļ…ƒļ„²ļ„’ļ„ŗ ļ…ƒļ„øļ…žļ„  ļ„³ļ„»ļ…žļ„Ŗļ„ø
ā€¢ ļ„”ļ…‹ļ„„ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡:ļ„”ļ…‹ļ„„ļ…‡ ļ„§ļ…‡ļ„„ļ…‚ļ„ŗļ…‰ļ„„ļ…‚ļ„ ļ„®ļ…‚ļ„¶ ļ„›ļ…œļ„³ ļ„›ļ„µļ„¬ļ…‡ ļ„ŗļ„³ļ…ˆ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„¾ļ„µļ…†ļ„µļ…„ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰, ļ„¢ļ…‹ ļ…ƒļ„› ļ„³ļ„®ļ…‹ļ…ƒļ„øļ…ƒļ„ļ„’ļ„®, ļ„¬ļ„øļ…‚ļ„”
ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„³ļ…‚ļ…ƒļ„¢ļ„› ļ…ƒļ„øļ…ƒļ„ļ„’ļ„® ļ…ƒļ„øļ…žļ„  ļ„’ļ„³ ļ„»ļ…‰ī„”
ā€¢ ļ„‘ļ„©ļ„¢ ļ„© ļ…ƒļ„²ļ…œļ„®ļ„Ŗ :ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„±ļ„»ļ……ļ„Ŗ ļ„žļ…žļ„„ ļ„¢ļ…‚ļ„©ļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰, ļ„“ļ„ŗ ļ„¶ļ„” ttest ztest ļ„®ļ…‚ļ„¶ļ…Œ
ļ„øļ„­ļ…‡ļ„µļ…‡ ļ…ƒļ„øļ„»ļ…‚ļ„µļ„› ļ„»ļ…‰ī„”
ā€¢ ļ„³ļ„¾ļ„±ļ…†ļ„Ŗļ…„:ļ„²ļ…‚ļ„øļ…ˆ ļ„§ļ…‡ļ„„ļ…‚ ļ„Æļ…†ļ„µļ…„ ļ„Ŗļ„µļ…§ļ…‚ļ„ ļ„’ļ„³ ļ„®ļ…‚ ļ„»ļ…‹ļ„øļ…‡, ļ„„ļ…‰ļ„ŗļ„„ ļ„‘ļ„›ļ„ŗļ„µ ļ„øļ„­ļ…„ļ„’ ļ„›ļ…œļ„³ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰, ļ„œļ…‚ļ„ŗ ļ„›ļ„µļ„›ļ…‡
ļ„¬ļ„µļ…ƒļ„³ļ„’ļ„®ļ…‡ ļ„ŗļ…Šļ„Æļ„¶ ļ„’ļ„›ļ…‚ļ„µļ…‚ļ„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ī„”
󹶜󹶟󹶝󹶞󹶠󹶔󹶢󹶣󹶤󹶄󹶦󹶧ļ„³ļ……ļ…žļ„œ ļ„¢ ļ„“ļ„¬ ļ„¬ ļ„ ļ„¬ ļ„ŗ ļ„µ
1. ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„®ļ…†ļ…œ ļ„“ļ„ŗ ļ„Ŗļ„µļ…§ļ…‚ļ„ ļ„Æļ…ƒļ„µļ„²ļ…‚ļ…ƒļ„¹ļ„Ŗ ļ„›ļ…„ļ„Ŗļ…‚ ļ…ƒļ„ļ„’ ļ„»ļ…‰:
ļ…ƒļ„¢ļ…žļ„«ļ…‡ ļ„“ļ„» nāˆ’1n-1 ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ ļ„“ļ…žļ„› tļ„øļ…œļ„§ ļ„¬ļ…„ ļ„Æļ…‚ļ„¶ļ„©ļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
2. ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„ļ……ļ„©:
o ļ…ƒļ„ŗļ…€ļ„µ ļ„¬ļ…‡ ļ„±ļ…‚ļ„µļ…‡ ļ„ŗļ„³ļ…ƒļ„³ļ„Ŗļ…„ī„”
o ļ„šļ„ŗļ„Ŗ = 0 (df > 1 ļ„¶ļ„”)ī™€
o ļ„øļ…‡ļ„µļ…„ļ„‘ļ…œļ„ŗ = v/(vāˆ’2)v/(v-2) (df > 2 ļ„¶ļ„”)ī™€
o ļ„’ļ„³ ļ„øļ…œļ„§ ļ„®ļ…‚ļ„¶ļ…Œ ļ„²ļ…‚ļ„µļ…„ ļ„Æļ…†ļ„”ļ…‚ļ„ī„”
o ļ„’ļ„›ļ…‚ļ„µ ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„µļ„²ļ„µ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
o df ā†’ āˆž ļ„¬ļ…‡ ļ„µļ…†ļ„Æ ļ…ƒļ„øļ…žļ„  ļ„’ļ„³ ļ„øļ…œļ„§ ļ„Ŗļ…žļ„› ļ„Æļ„»ļ……ļ…œļ„ ļ„¬ļ…‚ ļ„»ļ…‰ī„”
󷘹󷘓󷘵󷘶󷘷ó·˜øļ…ƒļ„ŗļ…žļ„„
ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„¬ļ…‚ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„Ŗ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ„¬ļ…‡ ļ„‘ļ„­ļ…‚ļ„µļ…‚ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„“ļ…žļ„› ļ„»ļ…‰ī„” ļ„“ļ„» ļ„“ļ…žļ„› ļ…ƒļ„øļ„»ļ…‚ļ„µļ„› ļ„¶ļ…‹ļ„æ ļ„Ŗļ…Œ ļ„Æļ…‰ļ„¬ļ…‚
ļ„»ļ…‹ļ„“ļ„’ ļ„ŗļ…„: ļ„¢ļ„¬ļ…Œ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„”ļ…‹ļ„„ļ…‚ ļ„»ļ…‹ļ„øļ…‡ ļ„‘ļ„Ŗļ…‡ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„‘ļ„©ļ„¢ļ…‚ļ„© ļ„»ļ…‹ļ„øļ…‡ ļ„Ŗļ…‚ļ„ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„±ļ…‚ļ„µļ…‡ ļ„²ļ„µļ…‹ļ„ŗļ…‡ļ„“ļ…‹ļ„ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„® ļ…ƒļ„›ļ„øļ…ˆ
ļ„¶ļ„ļ…‚ļ„— ļ„¢ļ…‚ļ„©ī„”
ļ„“ļ„ŗ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„øļ„¹ļ…‡ļ„¹ļ„Ŗļ…‚ļ„øļ…‚ļ„ā€”ļ„ŗļ„³ļ„µļ…†ļ„Æļ„Ŗļ…‚, ļ„²ļ…‚ļ„µļ…„ ļ„Æļ…†ļ„”ļ…‚ļ„, ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„µļ„²ļ„µļ„Ŗļ…‚, ļ„‘ļ„Ŗļ…‡ ļ„’ļ„³ ļ„øļ…œļ„§
ļ„¶ļ„” ļ„›ļ„®ļ„øļ„µļ„¢ļ…Šļ„ŗā€”ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„ŗļ…‚ļ„øļ„­ļ…‚ļ„® ļ„‘ļ„Ŗļ…‡ ļ„¹ļ„›ļ„Ŗļ…„ļ„¹ļ…‚ļ„¶ļ…„ ļ„¬ļ…‹ļ„øļ…ˆ ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…„ļ„’ļ„ ļ„»ļ„®ī„” ļ„“ļ„» ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„“ļ…‚ļ„¬ ļ…ƒļ„¬ļ„øļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰
ļ…ƒļ„› ļ„‘ļ…œļ„›ļ„æļ…‡ ļ…ƒļ„ŗļ„µļ…€ ļ„°ļ…‚ļ„µļ„³ļ…†ļ…ƒļ„¶ļ„’ļ„ ļ„±ļ…‚ļ„µļ…‡ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ„®, ļ„ŗļ„ļ…Œ ļ…ƒļ„®ļ„³ļ„µļ„Ŗļ…‚ ļ„±ļ…‚ļ„µļ…‡ ļ„»ļ„®: ļ„‘ļ…ƒļ„®ļ„¹ļ…ƒļ„ ļ„Ŗļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ„ŗļ„øļ…„ļ„›ļ…‚ļ„µ ļ„›ļ„µļ„®ļ…‚
ļ„‘ļ„Ŗļ…‡ ļ„“ļ„ŗļ„¬ļ…‡ ļ„¶ļ„” ļ„ŗļ„³ļ…‚ļ„“ļ…‹ļ„¢ļ„® ļ„›ļ„µļ„®ļ…‚ī„”
ļ„“ļ„ŗ ļ„¶ļ„”, ļ„‘ļ„ļ„¶ļ…„ ļ„øļ…‚ļ„µ ļ„¢ļ„¬ļ…Œ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„øļ„­ļ…„ļ„’ ļ„®ļ„Ŗļ…„ļ„¢ļ…‚ ļ„¬ļ…‡ļ„œļ…‹ļ„ļ…‡, ļ„Ŗļ…‚ļ„ ļ„ļ…‹ļ„ŗļ…‡ļ„„, "ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„" ļ„¬ļ…„ ļ„›ļ„»ļ…‚ļ„©ļ…„ ļ„“ļ…‚ļ„¬
ļ„µļ…žļ„œļ…‹, ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„›ļ„øļ…ˆ ļ„•ļ„ŗļ„¬ļ…‚ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„¬ļ……ļ„®ļ…„ļ„’ ļ„²ļ„µ ļ„¬ļ…‡ ļ„œļ…‹ļ„¢ļ„›ļ„µļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¶ļ„” ļ„“ļ…žļ„› ļ„²ļ„µļ…‹ļ„ŗļ…‡ļ„“ļ…‹ļ„ ļ„ŗļ…‚ļ„«ļ…„ ļ„±ļ„© ļ…ƒļ„ļ„’ī„”
ļ„² ļ„-ļ„ŗļ…„
5. (ļ…”) 500 ļ…ƒļ„øļ„‘ļ„›ļ„Ŗļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ…ƒļ„øļ…žļ„ , 280 ļ„ ļ…ļ„¶ ļ„œ ļ„© ļ„ø ļ„¶ļ…‡ ļ„Æ ļ„— ļ„ļ„— ļ„»ļ„® ļ„‘ļ„Ŗļ…‡ ļ„± ļ„›ļ…„ ļ„›ļ„©ļ„› ļ„œ ļ„©
ļ„ø ļ„¶ļ…‡ ļ„»ļ„®ī„” ļ„›ļ…„ ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ„» ļ„³ļ…œļ„® ļ„ŗļ„›ļ„¬ļ…‡ ļ„» ļ„ ļ…ƒļ„› ļ„¬ļ…‹ļ„øļ…ˆ ļ„ ļ…„ļ„¾ ļ„ ļ„±ļ„µ ļ„±ļ„µ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ„®?
(ļ„‘) Z ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„•ļ„Æļ„“ļ…‹ļ„ ļ„ ļ„± ļ„µļ…‡ ļ„ ļ„µļ„  ļ„›ļ„µļ…‹ī„”
ļ„•ļ…žļ„Ŗļ„µ:ļ„“ļ…žļ„› ļ…ƒļ„Æļ…œļ„§ ļ„¬ļ…‡ ļ„ŗļ„µļ„øļ…‡ļ„œļ„© ļ„¬ļ…„ ļ„›ļ„» ļ„©ļ…„ ļ„µ ļ„»ļ…„
ļ„
ļ„ ļ…ļ„¶ ļ„ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„¬ļ…„ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ļ…„ ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„©
ļ„ļ…„ļ…‡ļ„®ļ…ƒļ„øļ„¶ ļ„®ļ…‚ļ„³ļ„› ļ„“ļ…žļ„› ļ„”ļ…‹ļ„„ļ…‡ ļ…ƒļ„¢ļ„»ļ…‡ ļ„›ļ„ŗļ„±ļ…‡ ļ„¬ļ…„ ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹, ļ…ƒļ„¢ļ…žļ„«ļ…‡ ļ„¶ļ…‹ļ„› ļ„ŗļ…‚ļ„¬ļ…‚ ļ„¢ļ…„ļ„øļ„® ļ…ƒļ„¢ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ„®, ļ„‘ļ„Ŗļ…‡ ļ„²ļ…‹ļ„¢ļ„® ļ„ ļ…ļ„¶ļ…‚ļ„
ļ„¢ļ…‚ļ„ ļ„›ļ„©ļ„› ļ„¬ļ…‡ ļ„’ļ„¶ļ…‡-ļ„¬ļ……ļ„’ļ„¶ļ…‡ ļ„žļ……ļ…œļ„³ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„›ļ……ļ„£ ļ…ƒļ„®ļ„øļ…‚ļ„ŗļ…„ ļ„ŗļ„±ļ„¾ļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ ļ„ļ„µļ„³ ļ„ ļ…ļ„¶ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„²ļ……ļ…œļ„¶ļ„® ļ„¬ļ…‚ ļ„’ļ„®ļ…œ ļ„¬
ļ„³ļ…‚ļ„©ļ„¬ļ…‡ ļ„»ļ„®, ļ„¢ļ„¬ļ…Œ ļ…ƒļ„› ļ„›ļ……ļ„£ ļ„’ļ„Æļ„©ļ…„ ļ„›ļ„µļ…„ ļ„®ļ…‚ļ„¶ ļ„ŗļ……ļ„®ļ…ƒļ„»ļ„µļ…„ ļ„›ļ„©ļ„› ļ„¬ļ…„ļ„’ļ„ ļ„µļ…‹ļ„„ļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„ŗļ„»ļ……ļ…œ ļ„œļ…‚ļ„ļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„“ļ…žļ„› ļ…ƒļ„¬ļ„®,
ļ„®ļ„ļ„µ ļ„›ļ…Žļ„ŗļ„¶ ļ„“ļ„» ļ„Æļ„Ŗļ…‚ ļ„¶ļ„ļ…‚ļ„•ļ„© ļ„¬ļ…‚ ļ„°ļ…‰ļ„ŗļ„¶ļ…‚ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ ļ…ƒļ„› ļ…ƒļ„›ļ„»ļ„æļ…‚ ļ„³ļ……ļ…žļ„œ ļ„²ļ…‹ļ„¢ļ„® ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ…‰ - ļ„ ļ…ļ„¶ ļ„¢ļ…‚ļ„ ļ„›ļ„©ļ„›
- ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„•ļ„» ļ„‘ļ„ļ„¶ļ…‡ ļ„ŗļ…„ļ„¾ļ„® ļ„¶ļ„” ļ„‘ļ„®ļ…‚ļ„¢ ļ„ŗļ„Æļ„¶ļ…‚ļ„” ļ„¬ļ…„ ļ„“ļ…‹ļ„¢ļ„®ļ…‚ ļ„±ļ„©ļ…‚ļ„•ļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„“ļ…žļ„› ļ„ŗļ„Æļ„¹ļ„„ ļ„Ŗļ„ŗļ„øļ…„ļ„µ ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ„µļ„® ļ„¶ļ„”, ļ„›ļ…Žļ„ŗļ„¶ 500 ļ„¶ļ…‹ļ„›ļ…‚ļ„ ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„ŗļ„µļ„øļ…‡ļ„œļ„© ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ī„” ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶
ļ…ƒļ„ļ„©ļ„Ŗļ…„ ļ„›ļ„µļ„® ļ„Ŗļ…Œ ļ„±ļ…‚ļ„‘ļ„¬, ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„›ļ……ļ„£ ļ…ƒļ„¬ļ„¶ļ„ ļ„ŗļ„Æ ļ„¶ļ…žļ„ļ„¬ļ…‚ ļ„»ļ…‰:
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ā€¢ 280 ļ„¶ļ…‹ļ„› ļ„ ļ…ļ„¶ ļ„œ ļ„ļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ 220 ļ„¶ļ…‹ļ„› ļ„›ļ„©ļ„› ļ„œ ļ„ļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„»ļ……ļ„©, ļ„•ļ„®ļ…§ļ…‚ļ„ ļ„›ļ…‹ļ„¶ ļ„“ļ…žļ„› ļ„ŗļ„øļ…‚ļ„¶ ļ„»ļ…‰: "ļ„›ļ…„ ļ„‘ļ„ŗļ…„
ļ„
ļ„›ļ…ƒļ„» ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‚ļ„ ļ…ƒļ„› ļ„ ļ…ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ„®?" ļ„“ļ„ŗļ„¬ļ…‚
ļ„¢ļ„øļ…‚ļ„± ļ„¬ļ…‡ļ„© ļ„¶ļ„”, ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ…ƒļ„ŗļ„µļ…€ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ„®ļ…†ļ…œ ļ„øļ…‡ļ„œļ„© ļ„Ŗļ…Œ ļ„Æļ„µļ…‡ ļ„¢ļ…‚ļ„©ļ…‚ ļ„Æļ„øļ…‡ļ„ļ…‚ ļ„‘ļ„Ŗļ…‡ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ„¬ļ…„ ļ„¬ļ……ļ„®ļ…„ļ„’
ļ…ƒļ„¶ļ„’ļ„•ļ„©ļ…„ ļ„Æļ„øļ…‡ļ„ļ…„, ļ„¢ļ…‹ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ…ƒļ„®ļ„µļ…„ļ„œļ„©ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„‘ļ„µļ„«ļ„Æļ…†ļ„µļ„® ļ…ƒļ„ŗļ…žļ…ƒļ„„ļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„±ļ„¬ļ„¶ļ„© ļ…ƒļ„øļ…žļ„  ļ„³ļ„¬ļ„¬ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„² ļ„ (ļ…”): ļ„›ļ…„ ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ„» ļ„³ļ…œļ„® ļ„ŗļ„›ļ„¬ļ…‡ ļ„» ļ„ ļ…ƒļ„› ļ„ ļ…ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„±ļ„µ ļ„±ļ„µ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ„®?
ļ„Æļ…ƒļ„»ļ„¶ļ…„ ļ„®ļ„¾ļ„µ 'ļ„Ŗļ…‡, ļ„›ļ…‹ļ„” ļ„›ļ…ƒļ„» ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰, "280 220 ļ„¬ļ…‡ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‰, ļ„“ļ„ŗ ļ„¶ļ„” ļ„ ļ…ļ„¶ ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ„®ī„”"
ļ„Æļ„µ ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ…ƒļ„ŗļ„œļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ„® ļ…ƒļ„› ļ…ƒļ„ŗļ„µļ…€ ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„Æļ…†ļ„µļ…„ ļ„›ļ„»ļ…‚ļ„©ļ…„ ļ„®ļ„»ļ…„
ļ„
ļ„¬ļ…žļ„ŗļ„¬ļ…‡ī„” ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„Æļ……ļ…žļ„”ļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‚ ļ„»ļ…‰: ļ„›ļ…„ ļ„“ļ„»
ļ„‘ļ…œļ„Ŗļ„µ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„³ļ…ļ„›ļ…‚ ļ„¬ļ…‡ ļ„›ļ…‚ļ„µļ„® ļ„»ļ…‰, ļ„¢ļ…‚ļ„ ļ„“ļ„» ļ„¶ļ…‹ļ„›ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„› ļ„‘ļ„ŗļ„¶ ļ„Æļ„ŗļ…œļ„¬ ļ„®ļ…†ļ…œ ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰?
