ISM Chapter 13

ISM Chapter 13 - Chapter 13 13.1a Equal-variances estimator...

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Unformatted text preview: Chapter 13 13.1a Equal-variances estimator + - 2 1 2 p 2 / 2 1 n 1 n 1 s t ) x x ( = (524 469) 2.009 + - +- +- 25 1 25 1 2 25 25 131 ) 1 25 ( 129 ) 1 25 ( 2 2 = 55 73.87 b Equal-variances estimator + - 2 1 2 p 2 / 2 1 n 1 n 1 s t ) x x ( = (524 469) 2.009 + - +- +- 25 1 25 1 2 25 25 260 ) 1 25 ( 255 ) 1 25 ( 2 2 = 55 146.33 c The interval widens. d Equal-variances estimator + - 2 1 2 p 2 / 2 1 n 1 n 1 s t ) x x ( = (524 469) 1.972 + - +- +- 100 1 100 1 2 100 100 131 ) 1 100 ( 129 ) 1 100 ( 2 2 = 55 36.26 e The interval narrows. 13.2 ) ( : H 2 1 - = 0 ) ( : H 2 1 1 - a Equal-variances test statistic Rejection region: =- < , 2 / t t =- 22 , 025 . t 2.074 or = , 2 / t t = 22 , 025 . t 2.074 + - -- = 2 1 2 p 2 1 2 1 n 1 n 1 s ) ( ) x x ( t = + - +- +--- 12 1 12 1 2 12 12 16 ) 1 12 ( 18 ) 1 12 ( ) 71 74 ( 2 2 = .43, p-value = .6703. There is not enough evidence to infer that the population means differ. b Equal-variances test statistic Rejection region: =- < , 2 / t t =- 22 , 025 . t 2.074 or = , 2 / t t = 22 , 025 . t 2.074 + - -- = 2 1 2 p 2 1 2 1 n 1 n 1 s ) ( ) x x ( t = + - +- +--- 12 1 12 1 2 12 12 198 ) 1 12 ( 210 ) 1 12 ( ) 71 74 ( 2 2 = .04, p-value = .9716. There is not enough evidence to infer that the population means differ. c The value of the test statistic decreases and the p-value increases. 13 d Equal-variances test statistic Rejection region: =- < , 2 / t t =- 298 , 025 . t 1.960 or = , 2 / t t = 298 , 025 . t 1.960 + - -- = 2 1 2 p 2 1 2 1 n 1 n 1 s ) ( ) x x ( t = + - +- +--- 150 1 150 1 2 150 150 16 ) 1 150 ( 18 ) 1 150 ( ) 71 74 ( 2 2 = 1.53, p-value = .1282. There is not enough evidence to infer that the population means differ. e The value of the test statistic increases and the p-value decreases. f Rejection region: =- < , 2 / t t =- 22 , 025 . t 2.074 or = , 2 / t t = 22 , 025 . t 2.074 + - -- = 2 1 2 p 2 1 2 1 n 1 n 1 s ) ( ) x x ( t = + - +- +--- 12 1 12 1 2 12 12 16 ) 1 12 ( 18 ) 1 12 ( ) 71 76 ( 2 2 = .72, p-value = .4796. There is not enough evidence to infer that the population means differ....
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This homework help was uploaded on 04/18/2008 for the course STAT 212 taught by Professor Holt during the Spring '08 term at UVA.

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ISM Chapter 13 - Chapter 13 13.1a Equal-variances estimator...

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