Testing-Difference-in-Means.xls

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Testing the Difference in Two Population Means Data Current Previous Evidence Sample1 Sample2 1 40 405 33 334 2 125 150 3 4 5 6 7 % 9 10 11

540 100 200 30 1200 265 90 206 1%

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4%9 590 310

Sample Sample1 1 Sample Sample2 2 n Size 16 16 Mean 352.375 319.5625   x-bar 

Assumptions Either 1. Populations normal r 2. !ar"e samples σ , σ  -non 1 2

520 Popn. 1 Popn. 2 σ 95 Popn. St#. $evn. 152 12% 212 30 Hpothesis Testing 1055 300 &est Statisti'   0.6605 z  At an  of  %5  p'value 129 !ull Hpothesis 5( "onfidence #nterval for the Difference in Means H() 1  * 40 0   0.50%9 "onfidence #nterval 2 H )  +* 440 0   0.7455 95( 32.%125 32.% 125 ) 97.369 97.369 * $   +64.556 %   130.1%1 & ( 1 2 H() 1  ,* 610 0   0.2545 2 20%

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"omparing Two population Means

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/me vs isa

Evidence Size Mean

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Popn. St#. $evn.

Sample1 Sample2 25 36 n %0 75   x-bar  Popn. 1 5

Popn. 2 3

Assumptions Either 1. Populations normal r 2. !ar"e samples σ , σ  -non 1 2

σ

Hpothesis Testing &est Statisti'



!ull Hpothesis H() 1  * 2000 2 H() 1  +* 2000 2 H() 1  ,* 2000 2

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0.0000

At an  of  5( -eect

 

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-eect

 

1.0000

 p'value

"onfidence #nterval for the Difference in Means "onfidence #nterval 94(

5 ) 2.10279 * $   2.%9721 %   7.10279 &

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Data ame1 ame2 Sample1 Sample2

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1 2 3 4

1547 1299 150% 1323

1366 1547 1530 1500

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1294

1411

6 7 % 9 10 11

1566 131% 1349 1254 1465 1474

1290 1313 1390 1466 152% 1369

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1271 1325 123%

1239 1293 1316

15 16 17 1% 19

1340 1333 1239 1314 1436

151% 1435 1264 1293 1359

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1342 1524 1490 1400

12%0 1352 1426 1302

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t 'Test for Difference in Population Means

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Evidence Sample1 Sample2 Size 27 27 n Mean 13%1.3 1374.96   x-bar  St#. $eviation 107.005 95.6056 s

Assumptions Populations ormal 0 Population arian'es Eual   F  ratio 1.2526%    p+value 0.569%

Assuming Population /ariances are E0ual 2

Poole# arian'e 10295.2  s p &est Statisti'   0.2293 t  # 52 !ull Hpothesis H() 1  * 0   2 H() H()

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 +* 0  ,* 0 2 2

   

At an  of  "onfidence #nterval for difference in Population Means 5( "onfidence #nterval 0.%195 95( 6.33333 ) 55.4144 * $   +49.0%1 %   61.7477 &

 p'value

0.5902 0.409%

Assuming Population /ariances are ne0ual &est Statisti'   0.22934 t  # 51 !ull Hpothesis H() 1  * 0   2 H() 1  +* 0   2 H() 1  ,* 0   2

At an  of  "onfidence #nterval for difference in Population Means 5( "onfidence #nterval  p'value 0.%195 95( 6.33333 ) 55.4402 * $   +49.1069 % 61.77357 & 0.5902 0.409%

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t 'Test for Difference in Population Means

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Evidence Sample1 Sample2

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Size Mean St#. $eviation

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n 25 1%   x-bar  s 4

Assumptions Populations ormal 0 Population arian'es Eual F  ratio 4    p+value 0.0075

Assuming Population /ariances are E0ual 2

arning) E0ual variance assumption is 0uestiona3le.

Poole# arian'e 11.3%46  s p &est Statisti'   +3.1474 t  # 39 !ull Hpothesis H() 1  * 1   2 H() H()

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 +* 1  ,* 1 2 2

   

At an  of  "onfidence #nterval for difference in Population Means 5( "onfidence #nterval 0.0032 -eect 95( +2.4 ) 2.1%5 * $   +4.5%5 %   +0.215 &

 p'value

0.0016 0.99%4

-eect

Assuming Population /ariances are ne0ual &est Statisti'  +3.60399 t  # 37 !ull Hpothesis H() 1  * 1   2 H() 1  +* 1   2 H() 1  ,* 1   2

At an  of  "onfidence #nterval for difference in Population Means  p'value 5( "onfidence #nterval 0.0009 -eect 95( +2.4 ) 1.91151 * $   +4.3115 % +0.4%%49 & 0.0005 0.9995

-eect

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