ļ„“ļ„» ļ„•ļ„» ļ„«ļ…‚ļ„ ļ„»ļ…‰ ļ…ƒļ„¢ļ…žļ„«ļ…‡ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„¶ļ„” Z ļ„„ļ…‰ļ„ŗļ„„ ļ„›ļ…œļ„³ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„” Z ļ„„ļ…‰ļ„ŗļ„„ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„› ļ…ƒļ„øļ„­ļ…„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„“ļ„»
ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ…ƒļ„¬ļ…œļ„¬ļ…„ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ„“ļ…žļ„› ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„“ļ…žļ„› ļ„‘ļ„®ļ……ļ„³ļ…‚ļ…ƒļ„®ļ„Ŗ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„Ŗļ…Œ ļ„›ļ…‚ļ…€ļ…„ ļ„øļ…žļ„œļ„µļ…‚ ļ„»ļ…‰ī„”
ļ„›ļ„¬ļ„³ 1: ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® ļ„ø ļ„ ļ„®ļ…†ļ…œ ļ„Æļ…ƒļ„µļ„² ļ…ƒļ„¹ļ„Ŗ ļ„›ļ„µļ…‹
ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ„¬ļ…‡ ļ„¹ļ„±ļ„¬ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ , ļ„‘ļ„ŗļ…„
ļ„
ļ„Æļ…ƒļ„»ļ„¶ļ…‚ļ„ ļ„¬ļ…‹ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ…‚ļ„:
ā€¢ ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® (Hā‚€):ļ„ ļ…ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„³ļ„¹ļ„»ļ…†ļ„µ ļ„»ļ„®ī„”
ā€¢ ļ…ƒļ„øļ„›ļ„¶ļ…ƒļ„Æļ„› ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® (Hā‚):ļ„ ļ…ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„“ļ…žļ„›ļ…‹ ļ…ƒļ„¢ļ„»ļ…‡ ļ„³ļ„¹ļ„»ļ…†ļ„µ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ„®ī„”
ļ„ļ…ƒļ„©ļ…ƒļ„Ŗļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡, ļ„¢ļ…‡ļ„›ļ„µ ļ„¬ļ…‹ļ„øļ…ˆ ļ„‘ļ„®ļ…‚ļ„¢ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ„®, ļ„Ŗļ…‚ļ„ ļ„»ļ„µļ…‡ļ„› ļ„®ļ…†ļ…œ 50% ļ„¶ļ…‹ļ„›ļ…‚ļ„ ļ„¬ļ……ļ„’ļ„µļ…‚ ļ„œļ…‚ļ„­ļ…‚ ļ„¢ļ…‚ļ„©ļ…‚
ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„“ļ„ŗļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± ļ„»ļ…‰:
ā€¢ ļ„ŗļ…œļ„²ļ…‚ļ…ƒļ„øļ„Ŗ ļ„ ļ…ļ„¶ ļ„œļ…‚ļ„© ļ„øļ…‚ļ„¶ļ…‡ = 500 Ɨ 0.5 = 250
ā€¢ ļ„›ļ„©ļ„› ļ„œļ…‚ļ„© ļ„øļ…‚ļ„¶ļ…‡ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ„Ŗ = 500 Ɨ 0.5 = 250
ļ„›ļ„¬ļ„³ 2: ļ„‘ļ…œļ„Ŗļ„µ ļ„øļ…‡ļ„œļ…‹
ļ„ŗļ„µļ„øļ…‡ļ„œļ„© ļ„Ŗļ…Œ:
ā€¢ ļ„‘ļ„ŗļ„¶ ļ„ ļ…ļ„¶ ļ„œļ…‚ļ„© ļ„øļ…‚ļ„¶ļ…‡ = 280
ā€¢ ļ„‘ļ„ŗļ„¶ ļ„›ļ„©ļ„› ļ„œļ…‚ļ„© ļ„øļ…‚ļ„¶ļ…‡ = 220
ļ„¬ļ…‡ļ„œļ…‡ ļ„ļ„— ļ„‘ļ„Ŗļ…‡ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ…ƒļ„®ļ„Ŗ ļ„ ļ…ļ„¶ ļ„œļ…‚ļ„© ļ„øļ…‚ļ…ƒļ„¶ļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„‘ļ…œļ„Ŗļ„µ = 280 ā€“ 250 = 30
ļ„»ļ……ļ„©, ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„“ļ„» ļ„¬ļ…‡ļ„œļ„© ļ„¬ļ…„ ļ„¶ļ…‹ļ„æ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ 30 ļ„¬ļ…‚ ļ„“ļ„» ļ„‘ļ…œļ„Ŗļ„µ ļ„“ļ…œļ„®ļ…‚ ļ„øļ…žļ„§ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„“ļ„» ļ…ƒļ„›ļ„»ļ…‚ ļ„¢ļ…‚ ļ„ŗļ„›ļ…‡ ļ…ƒļ„› ļ„ ļ…ļ„¶
ļ„ŗļ…žļ„ ļ„³ļ……ļ…žļ„  ļ„øļ„­ļ…‡ļ„µļ…‡ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ„®, ļ„¢ļ…‚ļ„ ļ„›ļ…„ ļ„“ļ„» ļ„ŗļ…œļ„¢ļ…‹ļ„ ļ„®ļ…‚ļ„¶ ļ„»ļ…‹ļ„“ļ„’ ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„›ļ„¬ļ„³ 3: ļ„‘ļ„®ļ……ļ„Æ ļ„Ŗ ļ„¶ļ„” Z ļ„° ļ„µļ„³ļ…†ļ„¶ ļ„¶ ļ„ļ…† ļ„›ļ„µļ…‹
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„„ļ…‰ļ„ŗļ…ƒļ„„ļ…œļ„ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ…ƒļ„øļ…žļ„  Z ļ„¶ļ„” ļ„°ļ…‚ļ„µļ„³ļ…†ļ„¶ļ…‚ ļ„“ļ„» ļ„»ļ…‰:
ļ…ƒļ„›ļ…žļ„«ļ…‡:
ā€¢ p = ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ (ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ…ƒļ„ļ„’ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ)
ā€¢ P = ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ (ļ„•ļ„³ļ…„ļ„¬ ļ„›ļ…„ļ„Ŗļ…„ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ)
ā€¢ n = ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„’ļ„›ļ…‚ļ„µ
ļ„’ļ„™ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ…„ļ„—:
ļ„›ļ„¬ļ„³ 4: Z ļ„³ļ……ļ…žļ„¶ ļ„¬ļ…„ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’ ļ„›ļ„µļ…‹
ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ…ƒļ„øļ…žļ„ , ļ„‘ļ„ŗļ…„
ļ„
ļ„‘ļ„›ļ„ŗļ„µ Z ļ„³ļ……ļ…žļ„¶ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ 5% ļ„³ļ„»ļ…žļ„Ŗļ„ø ļ„Æļ…žļ„­ļ„µ 'ļ„Ŗļ…‡ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„®ļ…‚ļ„¶ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‚ļ„:
ā€¢ ļ„¬ļ…‹-ļ„Æļ…†ļ„” ļ„øļ…‚ļ„¶ļ…‚ ļ„„ļ…‰ļ„ŗļ„„: ļ„®ļ…‚ļ„¾ļ……ļ„› Z ā‰ˆ Ā±1.96
2.68 > 1.96 ļ„Ŗļ…Œ, ļ„‘ļ„ŗļ…„
ļ„
ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„”
ļ…ƒļ„ŗļ…žļ„„ :ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ļ…„ ļ…ƒļ„øļ…žļ„  ļ„‘ļ…œļ„Ŗļ„µ ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„»ļ…‰ī„” ļ„“ļ„ŗļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± ļ„»ļ…‰ ļ…ƒļ„› ļ„ļ…„ļ…‡ļ„®ļ…ƒļ„øļ„¶ ļ„¬ļ…‡ ļ„¶ļ…‹ļ„›ļ…‚ļ„
ļ…ƒļ„øļ…žļ„  ļ„ ļ…ļ„¶ ļ„›ļ„©ļ„› ļ„®ļ…‚ļ„¶ļ…Œ ļ„«ļ…‹ļ„æļ…§ļ…‚ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ ļ„“ļ„» ļ„‘ļ…œļ„Ŗļ„µ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„ŗļ…œļ„¢ļ…‹ļ„ ļ„¬ļ…‡ ļ„›ļ…‚ļ„µļ„® ļ„‘ļ„ŗļ…œļ„²ļ„ø ļ„»ļ…‰ī„”
ļ„² ļ„ (b): Z ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„•ļ„Æļ„“ļ…‹ļ„
ļ„»ļ……ļ„© ļ„¢ļ„¬ļ…Œ ļ„‘ļ„ŗļ…„
ļ„
ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ„»ļ…‰ ļ…ƒļ„› Z ļ„„ļ…‰ļ„ŗļ„„ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„ ļ…ļ„¶ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„¬ļ…„ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ļ…„ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ…ƒļ„øļ…žļ„  ļ…ƒļ„›ļ„øļ…ˆ ļ„³ļ„¬ļ„¬
ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰, ļ„’ļ„™ ļ„“ļ…žļ„› ļ„›ļ„¬ļ„³ ļ…ƒļ„Æļ…žļ„”ļ…‡ ļ„»ļ„„ ļ„›ļ…‡ Z ļ„øļ…œļ„§ ļ„±ļ…‚ļ„µļ…‡ ļ„ļ…žļ„¶ ļ„›ļ„µļ…„ļ„—, ļ„¢ļ…‹ ļ„“ļ„ŗ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„®ļ…†ļ…œ ļ„ŗļ…œļ„²ļ„ø ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„“ļ…žļ„› ļ„‘ļ…œļ„›ļ„æļ…‚ ļ…ƒļ„øļ…ƒļ„ļ„’ļ„®ļ…„ ļ„¬ļ…‡ ļ„„ļ…†ļ„¶ļ…ƒļ„›ļ…žļ„„ ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„› ļ„¹ļ„›ļ„Ŗļ…„ļ„¹ļ…‚ļ„¶ļ…„ ļ„ŗļ…œļ„¬ ļ„øļ„¢ļ…Œ ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹, ļ„¢ļ…‹ ļ…ƒļ„› ļ„±ļ„»ļ……ļ„Ŗ
ļ„ŗļ…‚ļ„µļ…„ļ„’ļ„ ļ„‘ļ„ŗļ„¶-ļ„ŗļ…œļ„ŗļ…‚ļ„µ ļ„ŗļ„³ļ…žļ…ƒļ„ŗļ„’ļ„øļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„»ļ…žļ„¶ ļ„›ļ„µļ„® ļ„¶ļ„” ļ…ƒļ„Ŗļ„’ļ„µ ļ„»ļ…‰ī„”
Z ļ„øļ…œļ„§, ļ…ƒļ„¢ļ„ŗļ„®ļ…†ļ…œ ļ„ŗļ„„ļ…Šļ„§ļ„µļ„§ ļ„ŗļ…‚ļ„­ļ…‚ļ„µļ„® ļ„øļ…œļ„§ ļ„øļ…„ ļ…ƒļ„›ļ„»ļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰, ļ„“ļ…žļ„› ļ„žļ…œļ„„ļ…„-ļ„’ļ„›ļ…‚ļ„µ ļ„¬ļ…‚ ļ„øļ„›ļ„µ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„¾ļ…„ļ„µļ…‹ 'ļ„Ŗļ…‡ ļ„›ļ…ˆļ„¬ļ…ƒļ„µļ„Ŗ
ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„¢ļ„ŗļ„¬ļ…‚ ļ„ŗļ„„ļ…Šļ„§ļ„µļ„§ ļ…ƒļ„§ļ„øļ…„ļ„—ļ„¹ļ„® ļ„“ļ…žļ„› ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„»ļ„µ Z ļ„³ļ……ļ…žļ„¶ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„¬ļ…žļ„ŗļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„“ļ…žļ„› ļ„§ļ…‡ļ„„ļ…‚ ļ„Æļ……ļ„’ļ„“ļ…œļ„„ ļ„šļ„ŗļ„Ŗ
ļ„Ŗļ…Œ ļ…ƒļ„›ļ…œļ„®ļ…„ ļ„¬ļ…†ļ„µ ļ„»ļ…‰, ļ„¢ļ…‹ ļ„ŗļ„„ļ…Šļ„§ļ„µļ„§ ļ…ƒļ„§ļ„øļ…„ļ„—ļ„¹ļ„® ļ…ƒļ„øļ…žļ„  ļ„³ļ…‚ļ…ƒļ„Æļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„“ļ…žļ„› ļ„µļ…†ļ„¶ļ„µ ļ„øļ…‚ļ„ļ„ ļ„ŗļ…‹ļ„ ļ…‹: ļ„“ļ…žļ„› ļ…ƒļ„ŗļ„µļ…‚ ļ„‘ļ„ŗļ„­ļ…‚ļ„µļ„® ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„žļ…žļ„„ ļ„³ļ……ļ…žļ„¶ ļ…ƒļ„¬ļ„œļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰, ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µļ„¶ļ…‚ ļ„’ļ„³ ļ„³ļ……ļ…žļ„¶
ļ…ƒļ„¬ļ„œļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ ļ„¬ļ…†ļ„¢ļ…‚ ļ…ƒļ„ŗļ„µļ…‚ ļ„‘ļ„ŗļ„­ļ…‚ļ„µļ„® ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„•ļ…žļ„  ļ„³ļ……ļ…žļ„¶ ļ…ƒļ„¬ļ„œļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ī„”
Z ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„³ļ……ļ…žļ„œ ļ„•ļ„Æļ„“ļ…‹ļ„
1. ļ„ŗ ļ„­ļ„® ļ„ ļ„‘ļ„Ŗļ…‡ ļ„‘ļ„®ļ……ļ„Æ ļ„Ŗ ļ„± ļ„µļ…‡ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® ļ„ø ļ„ ļ„¬ļ…„ ļ„¢ ļ„ļ„  ļ„›ļ„µļ„®
ā€¢ ļ„‘ļ„ŗļ…„
ļ„
ļ„»ļ……ļ„©ļ…‡ ļ„ ļ…ļ„¶ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„¬ļ…„ ļ„“ļ…žļ„› ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„© ļ„¬ļ…‡ļ„œļ…„ ļ„»ļ…‰ī„”
ā€¢ Z ļ„„ļ…‰ļ„ŗļ„„ ļ„“ļ„» ļ…ƒļ„®ļ„µļ„­ļ…‚ļ„µļ„Ŗ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ„® ļ…ƒļ„› ļ„›ļ…„ ļ„“ļ…žļ„› ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…‚ļ„ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…‚ļ„
ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„Ŗļ…Œ ļ„›ļ…‚ļ…€ļ…„ ļ„øļ…žļ„œļ„µļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„“ļ„» ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„®ļ…‚ ļ…ƒļ„› ļ„›ļ…„ ļ„ŗļ„›ļ…†ļ„¶ ļ„¬ļ…‡ ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„šļ„°ļ„¶ļ…‚ļ„”ļ„® ļ„›ļ„¶ļ…‚ļ„ŗļ…‚ļ„ ļ„®ļ…‚ļ„¶ļ…Œ ļ„šļ„®ļ„¶ļ…‚ļ„”ļ„®
ļ„›ļ„¶ļ…‚ļ„ŗļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„Ŗļ„µļ„¢ļ…„ļ„» ļ…ƒļ„¬ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„”
2. ļ„ŗļ…œļ„² ļ„øļ„® ļ„ø ļ„ ļ„¶ļ…žļ„²ļ„©
ā€¢ Z ļ„øļ…œļ„§ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„ļ„©ļ„®ļ…‚ļ„øļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„•ļ„Æļ„“ļ…‹ļ„ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„» ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„“ļ„ŗ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„±ļ…‚ļ„µļ…‡ ļ„¬ļ…žļ„ŗļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…‹ļ„” ļ„œļ…‚ļ„ŗ ļ…ƒļ„®ļ„µļ…„ļ„œļ„© ļ„œļ…‚ļ„ŗ ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„¬ļ…‡ ļ„•ļ…žļ„Æļ„µ, ļ„»ļ…‡ļ„¦ļ…‚ļ„, ļ„¢ļ…‚ļ„
ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ…ƒļ„§ļ…žļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„“ļ„ŗ ļ„ļ…žļ„¶ ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„›ļ…„ ļ„»ļ…‰ ļ…ƒļ„› ļ„“ļ…žļ„› ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„ ļ……ļ…ƒļ„©ļ„’ ļ…ƒļ„ļ„’ ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„
ļ„“ļ…žļ„› ļ„Æļ…„ļ…„ļ…ƒļ„œļ„’ ļ…ƒļ„øļ…žļ„  80% ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„‘ļ…œļ„› ļ„Æļ…„ļ…‚ļ„Æļ„Ŗ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰?
3. ļ„ŗļ„›ļ…‹ļ„µ ļ„ ļ„¬ ļ…ƒļ„³ļ„’ļ„µļ…„ļ„›ļ„µļ„®
ā€¢ Z ļ„ŗļ„›ļ…‹ļ„µ ļ„“ļ…žļ„›ļ…‹ ļ„Æļ…‰ļ„³ļ…‚ļ„®ļ…‡ 'ļ„Ŗļ…‡ ļ„§ļ…‡ļ„„ļ…‚ ļ„¬ļ…‡ ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„ŗļ…‰ļ…žļ„„ļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„¬ļ…„ ļ„’ļ…ƒļ„ļ„’ ļ…ƒļ„¬ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„© ļ„øļ„¢ļ…Œ, ļ„¢ļ…‡ļ„›ļ„µ ļ„¬ļ…‹ ļ…ƒļ„øļ…ƒļ„¬ļ„’ļ„µļ„«ļ…„ ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„Æļ…„ļ…„ļ…ƒļ„œļ„’ļ„øļ…‚ļ„ ļ…ƒļ„¬ļ…œļ„¬ļ…‡ ļ„»ļ„®, ļ„Ŗļ…‚ļ„ ļ„•ļ„®ļ…§ļ…‚ļ„ ļ„¬ļ…‡ Z ļ„ŗļ„›ļ…‹ļ„µ ļ„¬ļ…žļ„ŗ ļ„ŗļ„›ļ„¬ļ…‡
ļ„»ļ„® ļ…ƒļ„› ļ„•ļ„®ļ…§ļ…‚ļ„ ļ„¬ļ…‡ ļ„ŗļ…ƒļ„»ļ„Æļ…‚ļ„¦ļ…„ļ„’ļ„ ļ„¬ļ…‡ ļ„³ļ……ļ„›ļ…‚ļ„±ļ„¶ļ…‡ ļ…ƒļ„›ļ„ŗļ„®ļ…‡ ļ…ƒļ„±ļ„»ļ„Ŗļ„µ ļ„Æļ…„ļ„¬ļ„µļ„¹ļ„® ļ„›ļ…„ļ„Ŗļ…‚ī„”
ā€¢ ļ„“ļ„» ļ„œļ…‡ļ„§ļ…‚ļ„, ļ„‘ļ„›ļ…‚ļ„¬ļ…ƒļ„³ļ„› ļ„‘ļ„Ŗļ…‡ ļ„Æļ…„ļ„¬ļ„µļ„¹ļ„® ļ„³ļ……ļ„¶ļ…‚ļ„ļ„›ļ„© ļ…ƒļ„øļ…žļ„  ļ…ƒļ„øļ„¹ļ…‡ļ„¹ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„³ļ„¬ļ„¬ļ„ļ…‚ļ„µ ļ„»ļ…‰ī„”
4. ļ„•ļ„¬ļ„“ļ…‹ļ„ ļ„ ļ…ƒļ„øļ…žļ„  ļ„ļ……ļ„©ļ„øļ…žļ„Ŗ ļ…ƒļ„®ļ„“ļ…œļ„Ŗļ„µļ„©
ā€¢ ļ„•ļ„¬ļ„“ļ…‹ļ„ ļ„•ļ„Ŗļ„Æļ…‚ļ„¬ ļ„¬ļ…„ ļ„ļ……ļ„©ļ„øļ…žļ„Ŗļ…‚ ļ„¬ļ…„ ļ…ƒļ„®ļ„ļ„µļ…‚ļ„®ļ…„ ļ„›ļ„µļ„® ļ„¶ļ„” ļ„›ļ…œļ„„ļ„µļ…‹ļ„¶ ļ„ ļ…‚ļ„µļ„„ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  Z ļ„øļ…œļ„§ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ
ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„“ļ„» ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„®ļ…‚ ļ…ƒļ„› ļ„›ļ…„ ļ„³ļ„¹ļ…„ļ„® ļ„¬ļ……ļ„’ļ„µļ…‚ ļ…ƒļ„Ŗļ„’ļ„µ ļ„›ļ…„ļ„Ŗļ…‡ ļ„±ļ…‹ļ„¶ļ„„ļ…‚ļ„ ļ„¬ļ…‚ ļ…ƒļ„øļ„’ļ„ŗ ļ„ŗļ„øļ…„ļ„›ļ…‚ļ„µļ„“ļ…‹ļ„
ļ„ŗļ…„ļ„³ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ„µļ…ƒļ„»ļ…œļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„¢ļ…‡ļ„›ļ„µ Z ļ„ŗļ„›ļ…‹ļ„µ ļ„±ļ„»ļ……ļ„Ŗ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ„¢ļ…‚ļ„ ļ„±ļ„»ļ……ļ„Ŗ ļ„žļ…žļ„„ ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ ļ„“ļ„» ļ„•ļ„Ŗļ„Æļ…‚ļ„¬ļ„® ļ…ƒļ„øļ…žļ„  ļ„ŗļ„³ļ…žļ…ƒļ„ŗļ„’ ļ„¬ļ…‚ ļ„ŗļ…œļ„›ļ…‡ļ„Ŗ ļ…ƒļ„¬ļ…œļ„¬ļ…‚
ļ„»ļ…‰ī„”
5. ļ„œļ…‹ļ„¢ ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„³ ļ…ƒļ„¢ļ„› ļ…ƒļ„øļ…ƒļ„ļ„’ļ„®
ā€¢ ļ„œļ…‹ļ„¢ļ„›ļ„µļ„Ŗļ…‚ ļ„ŗļ„µļ„øļ…‡ļ„œļ„© ļ„¬ļ…‡ ļ„®ļ„Ŗļ…„ļ…ƒļ„¢ļ„’ļ„ ļ„¬ļ…‚ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„›ļ„µļ„®, ļ„®ļ„øļ…„ļ„’ļ„ ļ„®ļ…„ļ„Ŗļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ„‘ļ„Ŗļ…‡
ļ„¬ļ„œļ„¶ļ„‘ļ…œļ„¬ļ…‚ļ„¾ļ…„ ļ„¬ļ…„ ļ„Æļ…„ļ„²ļ…‚ļ„øļ„¹ļ…„ļ„¶ļ„Ŗļ…‚ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ„¶ļ„” Z ļ„øļ…œļ„§ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„¬ļ„øļ…‚ļ„” ļ…ƒļ„øļ…žļ„ , ļ„“ļ„» ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„®ļ…‚ ļ…ƒļ„› ļ„›ļ…„ ļ„“ļ…žļ„› ļ„®ļ„øļ…„
ļ„
ļ„¬ļ„øļ…‚ļ„” ļ„¬ļ…‚ ļ„Æļ„¶ļ…‡ļ„ŗļ„±ļ…‹ ļ„¬ļ…‡ ļ„³ļ……ļ„›ļ…‚ļ„±ļ„¶ļ…‡
ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„Æļ…„ļ„²ļ…‚ļ„ø ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
6. ļ…ƒļ„øļ…žļ„Ŗ ļ„‘ļ„Ŗļ…‡ ļ„¢ļ…‹ļ„œļ„³ ļ„Æļ…„ļ„±ļ…œļ„­ļ„®
ā€¢ Z ļ„øļ…œļ„§ ļ„±ļ…Šļ„›ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„øļ…žļ„Ŗļ…„ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„›ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„„ļ…‚ļ„› ļ„³ļ…‚ļ„µļ„›ļ…„ļ„„ ļ„›ļ„µļ…‰ļ„¹ ļ„¢ļ…‚ļ„ ļ„‘ļ„ŗļ…‚ļ„­ļ…‚ļ„µļ„® ļ…ƒļ„µļ„„ļ„µļ„® ļ„øļ„µļ„ļ…„ļ„’ļ„
ļ„‘ļ…ƒļ„Ŗļ„‘ļ…œļ„Ŗ ļ„žļ„„ļ„®ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ļ„’ļ„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ„® ļ…ƒļ„øļ…žļ„  ļ„³ļ„¬ļ„¬ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ„“ļ…žļ„› ļ„›ļ„µļ„¾ļ…‚ ļ…ƒļ„§ļ„°ļ…‚ļ„¶ļ„„ ļ„¬ļ…‡ ļ„“ļ…žļ„› ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„Æļ…žļ„­ļ„µ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„»ļ…‹ļ„© ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„¬ļ…‚ ļ„Æļ„Ŗļ…‚
ļ„¶ļ„ļ…‚ļ„•ļ„©ļ…‚ī„”
7. ļ„¬ļ…‹ ļ„ŗļ„³ļ…†ļ„» ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„® ļ„›ļ„µļ„®
ā€¢ ļ„¬ļ…‹ ļ„’ļ„±ļ…‚ļ„¬ļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„øļ…‚ļ„¶ļ…‡ ļ„‘ļ…ƒļ„­ļ„˜ļ„®ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ , Z ļ„„ļ…‰ļ„ŗļ„„ļ…‚ļ„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„ŗļ…‚ļ„­ļ„®ļ…‚ļ„ ļ„¢ļ…‚ļ„ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ…ƒļ„øļ…žļ„ 
ļ„‘ļ…œļ„Ŗļ„µ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ„¶ļ„” ļ„›ļ…„ļ„Ŗļ…„ ļ„¢ļ…‚ ļ„ŗļ„›ļ„¬ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„®: ļ…ƒļ„›ļ„ŗļ…‡ ļ„ŗļ„›ļ…†ļ„¶ ļ…ƒļ„øļ…žļ„  ļ„³ļ……ļ…œļ…ƒļ„§ļ„’ļ„ ļ„‘ļ„Ŗļ…‡ ļ„›ļ……ļ„æļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„•ļ„ ļ…‚ļ„” ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„®ļ…‚, ļ„¢ļ…‚ļ„ ļ„œļ…‡ļ„Ŗļ„µļ…‚ļ„
ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„ ļ…‹ļ„© ļ„Æļ„ŗļ…œļ„¬ļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„®ļ…‚ī„”
ļ„¢ļ…‹ļ„æļ„® ļ„ø ļ„¶ ļ…ƒļ„»ļ…žļ„ŗ (a) ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„»ļ…žļ„ŗ (b)
ļ„ ļ…ļ„¶ļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„¬ļ…„ ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„© ļ„•ļ„¬ļ…Œ ļ„ŗļ„Æļ…žļ„¹ļ„„ ļ„»ļ…‹ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ ļ„¢ļ„¬ļ…Œ ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ„ŗļ„®ļ…†ļ…œ Z ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ…ƒļ„øļ„¹ļ…‚ļ„¶ ļ„•ļ„Æļ„“ļ…‹ļ„ļ…‚ļ„ ļ„®ļ…‚ļ„¶
ļ„¢ļ…‹ļ„æļ„¬ļ…‡ ļ„»ļ…‚ļ„:
ā€¢ ļ„ ļ…ļ„¶ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„©ļ„› ļ„œļ…‚ļ„© ļ„øļ…‚ļ…ƒļ„¶ļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ…ƒļ„ļ„’ ļ„‘ļ…œļ„Ŗļ„µ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„¶ļ„” Z ļ„„ļ…‰ļ„ŗļ„„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„›ļ…‡
ļ„³ļ…‚ļ…ƒļ„Æļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ Z ļ„³ļ……ļ…žļ„¶ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„¬ļ…žļ„ŗļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ…ƒļ„ļ„’ ļ„‘ļ…œļ„Ŗļ„µ ļ„‘ļ„µļ„«ļ„Æļ…†ļ„µļ„® ļ„»ļ…‰ ļ„¢ļ…‚ļ„ ļ…ƒļ„ŗļ„µļ…€ ļ„³ļ…ļ„›ļ…‚ ļ„¬ļ…‡ ļ„›ļ…‚ļ„µļ„® ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„»ļ…„ ļ…ƒļ„ŗļ„­ļ…‚ļ„ļ„Ŗ ļ„¶ļ„ļ„²ļ„ ļ…ƒļ„›ļ„ŗļ…‡ ļ„øļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ļ„Ŗļ„³ļ„› ļ„ŗļ„³ļ…žļ…ƒļ„ŗļ„’ 'ļ„Ŗļ…‡ ļ„¶ļ…‚ļ„ļ…† ļ„›ļ…„ļ„Ŗļ…‚ ļ„¢ļ…‚ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰: ļ„²ļ…‚ļ„øļ…ˆ ļ„„ļ…‰ļ„ŗļ„„
ļ„ŗļ„›ļ…‹ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ…„ļ„Ŗļ…„ ļ„¢ļ…‚ļ„øļ…‡, ļ„³ļ…‚ļ„µļ„›ļ…„ļ„„ ļ„¹ļ…‡ļ„‘ļ„µļ…‚ļ„ ļ„¬ļ…„, ļ„¢ļ…‚ļ„ ļ„³ļ„µļ…„ļ„¾ ļ„¬ļ…‡ ļ„®ļ„Ŗļ…„ļ…ƒļ„¢ļ„’ļ„ ļ„¬ļ…„ī„”
ļ„¬ļ…†ļ„¢ļ…‡ ļ„¹ļ„±ļ„¬ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ , Z ļ„øļ…œļ„§ ļ„“ļ…žļ„› ļ„“ļ…†ļ„®ļ…„ļ„øļ„µļ„ŗļ„¶ ļ„‘ļ„®ļ……ļ„øļ…‚ļ„¬ļ„› ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰ī„” ļ„²ļ…‚ļ„øļ…ˆ ļ„›ļ…‹ļ„” ļ„øļ…„ ļ„œļ…‡ļ„Ŗļ„µ ļ„»ļ…‹ļ„øļ…‡ - ļ…ƒļ„ŗļ…žļ…ƒļ„œļ„’, ļ„œļ…‡ļ„Ŗļ…„ļ„±ļ…‚ļ„æļ…„,
ļ„¬ļ„øļ…‚ļ„”, ļ„¢ļ…‚ļ„ ļ…ƒļ„øļ…žļ„Ŗ - ļ„“ļ„» ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„ŗļ…œļ„²ļ…‚ļ…ƒļ„øļ„Ŗ, ļ„Æļ…„ļ„³ļ…‚ļ…ƒļ„©ļ„Ŗ ļ„Ŗļ„µļ…„ļ„›ļ…‡ ļ„®ļ…‚ļ„¶ ļ„ŗļ…œļ…ƒļ„œļ„’ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’ ļ„›ļ„µļ„® ļ…ƒļ„øļ…žļ„  ļ„³ļ„¬ļ„¬
ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ…ƒļ„ļ„©ļ„Ŗļ…„ ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ„“ļ…žļ„› ļ„›ļ„» ļ„©ļ…„
ļ„ļ…„ļ…‡ļ„®ļ…ƒļ„øļ„¶ ļ„øļ…‚ļ„Æļ„ŗ ļ„’ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ…‹ļ„—, ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„„ļ…‚ļ„–ļ„® ļ„›ļ…Žļ„ŗļ„¶ ļ„»ļ……ļ„© ļ„“ļ…žļ„› ļ„³ļ…„ļ…ƒļ„„ļ…œļ„ ļ„›ļ„µ ļ„µļ„»ļ…„ ļ„»ļ…‰ ļ„Ŗļ…‚ļ„ ļ„¢ļ…‹ ļ„“ļ„»
ļ„°ļ…‰ļ„ŗļ„¶ļ…‚ ļ„›ļ…„ļ„Ŗļ…‚ ļ„¢ļ…‚ ļ„ŗļ„›ļ…‡ ļ…ƒļ„› ļ…ƒļ„›ļ„»ļ„æļ…‚ ļ„‘ļ„®ļ…‚ļ„¢ ļ„øļ…žļ„§ļ…„ ļ„³ļ…‚ļ„Ŗļ„µļ…‚ ļ…ƒļ„øļ…žļ„  ļ„ŗļ„„ļ…‚ļ„› ļ„›ļ„µļ„®ļ…‚ ļ„»ļ…‰ī„” ļ„•ļ„» ļ…ƒļ„ŗļ„µļ…€ ļ„‘ļ„®ļ……ļ„²ļ„ø 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„µļ„²ļ„µ
ļ„®ļ„»ļ…„
ļ„
ļ„›ļ„µļ„¬ļ…‡ī„” ļ„•ļ„» ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„ŗļ…žļ„ ļ…‚ļ„” ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„© ļ„¶ļ„” Z ļ„„ļ…‰ļ„ŗļ„„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„Æļ„Ŗļ…‚ ļ„¶ļ…žļ„ļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„ ļ…ļ„¶ļ…‚ļ„ ļ„¬ļ…„ ļ„“ļ…žļ„› ļ„ŗļ„Æļ…žļ„¹ļ„„ ļ…ƒļ„›ļ„®ļ…‚ļ„µļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„ŗ ļ„ŗļ…†ļ„£ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ļ„—, ļ„•ļ„» ļ„ ļ…ļ„¶ļ…‚ļ„ ļ„¬ļ…„ ļ„ŗļ„Æļ„¶ļ…‚ļ„” ļ„¬ļ…„ ļ„“ļ…‹ļ„¢ļ„®ļ…‚ ļ„•ļ„ŗ ļ„‘ļ„®ļ……ļ„ŗļ…‚ļ„µ ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ„®, ļ„“ļ„»
ļ„“ļ„›ļ…„ļ„®ļ…„ ļ„±ļ„©ļ…‚ļ„•
ļ„
ļ„¬ļ…‡ ļ„»ļ„® ļ…ƒļ„› ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ļ„Ŗļ„µ ļ„¶ļ…‹ļ„› ļ„œļ……ļ„¹ ļ„µļ…ƒļ„»ļ„©ī„”
ļ„“ļ„ŗ ļ„¬ļ…ļ„µļ…‚ļ„®, ļ„›ļ…Žļ„ŗļ„¶ Z ļ„øļ…œļ„§ ļ„±ļ…‚ļ„µļ…‡ ļ„øļ…„ ļ„¢ļ…‚ļ„©ļ„¬ļ…„ ļ„»ļ…‰, ļ„“ļ„» ļ„³ļ…ƒļ„»ļ„ŗļ…†ļ„ŗ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ļ„— ļ…ƒļ„› ļ„“ļ„»ļ…„ ļ„Æļ„»ļ……ļ…œļ„  ļ„ŗļ„›ļ…†ļ„¶ ļ„¬ļ…‡ ļ„¬ļ……ļ„Æļ…ƒļ„»ļ„µ ļ„¬ļ…‡
ļ„œļ…‚ļ„©ļ…‡, ļ„»ļ„ŗļ„Æļ„Ŗļ…‚ļ„¶ ļ„¬ļ…‡ ļ„œļ…‚ļ„©ļ…‡, ļ„¢ļ…‚ļ„ ļ„“ļ…žļ„«ļ…Œ ļ„Ŗļ…žļ„› ļ…ƒļ„› ļ„ ļ…‹ļ„© ļ„³ļ……ļ…ƒļ„»ļ…œļ„³ļ…‚ļ„ ļ„¬ļ…„ ļ„“ļ…‹ļ„¢ļ„®ļ…‚ ļ„±ļ„©ļ…‚ļ„•ļ„© ļ…ƒļ„øļ…žļ„  ļ„³ļ„¬ļ„¬ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
Z ļ„øļ…œļ„§ ļ„•ļ„®ļ…§ļ…‚ļ„ ļ„¬ļ…‡ ļ„›ļ„ŗļ„±ļ…‡ ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„› ļ„»ļ…„ļ„µļ…‹ ļ„±ļ„© ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ - ļ„“ļ…žļ„› ļ„‘ļ…ƒļ„¢ļ„»ļ…‚ ļ„ŗļ…‚ļ„­ļ„® ļ„¢ļ…‹ ļ„›ļ…žļ„ ļ…‡ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ„®ļ…†ļ…œ ļ„›ļ…‚ļ„µļ„øļ…‚ļ„”ļ„“ļ…‹ļ„
ļ„°ļ…‰ļ„ŗļ…ƒļ„¶ļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„±ļ„¬ļ„¶ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ…ƒļ„ŗļ…žļ„„
ļ„ŗļ…‚ļ„µļ…œļ„¹ ļ…ƒļ„øļ…žļ„ :
1. ļ„ ļ…ļ„¶ ļ„±ļ„® ļ„³ ļ„›ļ„©ļ„› ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ļ…„:500 ļ„¬ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ…ƒļ„øļ…žļ„ , ļ„ ļ…ļ„¶ ļ„œļ…‚ļ„© ļ„øļ…‚ļ„¶ļ…‡ (280) ļ„›ļ„©ļ„› ļ„œļ…‚ļ„© ļ„øļ…‚ļ…ƒļ„¶ļ„’ļ„ (220)
ļ„®ļ…‚ļ„¶ļ…Œ ļ„›ļ…‚ļ…€ļ…„ ļ…ƒļ„¾ļ„’ļ„¬ļ…‚ ļ„ŗļ„®ī„” ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„¶ļ„” Z ļ„„ļ…‰ļ„ŗļ„„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ļ„—, ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ„ŗ ļ…ƒļ„øļ„ ļ…‚ļ„µ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µ
ļ…ƒļ„¬ļ…žļ„Ŗļ…‚ ļ…ƒļ„› ļ„¬ļ…‹ļ„øļ…ˆ ļ„‘ļ„®ļ…‚ļ„¢ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„Æļ…„ļ…ƒļ„ŗļ…žļ„­ ļ„ŗļ„®ī„” ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ„®ļ…‡ ļ„®ļ„ļ„µ ļ„›ļ…Žļ„ŗļ„¶ ļ„®ļ…†ļ…œ ļ„‘ļ„®ļ……ļ„³ļ…‚ļ„®ļ…‚ļ„ 'ļ„Ŗļ…‡ ļ„²ļ„µļ…‹ļ„ŗļ…‚ ļ„›ļ„µļ„®
ļ„¬ļ…„ ļ„±ļ„¢ļ…‚ļ„— ļ„Ŗļ…žļ„«-ļ„‘ļ„­ļ…‚ļ„µļ„Ŗ ļ„°ļ…‰ļ„ŗļ„¶ļ…‚ ļ„¶ļ…‰ļ„© ļ„¬ļ…„ ļ„’ļ…ƒļ„ļ„’ ļ…ƒļ„¬ļ…žļ„Ŗļ…„ī„”
2. Z ļ„øļ…œļ„§ ļ„˜ļ„Æļ„¶ļ…„ļ„›ļ…‡ļ„¹ļ„®:Z ļ„øļ…œļ„§ ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„› ļ„±ļ„»ļ……ļ„Æļ…žļ„œļ…„ ļ„ŗļ…œļ„¬ ļ„»ļ…‰ī„” ļ„“ļ„ŗļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„¢ļ…‚ļ„ļ„ ,
ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„ļ„©ļ„®ļ…‚ļ„øļ…‚ļ„, ļ„ļ……ļ„©ļ„øļ…žļ„Ŗļ…‚ ļ…ƒļ„®ļ„“ļ…œļ„Ŗļ„µļ„©, ļ„ŗļ„›ļ…‹ļ„µļ…‚ļ„ ļ„¬ļ…‡ ļ„³ļ…‚ļ„®ļ„›ļ…„ļ„›ļ„µļ„®, ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„‘ļ„Ŗļ…‡
ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„œļ…‡ļ„Ŗļ„µļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„œļ…‹ļ„¢ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„¶ļ„” ļ„›ļ…„ļ„Ŗļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ī„”
Z ļ„øļ…œļ„§ ļ„¬ļ…‡ ļ„¶ļ…Šļ„ŗ ļ„µļ…‚ļ„»ļ…„
ļ„
ļ„ŗļ…œļ…ƒļ„œļ„’ļ„øļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¬ļ…‡ļ„œ ļ„›ļ…‡, ļ„‘ļ„ŗļ…„
ļ„
ļ„ŗļ„Æļ…žļ„¹ļ„„ ļ„Ŗļ…Œ ļ„Æļ„µļ…‡ ļ„¬ļ…‡ļ„œ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‚ļ„, ļ„‘ļ„µļ„«ļ„Æļ…†ļ„µļ„® ļ„‘ļ…œļ„Ŗļ„µļ…‚ļ„ ļ„¬ļ…‚ ļ„Æļ„Ŗļ…‚
ļ„¶ļ„ļ…‚ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‚ļ„, ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„³ļ„£ļ„¬ļ…‚ļ„µļ…„ ļ„®ļ…‚ļ„¶ ļ„°ļ…‰ļ„ŗļ„¶ļ…‡ ļ„¶ļ…‰ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„” ļ…ƒļ„¢ļ„øļ…ˆ ļ„ļ…„ļ…‡ļ„®ļ…ƒļ„øļ„¶ ļ…ƒļ„øļ…žļ„ , ļ„²ļ…‚ļ„øļ…ˆ ļ„“ļ„» ļ„ ļ…ļ„¶ ļ„»ļ…‹ļ„øļ…‡ ļ„¢ļ…‚ļ„
ļ„›ļ„©ļ„›, ļ„¢ļ…‚ļ„ ļ„›ļ…‹ļ„” ļ„»ļ…‹ļ„µ ļ„‘ļ„ŗļ„¶-ļ„ŗļ…œļ„ŗļ…‚ļ„µ ļ„ŗļ„³ļ…žļ…ƒļ„ŗļ„’, Z ļ„øļ…œļ„§ ļ„§ļ…‡ļ„„ļ…‚ ļ„®ļ…†ļ…œ ļ…ƒļ„ļ„’ļ„® ļ„‘ļ„Ŗļ…‡ ļ„›ļ…‚ļ„µļ„øļ…‚ļ„” ļ…ƒļ„øļ…žļ„  ļ„±ļ„¬ļ„¶ļ„© ļ…ƒļ„øļ…žļ„ 
ļ„³ļ„¬ļ„¬ ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ī„”
6. ļ„“ļ…žļ„› ļ„Æļ…„ļ„“ļ…‹ļ„ļ„¹ ļ„¶ ļ„Æļ…„ļ„“ļ…‹ļ„ ļ…ƒļ„øļ…žļ„ , ļ„¬ļ…‹ ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ ļ„®ļ…‡ ļ„»ļ…‡ļ„¦ ļ…ƒļ„¶ļ„œļ…‡ ļ„®ļ„Ŗļ…„ļ„¢ļ…‡ ļ…ƒļ„¬ļ…žļ„Ŗļ…‡:
ļ„®ļ„³ļ…†ļ„®
ļ„’ļ„› ļ„µ
ļ„ŗļ„­ ļ„µļ„® ļ„šļ„ŗļ„Ŗ
ļ„šļ„ŗļ„Ŗ ļ„Ŗļ…Œ ļ„²ļ„„ļ„›ļ„© ļ„ ļ„¬ļ…‡
ļ„øļ„µļ„ ļ„ ļ„¬ ļ„¢ļ…‹ļ„æ
1
10
15
90
2
12
14
108
5% ļ„³ļ„»ļ…žļ„Ŗļ„Ŗ ļ„¬ļ…‡ ļ„Æļ…žļ„­ļ„µ 'ļ„Ŗļ…‡ ļ„®ļ„³ļ…†ļ„® ļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„ø ļ„ ļ„¬ļ…„ ļ„ŗļ„³ ļ„®ļ„Ŗ ļ„¬ļ…„ ļ„¢ ļ„ļ„  ļ„›ļ„µļ…‹ī„”
ļ„•ļ…žļ„Ŗļ„µ:ļ„ŗļ„³ļ…žļ…ƒļ„ŗļ„’ ļ„ŗļ…‰ļ…žļ„„ļ„‘ļ…žļ„Æ ļ„‘ļ„Ŗļ…‡ ļ„‘ļ„®ļ……ļ„²ļ„ø
ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ…ƒļ„¬ļ…žļ„Ŗļ…‚ ļ…ƒļ„ļ„’ ļ„»ļ…‰:
ā€¢ ļ„®ļ„³ļ…†ļ„® 1:
o ļ„’ļ„› ļ„µ:n1=10
o ļ„®ļ„³ļ…†ļ„® ļ„³ļ„Ŗļ„¶ļ„±:xĖ‰1=15
o ļ„šļ„ŗļ„Ŗ ļ„Ŗļ…Œ ļ„²ļ„„ļ„›ļ„© ļ„ ļ„¬ļ…‡ ļ„øļ„µļ„ ļ„ ļ„¬ ļ„¢ļ…‹ļ„æ:ļ„˜ļ…žļ„ŗ ļ„˜ļ…žļ„ŗ 1=90
ā€¢ ļ„®ļ„³ļ…†ļ„® 2:
o ļ„’ļ„› ļ„µ:n2=12
o ļ„®ļ„³ļ…†ļ„® ļ„³ļ„Ŗļ„¶ļ„±:xĖ‰2=14
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
o ļ„šļ„ŗļ„Ŗ ļ„Ŗļ…Œ ļ„²ļ„„ļ„›ļ„© ļ„ ļ„¬ļ…‡ ļ„øļ„µļ„ ļ„ ļ„¬ ļ„¢ļ…‹ļ„æ:ļ„˜ļ…žļ„ŗ ļ„˜ļ…žļ„ŗ 2 = 108
ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ 5% ļ„³ļ„»ļ…žļ„Ŗļ„ø ļ„¬ļ…‡ ļ„Æļ…žļ„­ļ„µ 'ļ„Ŗļ…‡ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„ŗļ„³ļ…‚ļ„®ļ„Ŗļ…‚ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ„¶ļ„” ļ…ƒļ„›ļ„»ļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„“ļ„» F-
ļ„„ļ…‰ļ„ŗļ„„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ļ„— ļ„“ļ…žļ„› ļ„›ļ„¶ļ…‚ļ…ƒļ„ŗļ„› ļ„¬ļ…‹-ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„»ļ…‰, ļ„“ļ…žļ„› ļ„¬ļ…‹-ļ„Æļ…‚ļ„ŗļ„æ ļ…ƒļ„øļ„›ļ„¶ļ„Æ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ī„”
ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® ļ„‘ļ„Ŗļ…‡ ļ„„ļ…‰ļ„ŗļ„„ ļ„ ļ…‹ļ„©
ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ„‘ļ„ŗļ…„
ļ„
ļ„¬ļ…‹ ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„’ļ„³ ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ ļ„Ŗļ…Œ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µ ļ„µļ„»ļ…‡ ļ„»ļ…‚ļ„, ļ„›ļ……ļ„¬ļ„µļ„Ŗļ…„ ļ„„ļ…‰ļ„ŗļ„„ ļ„‘ļ…œļ„›ļ„æļ…‚ F-
ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„»ļ…‰, ļ„¢ļ…‹ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‡ ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„øļ„¢ļ…Œ ļ„±ļ„©ļ„¬ļ…‚ ļ„»ļ…‰ī„” ļ„„ļ…‰ļ„ŗļ„„ ļ„®ļ…†ļ…œ ļ„•ļ…žļ„Æļ„µļ„¶ļ…„ ļ„Æļ…†ļ„” ļ…ƒļ„øļ…žļ„  ļ„“ļ…žļ„›-ļ„Æļ…‚ļ„ŗļ„æ ļ„µļ…žļ„œļ„©
ļ„¶ļ„” (ļ„ŗļ„»ļ…†ļ„¶ļ„Ŗ ļ„¶ļ„”), ļ„‘ļ„ŗļ…„
ļ„
ļ„øļ…žļ„§ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ„‘ļ…œļ„¹ ļ…ƒļ„øļ…žļ„  ļ„µļ…žļ„œļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„”
ļ…ƒļ„¬ļ…žļ„Ŗļ…‡ ļ„ļ„— ļ„øļ„µļ„ ļ„ ļ„¬ļ…‡ ļ„¢ļ…‹ļ„æ ļ„ ļ„Ŗļ…Œ ļ„®ļ„³ļ…†ļ„® ļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„ø ļ„ ļ„¬ļ…„ ļ„ļ„©ļ„® ļ„›ļ„µļ…‹ī„”
ļ„»ļ„µļ…‡ļ„› ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¶ļ„” ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„“ļ„» ļ„»ļ…‰:
ā€¢ ļ„®ļ„³ļ…†ļ„® 1 ļ„¶ļ„”:
ā€¢ ļ„®ļ„³ļ…†ļ„® 2 ļ„¶ļ„”:
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„‘ļ…œļ„¹ ļ„‘ļ„Ŗļ…‡ ļ„²ļ…‚ļ„¢ ļ„¶ļ„” ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„ ļ„»ļ„®:
v1=n1āˆ’1=9,v2=n2āˆ’1=11
ļ„°ļ…‰ļ„ŗļ„¶ļ…‡ ļ„¬ ļ…ƒļ„®ļ„“ļ„³ ļ„‘ļ„Ŗļ…‡ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„³ļ……ļ…žļ„¶
ļ„¢ļ„¬ļ…Œ ļ…ƒļ„› ļ„ŗļ„»ļ…„ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„¶ļ„” ļ„„ļ…‡ļ„±ļ„¶ ļ„¢ļ…‚ļ„ ļ„ŗļ…ļ„°ļ„„ļ„øļ…‡ļ„‘ļ„µ ļ„¬ļ…„ ļ„¶ļ…‹ļ„æ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰, ļ„‘ļ„ŗļ…„
ļ„
ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„µļ…ˆļ„¢ļ…‚ļ„ 'ļ„Ŗļ…‡ ļ„²ļ„µļ…‹ļ„ŗļ…‚
ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‚ļ„:
ļ„ŗļ…‚ļ„§ļ…‚ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ…„ļ„Ŗļ…‚ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„“ļ„» ļ„»ļ…‰:
ļ„˜ļ„°ā‰ˆ1.0185
ļ„“ļ„» ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„¬ļ…‹ļ„øļ…‚ļ„ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„®ļ…‚ļ„¶ļ…Œ ļ„±ļ„»ļ……ļ„Ŗ ļ„”ļ…‹ļ„„ļ…‚ ļ„»ļ…‰, ļ„“ļ„ŗ ļ„¶ļ„” ļ„“ļ„» ļ„ŗļ„Æļ…žļ„¹ļ„„ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„‘ļ„ŗļ„øļ…„ļ„›ļ…‚ļ„µ ļ„œļ…‡ļ„Ŗļ„µ
ļ…ƒļ„øļ…žļ„  ļ„¬ļ…‚ļ„œļ„¶ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ……ļ…œļ„¬ļ…‚ī„”
ļ„Æļ…„-ļ„³ļ……ļ…žļ„¶ ļ…ƒļ„¬ļ…„ļ„¹ļ„„ļ…„ļ„›ļ…‹ļ„© (ļ„‘ļ…œļ„Ŗļ„µ-ļ„‘ļ„®ļ……ļ„²ļ„ø)
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ…ƒļ„ŗļ…žļ„„ ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’
ā€¢ ļ…ƒļ„ŗļ…žļ„­ ļ„¢ļ„ø ļ„±:ļ„‘ļ„ŗļ…„
ļ„
5% ļ„Æļ…žļ„­ļ„µ 'ļ„Ŗļ…‡ ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„®ļ„»ļ…„
ļ„
ļ„›ļ„µļ„¬ļ…‡ī„”
ā€¢ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’:ļ„¬ļ…‹ ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„‘ļ…œļ„Ŗļ„µ ļ„¬ļ…‚ ļ„›ļ…‹ļ„” ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„®
ļ„ŗļ„±ļ…†ļ„Ŗ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‰ī„” ļ„¬ļ…‡ļ„œļ…‡ ļ„ļ„— ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ (1010 ļ„‘ļ„Ŗļ…‡ 9.829.82) ļ„±ļ„»ļ……ļ„Ŗ ļ„®ļ…‡ļ„æļ…‡ ļ„»ļ„®, ļ„‘ļ„Ŗļ…‡ F-ļ„‘ļ…œļ„›ļ„æļ…‚
ļ„•ļ„ŗ ļ„®ļ…‡ļ„æļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„ŗļ…œļ„œļ…‡ļ„Æ ļ…ƒļ„øļ…žļ„ : ļ„“ļ„ŗ ļ„Æļ…„ļ„“ļ…‹ļ„ ļ„¬ļ…‡ ļ„’ļ„­ļ…‚ļ„µ 'ļ„Ŗļ…‡, ļ„¬ļ…‹ļ„øļ…‚ļ„ ļ„®ļ„³ļ…†ļ…ƒļ„®ļ„’ļ„ ļ„¬ļ…„ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗļ…‚ ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„±ļ„µļ…‚ļ„±ļ„µ
ļ„¢ļ…‚ļ„Æļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„Æļ…„ļ…„ļ…ƒļ„œļ„’ ļ„¬ļ…„ ļ„ŗļ„Æļ…žļ„¹ļ„„ļ„Ŗ ļ„¶ļ„” ļ„›ļ„¬ļ„³-ļ„¬ļ„µ-ļ„›ļ„¬ļ„³ ļ„ŗļ…œļ„œļ…‡ļ„Æ
ā€¢ ļ„‘ļ…œļ…ƒļ„Ŗļ„³ ļ…ƒļ„±ļ„’ļ„®:5% ļ„Æļ…žļ„­ļ„µ 'ļ„Ŗļ…‡, ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„³ļ…œļ…ƒļ„®ļ„’ ļ„¢ļ…‚ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„­ ļ„µļ„® ļ„ø ļ„ ļ„‘ļ„Ŗļ…‡ ļ„ ļ…œļ„ļ…‡ ļ„‘ļ…ƒļ„²ļ„’ļ„ŗ ļ„®ļ…‹ļ„„ļ„ŗ
F-ļ„„ļ…‰ļ„ŗļ„„ ļ„®ļ…†ļ…œ ļ„øļ…‰ļ„­ ļ„±ļ„©ļ…‚ļ„•ļ„© ļ„¶ļ„”, ļ„›ļ……ļ„£ ļ„¹ļ„µļ„Ŗļ…‚ļ„ ļ„¬ļ…‚ ļ„Æļ…‚ļ„¶ļ„© ļ„›ļ…„ļ„Ŗļ…‚ ļ„¢ļ…‚ļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‚ ļ„»ļ…‰:
ā€¢ ļ„’ļ„¾ ļ„¬ļ…„:
o ļ„¬ļ…‹ļ„øļ…ˆ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„“ļ…žļ„› ļ„¬ļ…†ļ„¢ļ…‡ ļ„Ŗļ…Œ ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„»ļ…‹ļ„©ļ…‡ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„ŗ ļ„­ ļ„µļ„®ļ„Ŗ :
o ļ„»ļ„µļ…‡ļ„› ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ„¶ļ„ļ„²ļ„ ļ„’ļ„³ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„øļ…œļ„§ļ…„ ļ„¢ļ…‚ļ„©ļ…„ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…„ ļ„»ļ…‰ī„” ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…„ ļ„ŗļ„³ļ…‚ļ„®ļ„Ŗļ…‚ ļ„¶ļ„”
F-ļ„„ļ…‰ļ„ŗļ„„ ļ„ļ…‰ļ„µ-ļ„ŗļ„­ļ…‚ļ„µļ„®ļ„Ŗļ…‚ ļ„Æļ…„ļ„Ŗļ…„ ļ„ŗļ…œļ„øļ…‡ļ„¬ļ„®ļ„¹ļ…„ļ„¶ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰; ļ…ƒļ„Ŗļ„µļ„”ļ…‡ ļ„øļ…œļ„§ļ…‚ļ„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶, ļ„¶ļ…‡ļ„øļ…‡ļ„® ļ„¢ļ…‚ļ„ ļ„±ļ…„ļ…‚ļ„–ļ„®-
ļ„°ļ…‹ļ„µļ„ŗļ…„ļ„« ļ„„ļ…‰ļ„ŗļ„„ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„‘ļ„›ļ„ŗļ„µ ļ„Ŗļ„µļ„¢ļ…„ļ„» ļ…ƒļ„¬ļ…žļ„Ŗļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ī„” ļ„±ļ„»ļ……ļ„Ŗ ļ„ŗļ…‚ļ„µļ…„ļ„’ļ„ ļ„Æļ…„ļ„“ļ…‹ļ„ļ„¹ļ…‚ļ„¶ļ…‚ ļ„ŗļ…‰ļ…ƒļ„„ļ…œļ„ļ…‚ļ„
ļ„¶ļ„”, ļ„ŗļ„­ļ…‚ļ„µļ„©ļ„Ŗļ…‚ ļ„“ļ…žļ„› ļ„øļ…‚ļ„¢ļ„± ļ„›ļ…‚ļ„µļ„¢ļ„¹ļ…„ļ„¶ ļ„­ļ…‚ļ„µļ„®ļ…‚ ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ā€¢ ļ„³ ļ„Æ ļ„ļ……ļ„©ļ„øļ…žļ„Ŗ :
o ļ„“ļ„›ļ…„ļ„®ļ…„ ļ„±ļ„©ļ…‚ļ„™ ļ…ƒļ„› ļ…ƒļ„¬ļ…žļ„Ŗļ…‡ ļ„ļ„— ļ„øļ„µļ„ļ…‚ļ„ ļ„¬ļ…‡ ļ„¢ļ…‹ļ„æļ…‚ļ„ ļ„¬ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„ŗļ…œļ„±ļ…œļ…ƒļ„­ļ„Ŗ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¬ļ…‡ ļ„ŗļ…‚ļ„­ļ„®ļ…‚ļ„ ļ„Ŗļ…Œ
ļ„²ļ„„ļ„›ļ„© ļ„øļ„¢ļ…Œ ļ„›ļ…„ļ„Ŗļ…„ ļ„ļ„” ļ„»ļ…‰; ļ„Ŗļ……ļ„ŗļ…„
ļ„
SS ļ„®ļ…†ļ…œ S2 ļ…ƒļ„øļ…žļ„  ļ„±ļ„¬ļ„¶ļ„¬ļ…‡ ļ„ŗļ„³ļ…ˆ ļ„“ļ„» ļ„ŗļ„»ļ…„ ļ„Øļ…œļ„ ļ„®ļ…‚ļ„¶ ļ„›ļ…„ļ„Ŗļ…‚ ļ„ŗļ…„ī„”
ā€¢ ļ„Æļ…„ļ„ŗļ…œļ„ ļ„³ ļ„“ļ„®ļ…‡ ļ„µļ…žļ„œļ„¬ ļ„»ļ…‰:
o ļ„²ļ…‚ļ„øļ…ˆ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„„ļ…‰ļ„ŗļ„„ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…„ ļ„ŗļ„³ļ…‚ļ„®ļ„Ŗļ…‚ ļ„¬ļ…‚ ļ„ŗļ……ļ„£ļ…‚ļ„‘ ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰, ļ…ƒļ„øļ„»ļ…‚ļ„µļ„› ļ…ƒļ„øļ„ ļ…‚ļ„µ (ļ„“ļ…œļ„Ŗļ„µ
ļ„¹ļ……ļ…žļ„­ļ„Ŗļ…‚, ļ„Æļ…„ļ„“ļ…‹ļ„ļ…‚ļ„Ŗļ„³ļ„› ļ„ŗļ…‰ļ…žļ„„ļ„‘ļ…žļ„Æ) ļ„‘ļ„¢ļ…‡ ļ„øļ…„ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ…ƒļ„øļ„›ļ„¶ļ„Æļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„Æļ…„ļ„²ļ…‚ļ„øļ„Ŗ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ„®,
ļ…ƒļ„¢ļ„øļ…ˆ ļ…ƒļ„› ļ„›ļ…„ ļ„±ļ…‚ļ„‘ļ„¬ ļ„¬ļ…‡ ļ„„ļ…„-ļ„„ļ…‰ļ„ŗļ„„ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„Æļ…†ļ„¶ ļ„›ļ„µļ„®ļ…‚ ļ„»ļ…‰ī„”
ļ„›ļ…‹ļ„³ļ„¶ ļ…ƒļ„±ļ„µļ„Ŗ ļ„ļ„Ŗļ„› ļ„ŗļ„³ ļ„®ļ„Ŗ
ļ„¬ļ…‹ ļ„„ļ…„ļ…‡ļ„’ļ„ 'ļ„Ŗļ…‡ ļ„”ļ…‹ļ„„ļ…‡ ļ„³ļ„©ļ…ƒļ„›ļ„’ļ„ ļ„¬ļ…‡ "ļ…ƒļ„œļ…œļ„§ļ„©" ļ„øļ…‚ļ„ļ„ ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„±ļ…‚ļ„µļ…‡ ļ„ŗļ…‹ļ„ ļ…‹ī„” ļ„¢ļ…‡ļ„›ļ„µ ļ„“ļ…žļ„› ļ„„ļ…„ļ…‡ ļ„¬ļ…‡ ļ„³ļ„©ļ„›ļ…‡ ļ„¬ļ…†ļ„¢ļ…‡ ļ„¬ļ…‡ ļ„›ļ…ˆļ„¬ļ„µ ļ„Ŗļ…Œ ļ„«ļ…‹ļ„æļ…‡
ļ„¬ļ…†ļ„µ ļ„±ļ…‰ļ„¦ļ„¬ļ…‡ ļ„»ļ„®, ļ„Ŗļ…‚ļ„ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„ŗļ…‹ļ„  ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‹: ļ„›ļ…„ ļ„•ļ„» ļ„”ļ…‹ļ„„ļ…‚ ļ…ƒļ„¢ļ„»ļ…‚ ļ„‘ļ…œļ„Ŗļ„µ ļ„‘ļ„ŗļ„¶ļ…„ ļ„»ļ…‰, ļ„¢ļ…‚ļ„ ļ…ƒļ„ŗļ„µļ…€ ļ„³ļ…ļ„›ļ…‚ ļ„¬ļ…‡ ļ„›ļ…‚ļ„µļ„®? F-
ļ„„ļ…‰ļ„ŗļ„„ ļ„“ļ…žļ„› ļ„³ļ…‚ļ„Æļ„© ļ„øļ…‚ļ„¶ļ…‚ ļ„°ļ„µļ…‡ļ„³ ļ„µļ…žļ„œļ„¬ļ…‚ ļ„»ļ…‰, ļ„ŗļ„Æļ…„ļ…‰ļ„§ļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ ļ„›ļ…ƒļ„»ļ…œļ„¬ļ…‚ ļ„»ļ…‰, "ļ„“ļ„» ļ„‘ļ…œļ„Ŗļ„µ 5% ļ„Æļ…žļ„­ļ„µ
'ļ„Ŗļ…‡ ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„‘ļ„ŗļ„¶ļ…„ ļ„›ļ…ƒļ„»ļ„© ļ„¶ļ„” ļ„±ļ„»ļ……ļ„Ŗ ļ„”ļ…‹ļ„„ļ…‚ ļ„»ļ…‰ī„”" ļ„ŗļ…‚ļ„§ļ…‡ ļ„³ļ…‚ļ„³ļ„¶ļ…‡ ļ…ƒļ„øļ…žļ„ , ļ„ŗļ„Æļ…„ļ…‰ļ„§ ļ„¶ļ„ļ„²ļ„ ļ„¢ļ……ļ„æļ„øļ…‚ļ„ ļ„»ļ„® - ļ„“ļ…œļ„®ļ…‡ ļ„®ļ…‡ļ„æļ…‡ ļ…ƒļ„›
ļ„„ļ…‰ļ„ŗļ„„ ļ„›ļ…ƒļ„»ļ…œļ„¬ļ…‚ ļ„»ļ…‰, "ļ„•ļ„®ļ…§ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„ŗļ„³ļ„£ļ…‹ī„”"
ļ„“ļ„» ļ„‘ļ…žļ„ļ…‡ ļ„›ļ…„ ļ„ŗļ„³ļ„µļ…žļ„« ļ„±ļ„© ļ„•
ļ„
ļ„¬ ļ„»ļ…‰
ļ…ƒļ„›ļ„•
ļ„
ļ…ƒļ„› ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„ŗļ„³ļ…‚ļ„®ļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„®ļ„»ļ…„
ļ„
ļ„›ļ…„ļ„Ŗļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚:
ā€¢ ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„» ļ„§ ļ„‘ļ„ļ„¶ ļ„›ļ„¬ļ„³ ļ„ŗ ļ„­ļ„® ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„® ļ„›ļ„µļ„® ļ„»ļ…‰,ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„Æļ…†ļ„¶ļ„§-ļ„øļ…‡ļ„µļ…„ļ„˜ļ„ļ„ŗ ļ„„ļ…„-ļ„„ļ…‰ļ„ŗļ„„
ļ„®ļ…‚ļ„¶ ļ„‘ļ…žļ„ļ…‡ ļ„øļ„­ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‹ (ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„øļ…‡ļ„µļ…„ļ„˜ļ„ļ„ŗ ļ„­ļ…‚ļ„µļ„®ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‡ ļ„Ŗļ…ƒļ„»ļ„Ŗ ļ„¬ļ…‹-ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ…ƒļ„øļ…žļ„ 
ļ„’ļ„³)ī™€
ā€¢ ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„²ļ…ƒļ„øļ…žļ„œ ļ„¬ļ…‡ ļ„Æļ…„ļ„“ļ…‹ļ„ ļ„ ļ„®ļ…†ļ…œ ļ…ƒļ„§ļ„¾ ļ„”ļ„® ļ„›ļ„µ ļ„µļ„»ļ…‡ ļ„»ļ…‹,ļ„“ļ„» ļ„®ļ„Ŗļ…„ļ„¢ļ…‚ ļ„ŗļ…ƒļ„«ļ„Ŗļ…„ļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„Æļ…„ļ„“ļ…‹ļ„ļ…‚ļ„Ŗļ„³ļ„›
ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗļ…‚ ļ…ƒļ„øļ…žļ„  ļ„“ļ„›ļ„ŗļ…‚ļ„µļ„Ŗļ…‚ ļ„¬ļ…‚ ļ„ŗļ……ļ„£ļ…‚ļ„‘ ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰, ļ„¢ļ…‹ ļ…ƒļ„› ļ„¢ļ…‚ļ„©ļ„›ļ…‚ļ„µļ…„ ļ„®ļ…†ļ…œ ļ„“ļ„›ļ…žļ„¦ļ…‚ ļ„›ļ„µļ„® ļ„‘ļ„Ŗļ…‡ ļ„¹ļ…‹ļ„µ
ļ„žļ„„ļ…‚ļ„•ļ„© ļ„¶ļ„” ļ„²ļ„µļ…‹ļ„ŗļ…‚ ļ„¬ļ…‡ļ„© ļ„øļ…‚ļ„¶ļ…‚ ļ„»ļ…‰ī„”
ļ„‘ļ…œļ…ƒļ„Ŗļ„³ ļ„°ļ…‰ļ„ŗļ„¶
ā€¢ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’:ļ„“ļ„ŗ ļ„ļ…žļ„¶ ļ„¬ļ…‚ ļ„›ļ…‹ļ„” ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„ŗļ„±ļ…†ļ„Ŗ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‰ ļ…ƒļ„› ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„øļ…žļ„œļ„µļ…„ļ„’ļ„ ļ„»ļ„®; ļ„±ļ…‚ļ„‘ļ„¬ ļ„¬ļ…‡
ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„¶ļ„” ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„ŗļ„³ļ„£ļ…‹ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„ŗļ…‰ļ„›ļ„¹ļ„®-ļ„§ļ…„
7. ļ„“ļ…žļ„› ļ„„ļ„µļ…žļ…ƒļ„›ļ…œļ„ ļ„›ļ…œļ„Æļ„®ļ…„ ļ„  ļ„µ ļ„±ļ…„ ļ„ļ„§ ļ„ ļ„¬ļ…‡ ļ„„ ļ„“ļ„µ ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„»ļ„µļ…‡ļ„› ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„•ļ„³ļ„µ ļ„¬ļ…„ ļ„¢ ļ„ļ„  ļ„›ļ„µļ„® ļ„  ļ„»ļ……ļ…œļ„¬ļ…„
ļ„»ļ…‰ī„” ļ„›ļ…œļ„Æļ„®ļ…„ ļ„ŗ ļ„µļ…‡ ļ„±ļ…„ ļ„ļ„§ ļ„ ļ„®ļ…†ļ…œ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„±ļ…‡ ļ„ ļ……ļ„©ļ…‡ ļ„»ļ…‹ļ„— ļ„„ļ„µļ…žļ„› ļ„ 'ļ„Ŗļ…‡ ļ„øļ„µļ„Ŗļ„¬ļ…„ ļ„»ļ…‰ī„” ļ…ƒļ„¾ļ…œļ„¬ļ„ļ…„ļ„’ļ„ (ļ„»ļ„¾ ļ„µ ļ„ ļ„³ļ…„ļ„¶)
ļ„¬ļ„µļ„ŗ ļ„•ļ„© ļ„ø ļ„¶ļ…‡ ļ…ƒļ„µļ„› ļ„µļ„§ ļ„»ļ…‡ļ„¦ ļ„ ļ…ƒļ„¬ļ…žļ„Ŗļ…„ ļ„ŗ ļ„µļ„©ļ…„ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„¬ļ…žļ„Ŗļ…‡ ļ„ļ„— ļ„»ļ„®:
ļ„±ļ…„ ļ„ļ„§ 1
ļ„±ļ…„ ļ„ļ„§ 2
ļ„±ļ…„ ļ„ļ„§ 3
ļ„±ļ…„ ļ„ļ„§ 4
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ļ„“ļ„ŗ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® ļ„¬ļ…„ ļ„¢ ļ„ļ„  ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„»ļ„µļ…‡ļ„› ļ„±ļ…„ ļ„ļ„§ ļ„¬ļ…‡ ļ„„ ļ„“ļ„µ ļ„ ļ„¬ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…„ļ„øļ„® ļ„“ļ…žļ„›ļ…‹ ļ…ƒļ„¢ļ„» ļ„»ļ……ļ…œļ„¬ ļ„»ļ…‰ī„”
ļ„•ļ…žļ„Ŗļ„µ:ļ„„ ļ„“ļ„µ ļ„ ļ„¬ļ…‡ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…„ļ„øļ„® ļ„¬ļ…„ ļ„ŗļ„³ ļ„®ļ„Ŗ ļ„¬ļ…„ ļ„¢ ļ„ļ„ : ļ„  ļ„µ ļ„±ļ…„ ļ„ļ„§ ļ„ ļ„¬ļ…„ ļ„›ļ„» ļ„©ļ…„
ļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„„ļ„µļ…žļ…ƒļ„›ļ…œļ„ ļ„›ļ…œļ„Æļ„®ļ…„ ļ„¬ļ…‡ ļ„³ļ…‚ļ„¶ļ„› ļ„»ļ…‹, ļ„¢ļ…‹ ļ„¬ļ…‡ļ„¹ ļ„²ļ„µ ļ…ƒļ„øļ…žļ„  ļ„žļ……ļ…œļ„³ļ„¬ļ…‡ ļ„„ļ„µļ…žļ„›ļ…‚ļ„ ļ„¬ļ…‡ ļ„±ļ…‡ļ„æļ…‡ ļ„¶ļ„”
ļ…ƒļ„¾ļ…œļ„³ļ…‡ļ„øļ…‚ļ„µ ļ„»ļ…‰ī„” ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„›ļ…‚ļ„µļ…‹ļ„±ļ…‚ļ„µ ļ„›ļ……ļ„¹ļ„¶ļ„Ŗļ…‚ 'ļ„Ŗļ…‡ ļ„øļ„­ļ„¬ļ…‚-ļ„°ļ……ļ…žļ„¶ļ„¬ļ…‚ ļ„»ļ…‰, ļ„‘ļ„Ŗļ…‡ ļ„»ļ„µ ļ„¬ļ…‡ļ„µļ…„ ļ„¢ļ…‚ļ„ ļ„„ļ……ļ…žļ„„ļ„© ļ„®ļ…‚ļ„¶ ļ„Æļ…‰ļ„ŗļ…‚ ļ„‘ļ„Ŗļ…‡ ļ„ŗļ…‚ļ„œ
ļ„¬ļ…‹ļ„øļ…ˆ ļ„»ļ…„ ļ„œļ„µļ„  ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„»ļ„µ ļ„›ļ……ļ„£ ļ„ŗļ…‚ļ„¶ļ…‚ļ„ ļ„±ļ…‚ļ„‘ļ„¬ ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„ŗļ…‚ļ„»ļ„³ļ„©ļ…‡ ļ„’ļ„•ļ„© ļ„øļ…‚ļ„¶ļ…‡ ļ„ŗļ„² ļ„Ŗļ…Œ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„°ļ…‰ļ„ŗļ…ƒļ„¶ļ„’ļ„
ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„“ļ…žļ„› ļ„“ļ„» ļ„»ļ…‰: ļ„³ļ…‰ļ„®ļ…†ļ…œ ļ„’ļ„Æļ„©ļ…‡ ļ„„ļ„µļ…žļ„›ļ…‚ļ„ 'ļ„Ŗļ…‡ ļ…ƒļ„›ļ„»ļ„æļ…‡ ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„¬ļ…‡ ļ„„ļ…‚ļ„“ļ„µ ļ„øļ„µļ„Ŗļ„©ļ…‡ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‡ ļ„»ļ„®? ļ„’ļ„¼ļ„µļ„›ļ…‚ļ„µ, ļ„„ļ…‚ļ„“ļ„µ
ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„øļ…‚ļ„»ļ„®ļ…‚ļ„ ļ„¬ļ…„ ļ„¢ļ…„ļ„øļ„® ļ„µļ…‡ļ„œļ…‚ ļ„»ļ„®ī„” ļ„“ļ…žļ„› ļ„„ļ…‚ļ„“ļ„µ ļ„¢ļ…‹ ļ„±ļ„»ļ……ļ„Ŗ ļ„¢ļ„¶ļ„¬ļ…„ ļ„œļ„µļ…‚ļ„± ļ„»ļ…‹ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰, ļ„®ļ…‚ ļ…ƒļ„ŗļ„µļ…€ ļ„ŗļ……ļ„µļ…žļ…ƒļ„œļ„’ ļ„®ļ…†ļ…œ
ļ„Æļ…„ļ„²ļ…‚ļ…ƒļ„øļ„Ŗ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ„±ļ„¶ļ…ƒļ„› ļ„µļ…žļ„œ-ļ„µļ„œļ…‚ļ„‘ ļ„¬ļ…„ ļ„¶ļ…‚ļ„ļ„Ŗ ļ„®ļ…†ļ…œ ļ„øļ…„ ļ„øļ„­ļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„»ļ……ļ„©, ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ„ ļ…‚ļ„µ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ„¬ļ…‡ ļ„„ļ…‚ļ„“ļ„µļ…‚ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„“ļ…žļ„› ļ…ƒļ„øļ„›ļ„¶ļ„Æ ļ„Æļ…‡ļ„¹ ļ„›ļ…„ļ„Ŗļ…‚ ļ…ƒļ„ļ„’ ļ„»ļ…‰ī„” ļ„»ļ„µļ…‡ļ„› ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„øļ„­ļ…„ļ„’ ļ…ƒļ„„ļ„›ļ…‚ļ„–ļ„Ŗļ…‚ ļ„¬ļ…‚
ļ„¬ļ…‚ļ„‘ļ„øļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰, ļ„Æļ„µ ļ„³ļ…‚ļ„µļ„›ļ…„ļ…ƒļ„„ļ…œļ„ ļ„øļ…‚ļ„‘ļ„¬ļ…‡ ļ„»ļ„³ļ…‡ļ„¹ļ…‚ ļ„»ļ„›ļ…„ļ„›ļ„Ŗ ļ„®ļ…‚ļ„¶ ļ„³ļ…‡ļ„¶ ļ„®ļ„»ļ…„
ļ„
ļ„œļ…‚ļ„ļ„¬ļ…‡ī„” ļ„“ļ…žļ„› ļ„ŗļ…†ļ…ƒļ„ ļ„Ŗ ļ„°ļ…‰ļ„ŗļ„¶ļ…‚ ļ„¶ļ…‰ļ„©
ļ„¶ļ„”, ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„»ļ„µļ…‡ļ„› ļ„„ļ…‚ļ„“ļ„µ ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„¬ļ…‡ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…„ļ„øļ„® ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ„¬ļ…‚ ļ„°ļ…‰ļ„ŗļ„¶ļ…‚ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ī„” ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„ŗļ…‚ļ„µļ…‡ ļ„ ļ…‚ļ„µ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ„®ļ…†ļ…œ
ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„±ļ…‡ ļ„ ļ……ļ„©ļ…‡ ļ„»ļ…‹ļ„— ļ„„ļ„µļ…žļ„›ļ…‚ļ„ 'ļ„Ŗļ…‡ ļ„ŗļ„«ļ…‚ļ…ƒļ„Æļ„Ŗ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ ļ„‘ļ„Ŗļ…‡ ļ„»ļ„¾ļ…‚ļ„µļ…‚ļ„ ļ„³ļ…„ļ„¶ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„•ļ„®ļ…§ļ…‚ļ„ ļ„¬ļ…‡ ļ„¢ļ…„ļ„øļ„® ļ„®ļ…†ļ…œ ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶
ļ…ƒļ„µļ„›ļ…‚ļ„µļ„§ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‹ī„” ļ„³ļ„»ļ…„ļ…ƒļ„®ļ„’ļ„ ļ„¬ļ…„ ļ…ƒļ„®ļ„ļ„µļ…‚ļ„®ļ…„ ļ„Ŗļ…Œ ļ„±ļ…‚ļ„‘ļ„¬, ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‚ ļ„§ļ…‡ļ„„ļ…‚ ļ„“ļ„ŗ ļ„Ŗļ„µļ…§ļ…‚ļ„ ļ…ƒļ„¬ļ„œļ…‚ļ„” ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰:
ļ„±ļ…„ ļ„ļ„§ 1
ļ„±ļ…„ ļ„ļ„§ 2
ļ„±ļ…„ ļ„ļ„§ 3
ļ„±ļ…„ ļ„ļ„§ 4
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ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„»ļ……ļ„© ļ„ŗļ„øļ…‚ļ„¶ ļ„“ļ„» ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ„“ļ„» ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…„ļ„øļ„® ļ…ƒļ„øļ…žļ„  ļ„ŗļ…žļ„ ļ„³ļ……ļ…žļ„  ļ„øļ…žļ„œļ„µļ…‡ ļ„»ļ„®, ļ„¢ļ…‚ļ„ ļ„›ļ…„ ļ„“ļ„» ļ„‘ļ…œļ„Ŗļ„µ ļ„‘ļ„ŗļ…„
ļ„
ļ…ƒļ„ŗļ„µļ…€
ļ„‘ļ„ ļ…‚ļ„®ļ„› ļ„³ļ…ļ„›ļ…‚ļ„Æļ…„ļ„ŗļ„Ŗļ…„ ļ„›ļ„µļ„›ļ…‡ ļ„¬ļ…‡ļ„œļ„¬ļ…‡ ļ„»ļ…‚ļ„?
ļ„“ļ„ŗļ„¬ļ…‚ ļ„¢ļ„øļ…‚ļ„± ļ„¬ļ…‡ļ„© ļ„¶ļ„”, ļ„‘ļ„ŗļ…„
ļ„
ļ„“ļ…žļ„› ļ„¹ļ„›ļ„Ŗļ…„ļ„¹ļ…‚ļ„¶ļ…„ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„ŗļ…œļ„¬ ļ„øļ…žļ„¶ ļ„³ļ……ļ„æļ„¬ļ…‡ ļ„»ļ…‚ļ„ ļ…ƒļ„¢ļ„ŗļ„®ļ…†ļ…œ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„’ļ…€
ļ„øļ…‡ļ„µļ…„ļ„˜ļ„ļ„ŗ (ANOVA) ļ…ƒļ„›ļ„»ļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„” ANOVA ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„¬ļ…‹ ļ„Ŗļ…Œ ļ„øļ…žļ„­ ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ„¬ļ…‡ ļ„ŗļ…‚ļ„­ļ„®ļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„¬ļ…„ ļ„’ļ…ƒļ„ļ„’
ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ„Ŗļ…‚ļ„ ļ„¢ļ…‹ ļ„“ļ„» ļ„¬ļ…‡ļ…ƒļ„œļ„’ ļ„¢ļ…‚ ļ„ŗļ„›ļ…‡ ļ…ƒļ„› ļ„›ļ…„ ļ„•ļ„»ļ„®ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„›ļ…‹ļ„” ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„‘ļ…œļ„Ŗļ„µ ļ„»ļ…‰ī„” ļ„“ļ„ŗ ļ„ŗļ…ƒļ„«ļ„Ŗļ…„ ļ…ƒļ„øļ…žļ„ , ļ„ŗļ…‚ļ„§ļ…‡
ļ„ ļ…‚ļ„µ ļ„ŗļ„³ļ…†ļ„» ļ„ ļ…‚ļ„µ ļ„„ļ…‚ļ„“ļ„µ ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„»ļ„®ī„”
ļ„›ļ„¬ļ„³ 1: ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® ļ„®ļ…†ļ…œ ļ„ŗļ„³ļ„£ļ„©
ļ…ƒļ„›ļ„ŗļ…‡ ļ„øļ…„ ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„„ļ…‰ļ„ŗļ„„ ļ…ƒļ„øļ…žļ„  ļ„Æļ…ƒļ„»ļ„¶ļ…‚ ļ„›ļ„¬ļ„³ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ļ„øļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ„Æļ„¹ļ„„ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ…ƒļ„±ļ„’ļ„® ļ„›ļ„µļ„®ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰:
ā€¢ ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® (Hā‚€):ļ„ ļ…‚ļ„µļ…‚ļ„ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ„¬ļ…‡ ļ„„ļ…‚ļ„“ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„•ļ„³ļ„µ ļ„“ļ…žļ„›ļ…‹ ļ…ƒļ„¢ļ„»ļ…„ ļ„»ļ…‰ī„” ļ„ļ…ƒļ„©ļ…ƒļ„Ŗļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡,
ā€¢ ļ…ƒļ„øļ„›ļ„¶ļ„Æļ„› ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„® (Hā‚):ļ„žļ…žļ„„ļ…‹-ļ„žļ…žļ„„ ļ„“ļ…žļ„› ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ…ƒļ„¾ļ…œļ„¬ļ„ļ…„ ļ„¬ļ…†ļ…ƒļ„¢ļ„’ļ„ ļ„Ŗļ…Œ ļ„øļ…žļ„œļ„µļ…„ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„‘ļ„¬ļ…‚ļ„¶ļ„Ŗļ…„ ļ„³ļ……ļ„›ļ…žļ„¬ļ„³ļ…‡ ļ„øļ…‚ļ„ļ„ ļ„ŗļ…‹ļ„ ļ…‹ī„” ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„¬ļ…‹ļ„¹ļ…„ ļ„ŗļ…‚ļ„±ļ„Ŗ ļ„»ļ…‹ļ„© ļ„Ŗļ…žļ„› ļ…ƒļ„®ļ„µļ„¬ļ…‹ļ„¹ ļ„»ļ…‰ī„” ļ„‘ļ„ŗļ…„
ļ„
ļ„³ļ…œļ„®ļ„¬ļ…‡ ļ„»ļ…‚ļ„ ļ…ƒļ„›
ļ„ŗļ…‚ļ„µļ…‡ ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„»ļ„® ļ„¢ļ„¬ļ…Œ ļ„Ŗļ…žļ„› ļ…ƒļ„› ļ„§ļ…‡ļ„„ļ…‚ ļ„ŗļ…‚ļ„®ļ…†ļ…œ ļ„»ļ…‹ļ„µ ļ„¦ļ…‹ļ„ŗ ļ„ŗļ„±ļ…†ļ„Ŗ ļ„®ļ„»ļ…„
ļ„
ļ…ƒļ„¬ļ…œļ„¬ļ…‚ī„”
ļ„›ļ„¬ļ„³ 2: ļ„§ļ…‡ļ„„ ļ„®ļ…†ļ…œ ļ…ƒļ„øļ„øļ„ŗļ…ƒļ„«ļ„Ŗ ļ„›ļ„µļ„®
ļ„ŗļ…‚ļ„§ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„ŗļ„µļ„¶ ļ„±ļ„©ļ…‚ļ„•ļ„© ļ„¶ļ„”, ļ„’ļ„™ ļ„»ļ„µļ…‡ļ„› ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„¶ļ„” ļ„§ļ…‡ļ„„ļ…‚ ļ„®ļ…†ļ…œ ļ„ŗļ„Æļ„¹ļ„„ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ…ƒļ„¶ļ„œļ…„ļ„—:
ā€¢ ļ„±ļ…„ļ…‚ļ„ļ„§ 1: 20, 23, 18, 17
ā€¢ ļ„±ļ…„ļ…‚ļ„ļ„§ 2: 19, 15, 17, 20, 16
ā€¢ ļ„±ļ…„ļ…‚ļ„ļ„§ 3: 21, 19, 20, 17, 16
ā€¢ ļ„±ļ…„ļ…‚ļ„ļ„§ 4: 15, 17, 16, 18
ļ…ƒļ„­ļ„’ļ„® ļ…ƒļ„¬ļ„™ ļ…ƒļ„› ļ„ŗļ…‚ļ„µļ…‡ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ„›ļ…‹ļ„¶ ļ„“ļ…žļ„›ļ…‹ ļ…ƒļ„¢ļ„»ļ…‡ ļ…ƒļ„®ļ„µļ…„ļ„œļ„© ļ„®ļ„»ļ…„
ļ„
ļ„»ļ……ļ…œļ„¬ļ…‡ī„” ļ„“ļ„ŗļ„®ļ…†ļ…œ ļ„‘ļ„ŗļ…œļ„Ŗļ……ļ…ƒļ„¶ļ„Ŗ ļ…ƒļ„§ļ„¾ļ…‚ļ„”ļ„® ļ…ƒļ„›ļ„»ļ…‚ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰,
ļ„Æļ„µ ļ„ŗļ„µļ„¶ļ„Ŗļ…‚ ļ„¶ļ„”, ļ„‘ļ„ŗļ…„
ļ„
ļ„‘ļ„¢ļ…‡ ļ„øļ…„ ļ…ƒļ„³ļ„’ļ„µļ…„ ļ„°ļ…‚ļ„µļ„³ļ…†ļ…ƒļ„¶ļ„’ļ„ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„›ļ…‡ ANOVA ļ„¶ļ…‚ļ„ļ…† ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„”
ļ„›ļ„¬ļ„³ 3: ļ„ŗ ļ„­ļ„® ļ„ ļ„¬ļ…„ ļ„ļ„©ļ„® ļ„›ļ„µļ„®
ļ„‘ļ„ļ„¶ļ…‚ ļ„›ļ„¬ļ„³ ļ„»ļ„µļ…‡ļ„› ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„¶ļ„” ļ„„ļ…‚ļ„“ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ (ļ„šļ„ŗļ„Ŗ ļ„•ļ„³ļ„µ) ļ„¬ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ„®ļ…‚ ļ„»ļ…‰ī„” ļ„’ļ„™ ļ„•ļ„®ļ…§ļ…‚ļ„ ļ„¬ļ…„
ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ…„ļ„—:
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
1. ļ„±ļ…„ ļ„ļ„§ 1 ļ„¬ ļ„³ļ„Ŗļ„¶ļ„±:
2. ļ„±ļ…„ ļ„ļ„§ 2 ļ„¬ ļ„³ļ„Ŗļ„¶ļ„±:
3. ļ„±ļ…„ ļ„ļ„§ 3 ļ„¬ ļ„³ļ„Ŗļ„¶ļ„±:
4. ļ„±ļ…„ ļ„ļ„§ 4 ļ„¬ ļ„³ļ„Ŗļ„¶ļ„±:
ļ„‘ļ…œļ„Ŗ ļ…ƒļ„øļ…žļ„ , ļ„‘ļ„ŗļ…„
ļ„
ļ„ŗļ…‚ļ„µļ…‡ ļ…ƒļ„®ļ„µļ…„ļ„œļ„©ļ…‚ļ„ ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ, ļ…ƒļ„øļ„¹ļ…‚ļ„¶ ļ„šļ„ŗļ„Ŗ ļ„¬ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‚ļ„:
ļ„ļ…„ļ…Šļ„§ ļ„³ļ…„ļ„§ļ…„ļ„‘ļ„³ ļ„„ļ…‚ļ„“ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ„ŗļ„³ļ……ļ…žļ„ ļ…„ ļ„šļ„ŗļ„Ŗ ļ„•ļ„³ļ„µ ļ„®ļ…†ļ…œ ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…‚ ļ„»ļ…‰, ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„¬ļ…‡ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ„®ļ„¾ļ„µļ„‘ļ…œļ„¬ļ…‚ļ„¾ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„›ļ„¬ļ„³ 4: ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗ ļ„¬ ļ…ƒļ„øļ„² ļ„¢ļ„® ļ„›ļ„µļ„®
ANOVA ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗļ…‚ ļ„¬ļ…‡ ļ„¬ļ…‹ ļ„ŗļ„µļ…‹ļ„Ŗļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„›ļ…‡ ļ„›ļ…œļ„³ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰:
1. ļ…ƒļ„øļ„ ļ„› ļ„µ-ļ„ŗļ„³ļ…†ļ„» ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗ (SSB):ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± ļ„ļ…„ļ…Šļ„§ ļ„³ļ…„ļ„§ ļ„Ŗļ…Œ ļ…ƒļ„›ļ…œļ„®ļ…‚ ļ„øļ…žļ„œļ„µļ…‚ ļ„»ļ…‰ī„”
2. ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗ (SSW):ļ…ƒļ„øļ„‘ļ„›ļ„Ŗļ…„ļ„ļ„Ŗ ļ„„ļ…‚ļ„“ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ…ƒļ„¾ļ…œļ„¬ļ„ļ…„ ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„¬ļ…‡ ļ„’ļ„Æļ„©ļ…‡
ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„¬ļ…‡ ļ„šļ„ŗļ„Ŗ ļ„Ŗļ…Œ ļ…ƒļ„›ļ…œļ„®ļ…„ ļ„øļ…žļ„œļ„µļ…„ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„›ļ„¬ļ„³ 4a: ļ„øļ„µļ„ ļ„ ļ„¬ļ…‡ ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…‡ ļ…ƒļ„øļ„ ļ„› ļ„µ ļ„¢ļ…‹ļ„æ (SSB)
ļ„°ļ…‚ļ„µļ„³ļ…†ļ„¶ļ…‚ ļ„“ļ„» ļ„»ļ…‰:
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ…ƒļ„›ļ…žļ„«ļ…‡:
ļ„›ļ„¬ļ„³ ļ„¬ļ„µ ļ„›ļ„¬ļ„³ ļ„ļ„©ļ„®ļ…‚:
ļ„›ļ„¬ļ„³ 4b: ļ„øļ„µļ„ ļ„ ļ„¬ļ…‡ ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ„¢ļ…‹ļ„æ (SSW)
ļ„°ļ…‚ļ„µļ„³ļ…†ļ„¶ļ…‚ ļ„“ļ„» ļ„»ļ…‰:
ļ„›ļ„¬ļ„³ 5: F-ļ„ŗļ„„ļ…‰ļ…ƒļ„„ļ„ŗļ…ƒļ„„ļ„› ļ„¬ļ…„ ļ„ļ„©ļ„® ļ„›ļ„µļ„®
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„»ļ……ļ„©, ļ„‘ļ„ŗļ…„
ļ„
ļ„šļ„ŗļ„Ŗ ļ„øļ„µļ„ļ…‚ļ„ ļ„¬ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‚ļ„:
1. ļ„’ļ„¾ļ…‚ļ„¬ļ…„ ļ„¬ļ…„ļ„’ļ„ ļ…ƒļ„§ļ„ļ„µļ…„ļ„’ļ„:
2. ļ„šļ„ŗļ„Ŗ ļ„øļ„µļ„:
ļ„‘ļ…œļ„Ŗ ļ…ƒļ„øļ…žļ„ , F-ļ„‘ļ…œļ„›ļ„æļ…‚ ļ„“ļ„» ļ„»ļ…‰:
ļ„›ļ„¬ļ„³ 6: F ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„® ļ„® ļ„¾ļ……ļ„› ļ„³ļ……ļ…žļ„¶ ļ„® ļ„¶ ļ„›ļ„µļ„®
ā€¢ ļ„ŗļ…‚ļ„§ļ…‡ ļ„¬ļ……ļ„’ļ„µļ…‚ ļ…ƒļ„ļ…ƒļ„©ļ„’ ļ…ƒļ„ļ„’ F = 1.67
ā€¢ ļ„®ļ…‚ļ„¾ļ……ļ„› F = 3.34
1.67 < 3.34 ļ„Ŗļ…Œ, ļ„‘ļ„ŗļ…„
ļ„
ļ„®ļ„¶ ļ„Æļ…ƒļ„µļ„›ļ„¶ļ„Æļ„®ļ…‚ ļ„®ļ…†ļ…œ ļ„µļ…žļ„¬ ļ„›ļ„µļ„® ļ…ƒļ„øļ…žļ„  ļ„‘ļ„ŗļ„°ļ„¶ ļ„µļ…ƒļ„»ļ…œļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„”
ļ„›ļ„¬ļ„³ 7: ļ„ŗļ„µļ„¶ ļ„¹ļ„±ļ„¬ ļ„ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’
ļ„“ļ„ŗļ„¬ļ…‚ ļ„³ļ„Ŗļ„¶ļ„± ļ„»ļ…‰ ļ…ƒļ„› ļ„ ļ…‚ļ„µ ļ„„ļ…‚ļ„“ļ„µ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ„¬ļ…‡ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…„ļ„øļ„® ļ…ƒļ„øļ…žļ„  ļ„‘ļ…œļ„Ŗļ„µ ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„®ļ„»ļ…„
ļ„
ļ„»ļ„®ī„” ļ„¬ļ…†ļ„¢ļ…‡ ļ„¹ļ„±ļ„¬ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ , ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„‘ļ„ŗļ…„
ļ„
ļ„¢ļ…‹ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…‡ļ„œļ„¬ļ…‡ ļ„»ļ…‚ļ„ ļ„•ļ„» ļ„Æļ…„ļ„¬ļ„µļ„¹ļ„® ļ…ƒļ„øļ…žļ„  ļ…ƒļ„›ļ„ŗļ…‡ ļ„‘ļ„ŗļ„¶ ļ„‘ļ…œļ„Ŗļ„µ ļ„¬ļ…„ ļ„±ļ„¢ļ…‚ļ„—
ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„³ļ…ļ„›ļ…‡ ļ„›ļ…‚ļ„µļ„® ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„“ļ…žļ„› ļ„„ļ„µļ…žļ…ƒļ„›ļ…œļ„ ļ„›ļ…œļ„Æļ„®ļ…„ ļ„¬ļ…‡ ļ„³ļ…‚ļ„¶ļ„› ļ„»ļ…‹ļ„© ļ„¬ļ…‡ ļ„®ļ…‚ļ„Ŗļ…‡, ļ„“ļ„» ļ„ŗļ……ļ„£ļ…‚ļ„‘ ļ…ƒļ„¬ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„ ļ…‚ļ„µ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ ļ…Œ ļ„›ļ…‹ļ„” ļ„øļ…„ ļ„ ļ……ļ…ƒļ„©ļ„’ ļ„¢ļ…‚
ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰, ļ„žļ…žļ„„ļ…‹ ļ„žļ…žļ„„ ļ„šļ„ŗļ„Ŗ ļ„¢ļ…„ļ„øļ„® ļ„¬ļ…‡ ļ…ƒļ„¬ļ…„ļ„¹ļ„„ļ…„ļ„›ļ…‹ļ„© ļ„Ŗļ…Œī„” ļ„¶ļ…‚ļ„ļ„Ŗ, ļ„•ļ„Æļ„¶ļ„±ļ„­ļ„Ŗļ…‚, ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„øļ„›ļ„µļ…„ ļ„Ŗļ…Œ ļ„±ļ…‚ļ„‘ļ„¬ ļ„¬ļ…„ ļ„ŗļ…‡ļ„øļ…‚
ļ„øļ„µļ„ļ…‡ ļ„»ļ…‹ļ„µ ļ„›ļ…‚ļ„µļ„› ļ„»ļ……ļ„© ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„°ļ…‰ļ„ŗļ„¶ļ…‡ ļ„®ļ…†ļ…œ ļ„ŗļ…‡ļ„­ ļ„¬ļ…‡ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„›ļ„¬ļ„³ 8: ļ„›ļ„» ļ„©ļ…„ ļ„®ļ…†ļ…œ ļ„³ļ„®ļ……ļ…ž ļ„œļ…„ ļ„±ļ„© ļ„•ļ„©
ļ„“ļ„ŗ ļ„±ļ…‚ļ„µļ…‡ ļ„“ļ„ŗ ļ„Ŗļ„µļ…§ļ…‚ļ„ ļ„ŗļ…‹ļ„ ļ…‹: ļ„Ŗļ……ļ„ŗļ…„
ļ„
"ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ„­ļ…„ļ„’" ļ„„ļ…‚ļ„“ļ„µ ļ„ ļ……ļ„©ļ„® ļ„¬ļ…‡ ļ…ƒļ„³ļ„¹ļ„® 'ļ„Ŗļ…‡ ļ…ƒļ„®ļ„›ļ„¶ļ…‡ ļ„»ļ…‹, ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶
ļ„§ļ…‚ļ„„ļ…‚ ļ„“ļ„›ļ…žļ„¦ļ…‚ ļ„›ļ„µļ„® ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„›ļ„µļ„® ļ„Ŗļ…Œ ļ„±ļ…‚ļ„‘ļ„¬, ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ„‘ļ…ƒļ„»ļ„ŗļ…‚ļ„ŗ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ……ļ„¬ļ„µļ„Ŗ (ļ„¢ļ…‚ļ„ ļ„³ļ…ļ„›ļ…‚)
ļ„šļ„ŗļ„Ŗļ„® ļ„ ļ…‚ļ„¶ ļ„œļ…‡ļ„§ļ„¬ļ…„ ļ„»ļ…‰ī„” ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„¬ļ……ļ„’ļ„µļ…‚ ļ„¬ļ…‡ļ„œļ…‡ ļ„ļ„— ļ„³ļ…‚ļ„³ļ…†ļ„¶ļ…„ ļ„‘ļ…œļ„Ŗļ„µ - ļ„±ļ…„ļ…‚ļ„ļ„§ 1 19.5 ļ„»ļ„¾ļ…‚ļ„µ ļ„³ļ…„ļ„¶ ļ„Ŗļ…žļ„› ļ„ ļ…žļ„¶ļ„¬ļ…‚ ļ„»ļ…‰
ļ„‘ļ„Ŗļ…‡ ļ„±ļ…„ļ…‚ļ„ļ„§ 4 16.5 ļ„»ļ„¾ļ…‚ļ„µ ļ„³ļ…„ļ„¶ ļ„Ŗļ…žļ„› ļ„ ļ…žļ„¶ļ„¬ļ…‚ ļ„»ļ…‰ - ļ„Æļ…ƒļ„»ļ„¶ļ…„ ļ„®ļ„¾ļ„µ ļ…ƒļ„øļ…žļ„  ļ„®ļ…‚ļ„„ļ„›ļ…„ ļ„¶ļ…žļ„ļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„Æļ„µ ļ„‘ļ…œļ„›ļ„æļ…‡ ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ
ļ„¬ļ…žļ„ŗļ„¬ļ…‡ ļ„»ļ„® ļ…ƒļ„› ļ„“ļ„» ļ„‘ļ…œļ„Ŗļ„µ ļ„›ļ……ļ„¬ļ„µļ„Ŗļ…„ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗļ…‚ ļ„¬ļ…„ ļ„ŗļ…„ļ„³ļ…‚ ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ„»ļ„®ī„”
ļ„“ļ„» ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„¹ļ…‰ļ…žļ„°ļ…‚ļ„ ļ„¬ļ……ļ„’ļ„µļ…‚ ļ„Æļ„›ļ…‚ļ„— ļ„ļ„— ļ„ ļ…‚ļ„µ ļ„›ļ…‡ļ„› ļ„ ļ…žļ„œļ„© ļ„øļ„µļ„ļ…‚ ļ„»ļ…‰ī„” ļ„“ļ…žļ„› ļ„¬ļ…†ļ„¢ļ…‡ ļ„®ļ…‚ļ„¶ļ…Œ ļ…ƒļ„³ļ…žļ„¦ļ…‚ ļ„¶ļ…žļ„ļ„¬ļ…‚ ļ„»ļ…‰, ļ„Æļ„µ ļ„“ļ…žļ„›
ļ„¬ļ„µļ„¢ļ„® ļ„¬ļ…‹ļ„ŗļ„Ŗļ…‚ļ„ ļ„®ļ…‚ļ„¶ ļ„ŗļ……ļ„’ļ„¬ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„¬ļ„µļ„ŗļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ ļ…ƒļ„› ļ„»ļ„µ ļ…ƒļ„›ļ„ŗļ…‡ ļ„¬ļ…„ ļ„­ļ…‚ļ„µļ„®ļ…‚ ļ„«ļ…‹ļ„æļ…§ļ…„ ļ„øļ…žļ„œļ„µļ…„ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„” ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„
ļ„¬ļ…‡ ļ„‘ļ„®ļ……ļ„ŗļ…‚ļ„µ, ļ„›ļ…‹ļ„” ļ„ŗļ„Æļ…žļ„¹ļ„„ ļ„¢ļ…‡ļ„Ŗļ…† ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‰ī„”
ļ„›ļ„¬ļ„³ 9: ANOVA ļ„Ŗļ…Œ ļ„ŗļ„±ļ„›
1. ļ„§ ļ„„ ļ„ŗļ…žļ„  ļ„¬ļ…žļ„ŗļ„¬ ļ„»ļ…‰, ļ„Æļ„µ ļ„ŗļ…œļ„¬ļ„µļ„² ļ„³ ļ„“ļ„®ļ…‡ ļ„µļ…žļ„œļ„¬ ļ„»ļ…‰ī„”ļ„²ļ…‚ļ„øļ…ˆ ļ„“ļ…žļ„› ļ„±ļ…„ļ…‚ļ„ļ„§ ļ„“ļ…žļ„› ļ„”ļ…‹ļ„„ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ…ƒļ„øļ…žļ„ 
"ļ…ƒļ„±ļ„»ļ„Ŗļ„µ" ļ„¢ļ…‚ļ„Æļ„¬ļ…‚ ļ„»ļ…‰, ļ„ŗļ„³ļ……ļ…žļ„ ļ…„ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„®ļ„¹ļ…„ļ„¶ļ„Ŗļ…‚ ļ„‘ļ„ŗļ„¶ ļ„‘ļ…œļ„Ŗļ„µļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„¶ļ……ļ„›ļ…‚ ļ„ŗļ„›ļ„¬ļ…„ ļ„»ļ…‰ī„”
2. ļ„‘ļ…œļ„›ļ„æ ļ„„ļ…‰ļ„ŗļ„„ ļ„¢ļ„¶ļ„¬ļ„± ļ„¾ļ…„ ļ„ø ļ„¶ļ…‡ ļ„°ļ…‰ļ„ŗļ…ƒļ„¶ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„µļ…‹ļ„›ļ„¬ļ…‡ ļ„»ļ„®ī„”ANOVA ļ„Ŗļ…Œ ļ…ƒļ„±ļ„®ļ…‚ļ„, ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„‘ļ…œļ„®ļ…§ļ…‡ļ„øļ…‚ļ„» ļ„±ļ…„ļ…‚ļ„ļ„§
1 ļ„®ļ…†ļ…œ ļ„ ļ……ļ…ƒļ„©ļ„’ ļ„»ļ…‹ļ„øļ…‡ļ„ļ…‚ ļ„‘ļ„Ŗļ…‡ ļ„±ļ…„ļ…‚ļ„ļ„§ 4 ļ„®ļ…†ļ…œ ļ„®ļ„¾ļ„µļ„‘ļ…œļ„¬ļ…‚ļ„¾ ļ„›ļ„µ ļ…ƒļ„¬ļ…žļ„Ŗļ…‚ ļ„»ļ…‹ļ„øļ…‡ļ„ļ…‚ī„”
3. ļ„²ļ…ƒļ„øļ…žļ„œ ļ„¬ļ…„ ļ„œļ…‹ļ„¢ ļ„°ļ…‰ļ„ŗļ…ƒļ„¶ļ„’ļ„ ļ„®ļ…†ļ…œ ļ„ŗļ……ļ„­ ļ„µ ļ„ŗļ„›ļ„¬ļ…„ ļ„»ļ…‰ī„”ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¬ļ…‡ ļ„’ļ„›ļ…‚ļ„µ ļ„®ļ…†ļ…œ ļ„øļ„­ļ…‚ļ„•ļ„©ļ…‚ ļ„¢ļ…‚ļ„ ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„ŗļ„æļ„›ļ…‚ļ„
ļ„¬ļ…„ļ„’ļ„ ļ„ŗļ…ƒļ„«ļ„Ŗļ…„ļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„„ļ…‚ļ„“ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„® ļ„®ļ…‚ļ„¶ ļ„“ļ„ŗ ļ„”ļ…‹ļ„„ļ…‡ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„¬ļ„œļ…‚ļ„” ļ„®ļ…‚ ļ„¬ļ…‡ļ„© ļ„øļ…‚ļ„¶ļ…‡
ļ„‘ļ…œļ„Ŗļ„µ ļ„Æļ…„ļ„ļ„„ ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ…ƒļ„ŗļ…žļ„„
ļ„ŗļ…œļ„œļ…‡ļ„Æ ļ…ƒļ„øļ…žļ„ , ANOVA ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„›ļ…‡ ļ„„ļ…‚ļ„“ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ…ƒļ„¾ļ…œļ„¬ļ„ļ…„ ļ„¬ļ…„ ļ„ŗļ„³ļ…‚ļ„®ļ„Ŗļ…‚ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„®ļ…‚ ļ„“ļ…žļ„› ļ„ŗļ…‚ļ„øļ„­ļ…‚ļ„® ļ„¢ļ…‚ļ„ŗļ…†ļ„ŗ
ļ„»ļ…‹ļ„© ļ„øļ…‚ļ„ļ„ ļ„»ļ…‰ī„” ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„¬ļ…‡ļ…ƒļ„œļ„’, ļ„ŗļ„±ļ…†ļ„Ŗ ļ„“ļ„›ļ…žļ„¦ļ…‡ ļ„›ļ…„ļ„Ŗļ…‡, ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‚ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„›ļ…„ļ„Ŗļ…‚, ļ„‘ļ„Ŗļ…‡ ļ„‘ļ…œļ„Ŗ ļ…ƒļ„øļ…žļ„  ļ„‘ļ…œļ„›ļ…ƒļ„æļ„’ļ„ ļ„®ļ…†ļ…œ
ļ„±ļ…‹ļ„¶ļ„© ļ…ƒļ„¬ļ…žļ„Ŗļ…‚ī„” ļ„“ļ„»ļ„®ļ…‚ļ„ ļ„ ļ…‚ļ„µ ļ„„ļ…‚ļ„“ļ„µ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ„¬ļ…„ ļ„›ļ„»ļ…‚ļ„©ļ…„ ļ„“ļ…žļ„› ļ„ŗļ„¬ļ…„ļ„øļ…„ ļ„ŗļ„±ļ„› ļ…ƒļ„ŗļ„œļ…‚ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰: ļ„›ļ„” ļ„øļ…‚ļ„µ, ļ„ŗļ„² ļ„Ŗļ…Œ
ļ„øļ„­ļ…„ļ„’ ļ„°ļ…‰ļ„ŗļ„¶ļ…‚ "ļ„ŗļ„² ļ„Ŗļ…Œ ļ„øļ„­ļ…„ļ„’" ļ„ ļ……ļ„©ļ„® ļ„±ļ…‚ļ„µļ…‡ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ……ļ…œļ„¬ļ…‚, ļ„ŗļ„ļ…Œ ļ„“ļ„» ļ„ŗļ„³ļ„£ļ„©ļ…‚ ļ„»ļ……ļ…œļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„ŗļ…‚ļ„µļ…‡ ļ…ƒļ„øļ„›ļ„¶ļ„Æ
ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„ŗļ…„ļ„³ļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ļ„“ļ…‹ļ„ ļ„»ļ„®ī„”
ļ„ŗļ…‚ļ„§ļ…‡ ļ„³ļ…‚ļ„³ļ„¶ļ…‡ ļ…ƒļ„øļ…žļ„ , ANOVA ļ„„ļ…‰ļ„ŗļ„„ ļ„®ļ…‡ ļ…ƒļ„¬ļ„œļ…‚ļ„“ļ„’ ļ…ƒļ„› ļ„ ļ…‚ļ„µļ…‚ļ„ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ„¬ļ…„ ļ„šļ„ŗļ„Ŗ ļ„•ļ„³ļ„µ ļ„‘ļ…œļ„›ļ„æļ…‚ļ„Ŗļ„³ļ„› ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„“ļ…žļ„›ļ…‹
ļ…ƒļ„¢ļ„»ļ…„ ļ„»ļ…‰ī„” ļ„“ļ„ŗ ļ„¶ļ„”, ļ„‘ļ„ļ„¶ļ…„ ļ„øļ…‚ļ„µ ļ„¢ļ„¬ļ…Œ ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„»ļ…‚ļ„”ļ„øļ…‡ļ„‘ 'ļ„Ŗļ…‡ ļ„¢ļ…‚ļ„™ļ„ļ…‡, ļ„Ŗļ…‚ļ„ ļ„¢ļ…‚ļ„©ļ…‹ ļ…ƒļ„› ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„„ļ…‚ļ„“ļ„µļ…‚ļ„ ļ„¬ļ…„ ļ…ƒļ„›ļ„ŗļ„³ļ„Ŗ
ļ…ƒļ„ŗļ„µļ…€ ļ„±ļ…„ļ…‚ļ„ļ„§ļ…‚ļ„ ļ„±ļ…‚ļ„µļ…‡ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‰ - ļ„“ļ„» ļ…ƒļ„­ļ„’ļ„® ļ„®ļ…‚ļ„¶ ļ„§ļ„µļ…‚ļ„”ļ…ƒļ„øļ…œļ„, ļ„ŗļ„æļ„› ļ„¬ļ…„ ļ„ŗļ…ƒļ„«ļ„Ŗļ…„ ļ„‘ļ„Ŗļ…‡ ļ„µļ…žļ„œ-ļ„µļ„œļ…‚ļ„‘ ļ„±ļ…‚ļ„µļ…‡ ļ„øļ…„ ļ„»ļ…‰ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
8. ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„¬ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„© ļ„›ļ…„ ļ„»ļ…‰? ļ„“ļ„ŗ ļ„¬ļ…„ļ„’ļ„ ļ„³ļ……ļ…žļ„œ ļ„­ ļ„µļ„® ļ„ø ļ„ 'ļ„Ŗļ…‡ ļ„ ļ„µļ„  ļ„›ļ„µļ…‹ī„” ļ„“ļ…žļ„› ļ„Æ ļ„ŗļ…‡
ļ„‘ļ„Ŗļ…‡ ļ„¬ļ…‹ ļ„Æ ļ„ŗļ…‡ ANOVA ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„ ļ…ƒļ„øļ…žļ„  ļ„øļ…„ ļ„‘ļ…œļ„Ŗļ„µ ļ„›ļ„µļ…‹ī„”
ļ„•ļ…žļ„Ŗļ„µ:ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„Ŗļ„›ļ„®ļ…„ļ„› ļ„¬ ļ…ƒļ„øļ„¹ļ„¶ļ…‡ļ„¹ļ„©
ANOVA ļ„“ļ…žļ„› ļ„‘ļ…œļ„›ļ„æļ…‚ ļ…ƒļ„øļ„­ļ…„ ļ„»ļ…‰ ļ„¢ļ…‹ ļ„“ļ„» ļ„¢ļ…‚ļ„ļ„ ļ„© ļ„¶ļ„” ļ„øļ„µļ„Ŗļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ…ƒļ„Ŗļ…œļ„® ļ„¢ļ…‚ļ„ ļ„øļ…žļ„­ ļ„ŗļ„³ļ…†ļ„» ļ„ŗļ…‚ļ„­ļ„®
ļ„³ļ„»ļ…žļ„Ŗļ„øļ„Æļ…†ļ„µļ„® ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„øļ…žļ„œļ„µļ…‡ ļ„»ļ„®ī„” ļ„ŗļ…‚ļ„­ļ„®ļ…‚ļ„ ļ„¬ļ…„ ļ„¢ļ…‹ļ„æļ…„ ļ„‘ļ„®ļ……ļ„ŗļ…‚ļ„µ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„¬ļ…„ ļ„±ļ„¢ļ…‚ļ„— (ļ„¢ļ…‹ ļ„ļ„¶ļ„Ŗļ…„ ļ„®ļ…†ļ…œ ļ„øļ„­ļ…‚ļ„•
ļ„
ļ„¬ļ…‚
ļ„»ļ…‰), ANOVA ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„ŗļ„µļ…‹ļ„Ŗļ…‚ļ„ ļ„¬ļ…‡ ļ„›ļ…‚ļ„µļ„® ļ„§ļ…‡ļ„„ļ…‚ ļ…ƒļ„øļ…žļ„  ļ„›ļ……ļ…žļ„¶ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ…ƒļ„»ļ…žļ…ƒļ„ŗļ„’ļ„ ļ…ƒļ„øļ…žļ„  ļ„øļ…œļ„§ļ„¬ļ…‚ ļ„»ļ…‰, ļ…ƒļ„°ļ„µ ļ„³ļ……ļ„¶ļ…‚ļ„ļ„›ļ„©
ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…‡ ļ„³ļ……ļ„›ļ…‚ļ„±ļ„¶ļ…‡ ļ„øļ…žļ„§ļ…„ ļ„»ļ…‰ī„”
ā€¢ ļ„³ļ……ļ…žļ„œ ļ…ƒļ„øļ„  ļ„µ:F-ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„›ļ…‡ "ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…‡ ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ" ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ "ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ"
ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„®ļ…‚ļ„¶ ļ„›ļ„µļ…‹:
ļ„¢ļ…‡ļ„›ļ„µ F ļ„øļ…žļ„§ļ…‚ ļ„»ļ…‰, ļ„Ŗļ…‚ļ„ ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ„¬ļ…‡ ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„ŗļ…‚ļ„­ļ„® ļ„»ļ…‹ļ„© ļ„¬ļ…„ ļ„ŗļ…œļ„²ļ…‚ļ„øļ„®ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„“ļ„» ļ„›ļ…„ ļ„¢ļ„ø ļ„± ļ…ƒļ„¬ļ…œļ„¬ ļ„»ļ…‰:"ļ„›ļ…„ ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…‡ ļ„‘ļ„µļ„« ļ„øļ…žļ„œļ„µļ…‡ ļ„»ļ„®?" ļ„“ļ„» ļ„“ļ„» ļ„®ļ„»ļ…„
ļ„
ļ„¬ļ…žļ„ŗļ„¬ļ…‚ ļ…ƒļ„› ļ…ƒļ„›ļ„»ļ„æļ…‡ ļ„¢ļ…‹ļ„æļ…‡
ļ„øļ…žļ„œļ„µļ…‡ ļ„»ļ„®; ļ„“ļ„ŗļ„¬ļ…‡ ļ„¶ļ„”, ļ„‘ļ„ŗļ…„
ļ„
ļ„Æļ…‹ļ„ŗļ„„-ļ„»ļ…‚ļ„› ļ„„ļ…‰ļ„ŗļ„„ļ…‚ļ„ (ļ„„ļ……ļ„›ļ…„, ļ„±ļ…‹ļ„®ļ„°ļ…‰ļ„µļ…‹ļ„®ļ…„) ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‚ļ„ī„”
ā€¢ ļ„“ļ„» ļ…ƒļ„›ļ…žļ„«ļ…‡ ļ„øļ„µļ…ƒļ„Ŗļ„’ ļ„¢ ļ„ļ„¬ ļ„»ļ…‰:ļ„œļ…‡ļ„Ŗļ…„ļ„±ļ…‚ļ„æļ…„ (ļ„œļ…‚ļ„¬ļ…‚ļ„ ļ„¬ļ…‡ ļ„Æļ…‚ļ„µ ļ„•ļ„Æļ„¢), ļ…ƒļ„ŗļ…žļ…ƒļ„œļ„’ (ļ…ƒļ„ŗļ…žļ…ƒļ„œļ„’ ļ„¬ļ…‡ ļ„Ŗļ„µļ…„ļ…ƒļ„›ļ„’ļ„ ļ„¬ļ…‡
ļ„Æļ…‚ļ„µ ļ„‘ļ…œļ„›), ļ„³ļ„®ļ…‹ļ…ƒļ„øļ…ƒļ„ļ„’ļ„® (ļ„“ļ„¶ļ…‚ļ„¢ļ…‚ļ„ ļ„¬ļ…‡ ļ„Æļ…‚ļ„µ ļ„Æļ…„ļ„Ŗļ…„ļ…ƒļ„›ļ…ƒļ„µļ„’), ļ„•ļ„¬ļ„“ļ…‹ļ„ (ļ„Æļ…„ļ…ƒļ„›ļ…ƒļ„µļ„’ ļ„¶ļ…‚ļ„”ļ„®ļ…‚ļ„)ī™€
ļ„˜ļ„®ļ…‹ļ„ø ļ„¬ļ…„ļ„’ļ„ ļ„³ļ……ļ…žļ„œ ļ„­ ļ„µļ„® ļ„ø ļ„
F-ļ„„ļ…‰ļ„ŗļ„„ 'ļ„Ŗļ…‡ ļ„²ļ„µļ…‹ļ„ŗļ…‚ ļ„›ļ„µļ„® ļ„¶ļ„”, ļ„›ļ……ļ„£ ļ„¹ļ„µļ„Ŗļ…‚ļ„ ļ„Æļ…†ļ„µļ…„ļ„’ļ„ ļ„»ļ…‹ļ„©ļ…„ļ„’ļ„ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…„ļ„’ļ„ ļ„»ļ„®:
ā€¢ ļ„’ļ„¾ ļ„¬ļ…„:ļ…ƒļ„®ļ„µļ…„ļ„œļ„© ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ„®ī„” ļ„•ļ„¶ļ…œļ„žļ„©ļ…‚ļ„øļ…‚ļ„ (ļ…ƒļ„¢ļ„øļ…ˆ ļ…ƒļ„›, ļ…ƒļ„±ļ„®ļ…‚ļ„
ļ„¶ļ…‡ļ„œļ…‚-ļ„¢ļ…‹ļ„œļ…‚ ļ„›ļ…„ļ„Ŗļ…‡ ļ„øļ…‚ļ„µ-ļ„øļ…‚ļ„µ ļ„³ļ…‚ļ„Æ) ļ„Æļ…žļ„œļ„Æļ…‚ļ„Ŗ ļ„¬ļ…‡ ļ„®ļ„Ŗļ…„ļ„¢ļ…‡ ļ„øļ„¢ļ…Œ ļ…ƒļ„®ļ„›ļ„¶ļ„¬ļ…„ļ„’ļ„ ļ„»ļ„®ī„”
ā€¢ ļ„ŗ ļ„­ ļ„µļ„®ļ„Ŗ :ļ„»ļ„µļ…‡ļ„› ļ„ŗļ„³ļ…†ļ„» ļ„¶ļ„”, ļ„®ļ„Ŗļ…„ļ„¢ļ…‚ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ ļ„¶ļ„ļ„²ļ„ ļ„’ļ„³ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„øļ…œļ…ƒļ„§ļ„’ ļ„¢ļ…‚ļ„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ANOVA ļ„»ļ„¶ļ„›ļ…‡ ļ„Æļ…„ļ„ŗļ„«ļ…‚ļ„®ļ…‚ļ„ ļ„¶ļ„” ļ„³ļ„¾ļ„±ļ…†ļ„Ŗ ļ„»ļ…‰, ļ„œļ…‚ļ„ŗ ļ„›ļ„µļ„›ļ…‡ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ„’ļ„›ļ…‚ļ„µļ…‚ļ„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ī„”
ā€¢ ļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„ø ļ„ ļ„¬ļ…„ ļ„“ļ„›ļ„ŗ ļ„µļ„Ŗ :ļ„ŗļ„³ļ…†ļ„» ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¶ļ„ļ„²ļ„ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ„»ļ„® (ļ„»ļ…‹ļ„³ļ…‹ļ„ŗļ„ŗļ…„ļ„§ļ…‡ļ„ŗļ„„ļ…„ļ…ƒļ„ŗļ„„ļ…„)ī™€ ļ„¢ļ…‡ļ„›ļ„µ
ļ„®ļ„»ļ…„
ļ„
, ļ„Ŗļ…‚ļ„ ļ„øļ…‰ļ„¶ļ„  ļ„¬ļ…‡ ANOVA ļ„¢ļ…‚ļ„ ļ„„ļ…„ļ…‚ļ„ļ„ŗļ„°ļ…‚ļ„µļ„³ ļ„§ļ…‡ļ„„ļ…‚ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ…‹ī„”
ā€¢ ļ„¢ļ…‹ļ„æļ„® ļ„‘ļ„Ŗļ…‡ ļ„µļ…‡ļ…ƒļ„œļ„›ļ„Ŗ :ļ„“ļ„» ļ„³ļ…‚ļ„§ļ„¶ ļ„‘ļ„¢ļ…„ļ„± ļ„ļ…‰ļ„µ-ļ„µļ…‡ļ…ƒļ„œļ„› ļ„Æļ„µļ„ŗļ„Æļ„µ ļ…ƒļ„›ļ…„ļ„’ļ„øļ…‚ļ„ ļ„Ŗļ…Œ ļ…ƒļ„±ļ„®ļ…‚ļ„ ļ„Æļ…„ļ„²ļ…‚ļ„ø ļ„¢ļ…‹ļ„æļ„® ļ„®ļ…†ļ…œ
ļ„³ļ…œļ„®ļ„¬ļ…‚ ļ„»ļ…‰ (ļ„“ļ…žļ„›-ļ„Æļ…‚ļ„ŗļ„æ ļ„³ļ…‚ļ„§ļ„¶ļ…‚ļ„ ļ…ƒļ„øļ…žļ„ )ī™€ ļ„¬ļ…‹-ļ„Æļ…‚ļ„ŗļ„æ ANOVA ļ„ŗļ„Æļ„¹ļ„„ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„Æļ„µļ„ŗļ„Æļ„µ ļ…ƒļ„›ļ…„ļ„’ ļ„®ļ…†ļ…œ ļ„³ļ…‚ļ„§ļ„¶
ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„ŗļ…ƒļ„«ļ„µ-ļ„Æļ…„ļ„² ļ„ø (ļ„›ļ„¶ ļ„ŗļ…„ļ„›ļ„¶ ANOVA ļ…ƒļ„øļ…žļ„ ):ļ„°ļ…‰ļ„›ļ„„ļ„µ ļ„Æļ…žļ„­ļ„µ ļ„œļ…‚ļ„ŗ ļ„‘ļ„Ŗļ…‡ ļ…ƒļ„¬ļ„¶ļ„ ļ„ŗļ„Æ ļ„»ļ„®; ļ„¢ļ…‡ļ„›ļ„µ ļ„Æļ…žļ„­ļ„µ
ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„»ļ„®, ļ„Ŗļ…‚ļ„ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„±/ļ…ƒļ„³ļ„›ļ„ŗļ„§-ļ„“ļ„°ļ…‰ļ„›ļ„„ ANOVA ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ„›ļ„µļ…‹ī„”
ā€¢ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„®ļ„³ļ…†ļ„® :ļ„’ļ„±ļ…‚ļ„¬ļ…„ļ„’ļ„ ļ„Ŗļ…Œ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„‘ļ„Ŗļ…‡ ļ„Æļ…„ļ„Ŗļ…„ļ…ƒļ„®ļ„­ ļ„»ļ„®ī„”
ļ„“ļ…žļ„›-ļ„Æ ļ„ŗļ„æ ļ„±ļ„® ļ„³ ļ„¬ļ…‹-ļ„Æ ļ„ŗļ„æ ļ„‘ļ„®ļ…‹ļ„ø
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„›ļ…‚ļ„µļ„›ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„§ļ…‡ļ„„ļ…‚ ļ„¬ļ…‡ ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„»ļ…‹ļ„© ļ„¬ļ…‡ ļ„›ļ…‚ļ„µļ„®ļ…‚ļ„ ļ„øļ„¢ļ…Œ ļ„ŗļ…‹ļ„ ļ…‹ī„” ļ„“ļ…žļ„›-ļ„Æļ…‚ļ„ŗļ„æ ANOVA ļ„¬ļ…‚ ļ„“ļ…žļ„› ļ„›ļ…‚ļ„µļ„® ļ„»ļ…‰; ļ„¬ļ…‹-ļ„Æļ…‚ļ„ŗļ„æ ļ„¬ļ…‡ ļ„¬ļ…‹
ļ„›ļ…‚ļ„µļ„® ļ„»ļ„® ļ„‘ļ„Ŗļ…‡ ļ„Æļ……ļ…žļ„”ļ„¬ļ…‡ ļ„»ļ„® ļ…ƒļ„› ļ„›ļ…„ ļ„•ļ„» ļ„’ļ„Æļ„ŗ ļ…ƒļ„øļ…žļ„  ļ„³ļ…‡ļ„¶ ļ„œļ…‚ļ„ļ„¬ļ…‡ ļ„»ļ„®ī„”
ļ„“ļ…žļ„›-ļ„Æ ļ„ŗļ„æ ļ„˜ļ„®ļ…‹ļ„ø
ā€¢ ļ…ƒļ„§ļ„¾ ļ„”ļ„®:ļ„“ļ…žļ„› ļ„›ļ…‚ļ„µļ„› (ļ…ƒļ„¢ļ„øļ…ˆ ļ…ƒļ„›, k ļ„Æļ…žļ„­ļ„µļ…‚ļ„ ļ„¬ļ…‡ ļ„®ļ…‚ļ„¶ ļ…ƒļ„ŗļ…žļ…ƒļ„œļ„’ ļ…ƒļ„øļ„­ļ…„)ī™€
ā€¢ ļ„³ ļ„§ļ„¶:
ā€¢ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„¬ļ…‡ ļ„ŗļ„µļ…‹ļ„Ŗ:
o ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ (ļ„›ļ…‚ļ„µļ„›)
o ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ (ļ„ļ„¶ļ„Ŗļ…„)
ā€¢ ļ„øļ„µļ„Ŗļ…Œ ļ„¢ļ„¬ļ…Œ:ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ ļ„›ļ…‹ļ„¶ ļ„“ļ…žļ„› ļ„¹ļ…„ļ…‡ļ„©ļ…„ļ„±ļ…žļ„­ ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µ ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ (ļ„°ļ…‰ļ„›ļ„„ļ„µ) ļ„‘ļ„Ŗļ…‡ ļ„“ļ…žļ„› ļ…ƒļ„®ļ„µļ…œļ„Ŗļ„µ ļ…ƒļ„®ļ„µļ„²ļ„µ
ļ„øļ…‡ļ„µļ…„ļ„—ļ„±ļ„¶ ļ„»ļ…‰ī„”
ā€¢ ļ„ŗļ„ø ļ„¶ ļ„¬ ļ„¢ļ„ø ļ„± ļ…ƒļ„¬ļ…žļ„Ŗ ļ…ƒļ„ļ„’:ļ„›ļ…„ k ļ„Æļ…žļ„­ļ„µļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„šļ„ŗļ„Ŗ ļ„®ļ„Ŗļ…„ļ„¢ļ…‡ ļ„øļ…žļ„œļ„µļ…‡ ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ„®?
ļ„¬ļ…‹-ļ„Æ ļ„ŗļ„æ ļ„˜ļ„®ļ…‹ļ„ø
ā€¢ ļ…ƒļ„§ļ„¾ ļ„”ļ„®:ļ„¬ļ…‹ ļ„›ļ…‚ļ„µļ„› (ļ…ƒļ„¢ļ„øļ…ˆ ļ…ƒļ„›, ļ…ƒļ„ŗļ…žļ…ƒļ„œļ„’ ļ…ƒļ„øļ„­ļ…„ ļ„‘ļ„Ŗļ…‡ ļ„›ļ„¶ļ…‚ļ„ŗ ļ„¬ļ…‚ ļ„’ļ„›ļ…‚ļ„µ), ļ„»ļ„µļ…‡ļ„› ļ„¬ļ…‡ ļ„›ļ„” ļ„Æļ…žļ„­ļ„µ ļ„»ļ„®;
ļ…ƒļ„øļ…žļ„  ļ„’ļ„Æļ„ŗļ…„ ļ„Ŗļ…‚ļ„¶ļ„³ļ…‡ļ„¶ ļ„¹ļ…‚ļ„³ļ„¶ ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„³ ļ„§ļ„¶:
ā€¢ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„¬ļ…‡ ļ„ŗļ„µļ…‹ļ„Ŗ:
o ļ„›ļ…‚ļ„µļ„› A ļ„³ļ……ļ…žļ„œ ļ„Æļ…„ļ„²ļ…‚ļ„ø
o ļ„°ļ…‰ļ„›ļ„„ļ„µ ļ„±ļ…„ ļ„³ļ……ļ…žļ„œ ļ„Æļ…„ļ„²ļ…‚ļ„ø
o ļ„Æļ„µļ„ŗļ„Æļ„µ ļ„Æļ…„ļ„²ļ…‚ļ„ø
o ļ„ļ„¶ļ„Ŗļ…„
ā€¢ ļ„øļ„µļ„Ŗļ…Œ ļ„¢ļ„¬ļ…Œ:ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„¬ļ…‹ ļ„ŗļ„Æļ…žļ„¹ļ„„ ļ„²ļ…ƒļ„øļ…žļ„œļ„±ļ…‚ļ„©ļ…„ļ„’ļ„ ļ„¬ļ…„ ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„®ļ…‚ ļ„ ļ…‚ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ…‹ ļ„‘ļ„Ŗļ…‡ ļ„›ļ…„ ļ„“ļ…žļ„› ļ„¬ļ…‚ ļ„Æļ…„ļ„²ļ…‚ļ„ø ļ„¬ļ…†ļ„¢ļ…‡ 'ļ„Ŗļ…‡
ļ…ƒļ„®ļ„µļ„²ļ„µ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ„ŗļ„ø ļ„¶ ļ„¬ ļ„¢ļ„ø ļ„± ļ…ƒļ„¬ļ…žļ„Ŗ ļ…ƒļ„ļ„’:ļ„›ļ…„ ļ„°ļ…‰ļ„›ļ„„ļ„µ A ļ…ƒļ„øļ…žļ„  ļ„ŗļ…‚ļ„­ļ„® ļ„øļ…žļ„œ-ļ„øļ…žļ„œ ļ„»ļ……ļ…œļ„¬ļ…‡ ļ„»ļ„®? ļ„°ļ…‰ļ„›ļ„„ļ„µ B? ļ„›ļ…„
ļ„°ļ…‰ļ„›ļ„„ļ„µ ļ„’ļ„Æļ„ŗ ļ…ƒļ„øļ…žļ„  ļ„³ļ…‡ļ„¶ ļ„œļ…‚ļ„ļ„¬ļ…‡ ļ„»ļ„®?
ļ„³ļ……ļ…žļ„œ ļ„‘ļ…œļ„Ŗļ„µ
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ā€¢ ļ„› ļ„µļ„› ļ„ ļ„¬ļ…„ ļ…ƒļ„ļ„©ļ„Ŗļ…„:ļ„“ļ…žļ„›-ļ„Æļ…‚ļ„ŗļ„æ ļ…ƒļ„øļ…žļ„  1 ļ„»ļ…‰; ļ„¬ļ…‹-ļ„Æļ…‚ļ„ŗļ„æ ļ…ƒļ„øļ…žļ„  2 ļ„»ļ„® (ļ„Æļ„¶ļ…žļ„ŗ ļ„“ļ…œļ„„ļ„µļ…‰ļ„›ļ„¹ļ„®)ī™€
ā€¢ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’:ļ„“ļ…žļ„›-ļ„Æļ…‚ļ„ŗļ„æā€”ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„‘ļ…œļ„Ŗļ„µī„” ļ„¬ļ…‹-ļ„Æļ…‚ļ„ŗļ„æā€”ļ„øļ…žļ„œļ„µļ…‡ ļ„³ļ……ļ…žļ„œ ļ„Æļ…„ļ„²ļ…‚ļ„øļ…‚ļ„ ļ„‘ļ„Ŗļ…‡ ļ„›ļ…„ ļ„Æļ…„ļ„²ļ…‚ļ„ø ļ„ļ…‰ļ„µ-
ļ„¢ļ…‹ļ„æļ„®ļ„“ļ…‹ļ„ ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„¢ļ…‹ļ„æļ„¬ļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„›ļ……ļ„¹ļ„¶ļ„Ŗ :ļ„¬ļ…‹-ļ„Æļ…žļ„œļ…„ ANOVA ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„¬ļ…‡ ļ„¬ļ…†ļ„¢ļ…‡ ļ„ŗļ„µļ…‹ļ„Ŗ ļ„®ļ…†ļ…œ ļ„›ļ…œļ„„ļ„µļ…‹ļ„¶ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ ļ„‘ļ„Ŗļ…‡ ļ„¹ļ……ļ…žļ„­ļ„Ŗļ…‚ ļ…ƒļ„øļ…žļ„ 
ļ„ŗļ……ļ„­ļ…‚ļ„µ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ā€¢ ļ…ƒļ„§ļ„¾ ļ„”ļ„® ļ„¬ļ…„ ļ„¶ļ…‹ļ„æ:ļ„¬ļ…‹-ļ„Æļ…‚ļ„ŗļ„æ ļ„‘ļ„›ļ„ŗļ„µ ļ„ŗļ…‚ļ…€ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’ ļ„¶ļ„” ļ„ŗļ…œļ„Ŗļ……ļ…ƒļ„¶ļ„Ŗ ļ„¢ļ…‚ļ„ ļ„¶ļ„ļ„²ļ„-ļ„ŗļ…œļ„Ŗļ……ļ…ƒļ„¶ļ„Ŗ
ļ…ƒļ„§ļ„¾ļ…‚ļ„”ļ„® ļ„¬ļ…„ ļ„¶ļ…‹ļ„æ ļ„»ļ……ļ…œļ„¬ļ…„ ļ„»ļ…‰ī„”
ļ„ŗļ…œļ„›ļ„¶ļ„Æ ļ…ƒļ„ ļ…žļ„Ŗļ„µ: ANOVA ļ„Æļ…„ļ„ø ļ„»
ļ…ƒļ„øļ„» ļ„µļ„› ļ„‘ļ„®ļ……ļ„²ļ„ø
ā€¢ ļ„ŗļ„³ļ…†ļ„»-ļ„ŗļ„³ļ…†ļ„» ļ…ƒļ„²ļ…œļ„®ļ„Ŗ :ļ„“ļ„» ļ„›ļ…‰ļ„Æļ„ ļ„µ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„ŗļ„³ļ…†ļ„» ļ„ŗļ…‚ļ„­ļ„® ļ„›ļ……ļ…žļ„¶ ļ„šļ„ŗļ„Ŗ ļ„Ŗļ…Œ ļ…ƒļ„›ļ…œļ„®ļ…„ ļ„¬ļ…†ļ„µ ļ„°ļ…‰ļ„¶ļ…‡ ļ„»ļ…‹ļ„—
ļ„»ļ„®ī„”
ā€¢ ļ„ŗļ„³ļ…†ļ„»-ļ„‘ļ…œļ„¬ļ„µ ļ…ƒļ„²ļ…œļ„®ļ„Ŗ :ļ„“ļ„» ļ„›ļ…‰ļ„Æļ„ ļ„µ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ…ƒļ„øļ„‘ļ„›ļ„Ŗļ…„ļ„ļ„Ŗ ļ…ƒļ„®ļ„µļ…„ļ„œļ„© ļ„•ļ„»ļ„®ļ…‚ļ„ ļ„¬ļ…‡ ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…‡ ļ„’ļ„¶ļ…‡-
ļ„¬ļ……ļ„’ļ„¶ļ…‡ ļ…ƒļ„›ļ…œļ„®ļ…‡ ļ…ƒļ„œļ…œļ„§ļ…‡ ļ„»ļ…‹ļ„— ļ„»ļ„®ī„”
ā€¢ ļ„¢ļ…‡ļ„›ļ„µ ļ„ŗļ„³ļ…†ļ„» ļ„ŗļ…žļ„ ļ„³ļ……ļ…žļ„  ļ„øļ…žļ„œļ„µļ…‡ ļ„»ļ„®:ļ„ŗļ„³ļ…†ļ„»-ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„ŗļ„³ļ…†ļ„»-ļ„‘ļ…œļ„¬ļ„µ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„®ļ…‚ļ„¶ļ…Œ
ļ„‘ļ„µļ„«ļ„Æļ…†ļ„µļ„® ļ„Ŗļ…ļ„µ 'ļ„Ŗļ…‡ ļ„øļ…žļ„§ļ…‚ ļ„»ļ…‹ļ„©ļ…‚ ļ„ ļ…‚ļ„»ļ…„ļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ„›ļ…œļ„³ ļ„›ļ…„ļ„Ŗ ļ„„ļ…‰ļ„ŗļ„„: 5% 'ļ„Ŗļ…‡ ļ„®ļ„³ļ…†ļ„® ļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„ø ļ„ ļ„¬ļ…„ ļ„ŗļ„³ ļ„®ļ„Ŗ (F-ļ„„ļ…‰ļ„ŗļ„„)
ļ„Ŗļ……ļ„»ļ…‚ļ„®ļ…†ļ…œ ļ…ƒļ„¬ļ…žļ„Ŗļ…‚ ļ…ƒļ„ļ„’ ļ„»ļ…‰:
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„›ļ„¬ļ„³ 1: ļ„®ļ„³ļ…†ļ„® ļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„ø ļ„ ļ„¬ļ…„ ļ„ļ„©ļ„® ļ„›ļ„µļ…‹
ļ…ƒļ„®ļ„µļ„Æļ…žļ„œ ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚:
ļ„›ļ„¬ļ„³ 3: ļ„°ļ…‰ļ„ŗļ„¶ ļ…ƒļ„®ļ„“ļ„³ (ļ„¬ļ…‹-ļ„Æ ļ„ŗļ„æ)
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„›ļ„¬ļ„³ 4: ļ…ƒļ„ŗļ…žļ„„
ā€¢ ļ„°ļ…‰ļ„ŗļ„¶ :H0H_0 ļ„®ļ…†ļ…œ ļ„‘ļ„ŗļ„øļ…„ļ„›ļ…‚ļ„µ ļ„®ļ…‚ ļ„›ļ„µļ…‹ī„”
ā€¢ ļ…ƒļ„øļ„’ļ…ƒļ„œļ„’:5% ļ„Æļ…žļ„­ļ„µ 'ļ„Ŗļ…‡, ļ„“ļ„ŗ ļ„ļ…žļ„¶ ļ„¬ļ…‚ ļ„›ļ…‹ļ„” ļ„ŗļ„±ļ…†ļ„Ŗ ļ„®ļ„»ļ…„
ļ„
ļ„»ļ…‰ ļ…ƒļ„› ļ„’ļ„±ļ…‚ļ„¬ļ…„ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„øļ…žļ„œļ„µļ…„ļ„’ļ„ ļ„»ļ„®ī„”
ļ„®ļ„³ļ…†ļ„®ļ…‚ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ (10 ļ„‘ļ„Ŗļ…‡ 9.82) ļ„¶ļ„ļ„²ļ„ ļ„“ļ…žļ„›ļ…‹ ļ…ƒļ„¢ļ„»ļ…„ļ„’ļ„ ļ„»ļ„®; F-ļ„‘ļ„®ļ……ļ„Æļ…‚ļ„Ŗ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„ŗļ„³ļ…‚ļ„®ļ„Ŗļ…‚
ļ„¬ļ…„ ļ„Æļ……ļ„¹ļ„„ļ…„ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ī„”
ļ…ƒļ„øļ„›ļ„¶ļ…ƒļ„Æļ„› ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„„ļ…‰ļ„ŗļ„„ ļ„ ļ„®ļ…†ļ…œ ļ„›ļ„¬ļ…Œ ļ„Ŗļ„µļ„¢ļ…„ļ„» ļ„¬ļ…‡ļ„©ļ…„ ļ„»ļ…‰
ā€¢ ļ„¢ļ…‡ļ„›ļ„µ ļ„ŗ ļ„­ ļ„µļ„®ļ„Ŗ ļ„¹ļ…žļ„›ļ…„ ļ„»ļ…‰:ļ„¶ļ…‡ļ„øļ…„ļ„® ļ„¬ļ…‡ ļ„„ļ…‰ļ„ŗļ„„ ļ„¢ļ…‚ļ„ ļ„±ļ…„ļ…‚ļ„–ļ„®-ļ„°ļ…‹ļ„µļ„ŗļ…„ļ„« ļ„„ļ…‰ļ„ŗļ„„ (ļ„ļ…‰ļ„µ-ļ„ŗļ„­ļ…‚ļ„µļ„®ļ„Ŗļ…‚ ļ„¶ļ„” ļ„øļ„­ļ…‡ļ„µļ…‡
ļ„³ļ„¾ļ„±ļ…†ļ„Ŗ) 'ļ„Ŗļ…‡ ļ…ƒļ„øļ„ ļ…‚ļ„µ ļ„›ļ„µļ…‹ī„”
ā€¢ ļ„¢ļ…‡ļ„›ļ„µ ļ„®ļ„³ļ…†ļ„®ļ…‡ ļ„¬ļ…‡ ļ„’ļ„› ļ„µ ļ„±ļ„»ļ……ļ„Ŗ ļ„øļ…žļ„œļ„µļ…‡ ļ„»ļ„®:ļ„³ļ„¾ļ„±ļ…†ļ„Ŗ ļ„„ļ…‰ļ„ŗļ„„ ļ„¢ļ…‚ļ„ ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„Ŗļ„µļ„¢ļ…„ļ„»ļ…„ ļ„»ļ…‹ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ„®ī„”
ANOVA ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„ŗļ„³ ļ„®ļ„Ŗ ļ„¬ļ…„ ļ„øļ„µļ„Ŗļ…Œ ļ…ƒļ„›ļ„øļ…ˆ ļ„›ļ„µļ„¬ ļ„»ļ…‰
ļ„›ļ„¶ļ…‚ļ„ŗļ…„ļ„›ļ„¶ ļ„øļ„®-ļ„øļ…‡ļ„‘ ļ„˜ļ„®ļ…‹ļ„øļ…‚ ļ…ƒļ„øļ…žļ„ , ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„±ļ„µļ…‚ļ„±ļ„µ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„­ļ…‚ļ„µļ„®ļ…‚ ļ„ŗļ„³ļ…†ļ„» ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„®ļ…†ļ…œ ļ„“ļ…žļ„›
ļ…ƒļ„ŗļ…œļ„ļ„¶ MSW ļ…ƒļ„øļ…žļ„  ļ„Æļ…†ļ„¶ ļ„›ļ„µļ„® ļ„¬ļ…‚ ļ„ŗļ„³ļ„µļ„«ļ„® ļ„›ļ„µļ„¬ļ…„ ļ„»ļ…‰ī„” ļ…ƒļ„Æļ„”ļ„¶ļ…‚ F-ļ„„ļ…‰ļ„ŗļ„„ ļ…ƒļ„±ļ„¶ļ„›ļ……ļ„¶ ļ„•ļ„ŗļ…‡ ļ„Ŗļ„µļ…§ļ…‚ļ„ ļ„¬ļ…„ ļ„Æļ…„ļ…„-ļ„ ļ…‰ļ…žļ„› ļ„»ļ…‰ ļ„¢ļ…‹
ļ„‘ļ„›ļ„ŗļ„µ ļ„¬ļ…‹ ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„¬ļ…‡ ļ„ŗļ„³ļ…ˆ ļ„›ļ…„ļ„Ŗļ…„ ļ„¢ļ…‚ļ„ļ„¬ļ…„ ļ„»ļ…‰ (ļ„•ļ„¬ļ…‚ļ„»ļ„µļ„® ļ„¶ļ„”, ļ„Æļ…†ļ„¶ļ„§ ļ„„ļ…„-ļ„„ļ…‰ļ„ŗļ„„ ļ„¢ļ…‚ļ„ ļ„øļ…‰ļ„¶ļ„  ļ„¬ļ…‡ ļ„„ļ…„-
ļ„„ļ…‰ļ„ŗļ„„ ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ ļ„°ļ…‰ļ„ŗļ„¶ļ…‚ ļ„›ļ„µļ„®ļ…‚)ī™€
ļ„“ļ…žļ„› ļ„Ŗļ…‡ļ„¾ ļ„‘ļ…ƒļ„­ļ„˜ļ„® ļ„ ļ„”ļ„§ ļ„ŗļ…œļ„œļ…‡ļ„Æ
ā€¢ ļ„‘ļ„®ļ…‹ļ„ø ļ„¬ ļ„•ļ„¬ļ…‡ļ„¹:ļ„“ļ…žļ„› F-ļ„ŗļ„„ļ…‰ļ…ƒļ„„ļ„ŗļ…ƒļ„„ļ„› ļ„µļ…‚ļ„»ļ…„
ļ„
ļ„ļ„µļ……ļ…žļ„Æ-ļ„‘ļ…œļ„¬ļ„µ-ļ„ŗļ„³ļ…†ļ„» ļ„Æļ…ƒļ„µļ„øļ„µļ„Ŗļ„® ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„›ļ…‡ ļ„¢ļ…‚ļ„ļ„ 
ļ„›ļ„µļ…‹ ļ…ƒļ„› ļ„›ļ…„ ļ„³ļ„¶ļ„„ļ…„ļ„Æļ„¶ ļ„ļ„µļ……ļ…žļ„Æ ļ„ŗļ…‚ļ„­ļ„® ļ„øļ…žļ„œļ„µļ…‡ ļ„»ļ„®ī„”
ā€¢ ļ„­ ļ„µļ„® ļ„ø ļ„:ļ„ŗļ……ļ„Ŗļ…œļ„Ŗļ„µļ„Ŗļ…‚, ļ„ŗļ…‚ļ„­ļ…‚ļ„µļ„®ļ„Ŗļ…‚, ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„“ļ„›ļ„ŗļ…‚ļ„µļ„Ŗļ…‚, ļ„¢ļ…‹ļ„æļ„®ļ„“ļ…‹ļ„ļ„Ŗļ…‚, ļ„ŗļ…ƒļ„«ļ„µ ļ„Æļ…„ļ„²ļ…‚ļ„ø,
ļ„±ļ…‡ļ„Ŗļ„µļ„Ŗļ…„ļ„± ļ„®ļ„³ļ…†ļ„®ļ…‚ī„”
ā€¢ ļ„“ļ…žļ„›-ļ„Æ ļ„ŗļ„æ ļ„±ļ„® ļ„³ ļ„¬ļ…‹-ļ„Æ ļ„ŗļ„æ:
o ļ„“ļ…žļ„›-ļ„Æļ…‚ļ„ŗļ„æ: ļ„“ļ…žļ„›-ļ„Æļ…‚ļ„ŗļ„æ ļ„›ļ…‚ļ„µļ„›, ļ„ŗļ„µļ…‹ļ„Ŗ = ļ…ƒļ„øļ„ ļ„›ļ…‚ļ„µ + ļ„‘ļ…œļ„¬ļ„µī„”
o ļ„¬ļ…‹-ļ„Æļ…žļ„œļ…„: ļ„¬ļ…‹ ļ„›ļ…‚ļ„µļ„› + ļ„Æļ„µļ„ŗļ„Æļ„µ ļ„Æļ…„ļ„²ļ…‚ļ„ø, ļ„ŗļ„µļ…‹ļ„Ŗ = A + B + AƗB + ļ„ļ„¶ļ„Ŗļ…„ī„”
ā€¢ ļ…ƒļ„²ļ…œļ„®ļ„Ŗ ļ„ŗļ„³ ļ„®ļ„Ŗ ļ„„ļ…‰ļ„ŗļ„„ (ļ„Æļ…„ļ„“ļ…‹ļ„ļ„¹ ļ„¶ ļ„•ļ„¬ ļ„»ļ„µļ„©):
o ļ„øļ„µļ„ļ…‚ļ„ ļ„¬ļ…‡ ļ„¢ļ…‹ļ„æļ…‚ļ„ ļ„Ŗļ…Œ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ ļ„¬ļ…„ ļ„ļ„©ļ„®ļ…‚ ļ„›ļ„µļ…‹ī„”
o ļ„•ļ…žļ„Æļ„µ ļ„øļ…žļ„§ļ…‚ ļ„øļ…‡ļ„µļ…„ļ„˜ļ„ļ„ŗ ļ„øļ…‚ļ„¶ļ…‚ ļ„°ļ…‚ļ„µļ„³ Fī™€
o ļ„®ļ…‚ļ„¾ļ……ļ„› ļ„³ļ……ļ…žļ„¶ļ…‚ļ„ ļ„®ļ…‚ļ„¶ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ…‹; ļ„“ļ…žļ„«ļ…‡, F ā‰ˆ 1.0185 ā†’ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ…ƒļ„øļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„ī„”
ļ„”ļ„¾ļ…„2ļ…ƒļ„ŗļ„›ļ„¹ļ…‚.ļ„›ļ…‚ļ…žļ„³
ļ„ŗļ„³ ļ„Æļ„Ŗļ…„ ļ„ŗļ„³ ļ„®ļ„Ŗ
ļ„ŗļ…‚ļ„§ļ…‡ ļ„ŗļ…œļ„ļ…„ļ„Ŗ ļ„»ļ…‚ļ„¶ ļ„øļ…žļ„¶ ļ„øļ…‚ļ„Æļ„ŗ: ANOVA ļ„¢ļ…žļ„¢ ļ„»ļ…‰ ļ„¢ļ…‹ ļ…ƒļ„ŗļ„µļ…€ ļ„•ļ…žļ„ ļ…„ ļ„’ļ„øļ…‚ļ„¾ļ…‚ļ„ ļ„®ļ…†ļ…œ ļ„»ļ…„ ļ„®ļ„»ļ…„
ļ„
ļ„ŗļ……ļ„©ļ„¬ļ…‚, ļ„ŗļ„ļ…Œ ļ„»ļ„µļ…‡ļ„› ļ„ŗļ„³ļ…†ļ„»
ļ„‘ļ„Ŗļ…‡ ļ„ŗļ„³ļ…†ļ„»ļ…‚ļ„ ļ„¬ļ…‡ ļ„‘ļ…œļ„¬ļ„µ ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ ļ„¬ļ…‡ ļ„Æļ…‰ļ„„ļ„µļ„® ļ„®ļ…†ļ…œ ļ„øļ…„ ļ„ŗļ……ļ„©ļ„¬ļ…‚ ļ„»ļ…‰, ļ„“ļ„» ļ„°ļ…‰ļ„ŗļ„¶ļ…‚ ļ„›ļ„µļ„¬ļ…‚ ļ„»ļ…‰ ļ…ƒļ„› ļ„›ļ…„ ļ„­ļ……ļ„®ļ…‚ļ„ ļ…ƒļ„øļ…žļ„  ļ„‘ļ…œļ„Ŗļ„µ
ļ„‘ļ„ŗļ„¶ļ…„ ļ„»ļ„® ļ„¢ļ…‚ļ„ ļ…ƒļ„ŗļ„µļ…€ ļ„¹ļ…‹ļ„µī„” ļ„‘ļ„Ŗļ…‡ ļ„­ļ……ļ„®ļ…‚ļ„ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µļ„® ļ„Ŗļ…Œ ļ„Æļ…ƒļ„»ļ„¶ļ…‚ļ„, ļ„‘ļ„ŗļ…„
ļ„
ļ„¢ļ…‚ļ„ļ„  ļ„›ļ„µļ„¬ļ…‡ ļ„»ļ…‚ļ„ ļ…ƒļ„› ļ„“ļ…œļ„Ŗļ„µ (ļ…ƒļ„²ļ…œļ„®ļ„Ŗļ…‚ļ„øļ…‚ļ„)
ļ„“ļ…žļ„›ļ…‹ ļ…ƒļ„¢ļ„»ļ…‡ ļ…ƒļ„„ļ„–ļ„® ļ„›ļ…„ļ„Ŗļ…‡ ļ„ļ„— ļ„»ļ„® - ļ„Ŗļ……ļ„»ļ…‚ļ„§ļ…‡ F-ļ„„ļ…‰ļ„ŗļ„„ ļ„®ļ…‡ ļ…ƒļ„±ļ„¶ļ„›ļ……ļ„¶ ļ„•ļ„»ļ…„ ļ„›ļ…„ļ„Ŗļ…‚; ļ„¬ļ…‹ļ„øļ…ˆ ļ„“ļ…œļ„Ŗļ„µ ļ„±ļ„µļ…‚ļ„±ļ„µ ļ…ƒļ„„ļ„–ļ„® ļ„›ļ…„ļ„Ŗļ…‡
ļ„ļ„— ļ„»ļ„®, ļ„“ļ„ŗ ļ„¶ļ„” ļ„Ŗļ……ļ„ŗļ…„
ļ„
ļ„‘ļ…žļ„ļ…‡ ļ„ŗļ…œļ„ļ…„ļ„Ŗ ļ„¬ļ…„ ļ„Ŗļ……ļ„¶ļ„®ļ…‚ ļ„›ļ„µ ļ„ŗļ„›ļ„¬ļ…‡ ļ„»ļ…‹ī„”
"ļ„“ļ„» ļ„Æļ…‡ļ„Æļ„µ ļ…ƒļ„øļ…ƒļ„¬ļ„‘ļ„› ļ„•ļ„¬ļ…‡ļ„¹ ļ„ ļ„¶ļ„” ļ…ƒļ„­ļ„’ļ„® ļ„® ļ„¶ ļ…ƒļ„Ŗļ„’ļ„µ ļ„›ļ…„ļ„Ŗ ļ…ƒļ„ļ„’ ļ„»ļ…‰ī„” ļ„¢ļ…‡ļ„›ļ„µ ļ„Ŗļ……ļ„» ļ„®ļ…†ļ…œ ļ„›ļ…‹ļ„” ļ„ļ„¶ļ„Ŗļ…„ ļ„®ļ„¾ļ„µ
ļ„’ļ„•
ļ„
ļ„¬ļ…„ ļ„»ļ…‰ ļ„¢ ļ„ ļ„Ŗļ……ļ„» ļ„§ļ…‡ ļ„›ļ…‹ļ„¶ ļ„›ļ…‹ļ„” ļ„ŗļ……ļ„£ ļ„‘ ļ„»ļ„®, ļ„Ŗ ļ„ ļ„’ļ„Æļ„©ļ…„ ļ„°ļ…„ļ„§ļ„±ļ…‰ļ„› ļ„ŗ ļ„ļ„£ļ…„ ļ„›ļ„µļ„® ļ„¶ļ„” ļ„±ļ…‡ļ…ƒļ„£ļ„¢ļ„› ļ„³ļ…ƒļ„»ļ„ŗļ…†ļ„ŗ ļ„›ļ„µļ…‹ī„”"