Chapter 13

# Chapter 13 - 209 Chapter 13 For all exercises in Chapters 13 and 14 we employed the F-test of two variances at the 5 significance level to decide

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209 Chapter 13 For all exercises in Chapters 13 and 14 we employed the F-test of two variances at the 5% significance level to decide which one of the equal-variances or unequal-variances t-test and estimator of the difference between two means to use to solve the problem. Additionally, for exercises that compare two populations and are accompanied by data files, our answers were derived by defining the sample from population 1 as the data stored in the first column (often column A in Excel and column 1 in Minitab). The data stored in the second column represent the sample from population 2. Paired differences were defined as the difference between the variable in the first column minus the variable in the second column. 13.1 ÷ ÷ø ö ç çè æ + ± - a 2 1 2 2 / 2 1 1 1 ) ( n n s t x x p = (524 4 469) ± 2.009 ÷ø ö çè æ + 25 1 25 1 261 , 18 = 55± 76.79 13.2 ÷ ÷ø ö ç çè æ + ± - a 2 1 2 2 / 2 1 1 1 ) ( n n s t x x p = (524 4 469) ± 2.009 ÷ø ö çè æ + 25 1 25 1 637 , 79 = 55± 160.35 13.3 The interval widens. 13.4 ÷ ÷ø

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ö ç çè æ + ± - a 2 1 2 2 / 2 1 1 1 ) ( n n s t x x p = (524 & 469) ± 1.972 ÷ø ö çè æ + 100 1 100 1 261 , 18 = 55± 37.69 13.5 The interval narrows. 13.6 to 13.12 ) ( : 2 1 0 m - m H = 0 ) ( : 2 1 1 m - m H ¹ 0 13.6 Rejection region: = - < n a , 2 / t t = - 22 , 025 . t -2.074 or = > n a , 2 / t t = 22 , 025 . t 2.074 ÷ ÷ø ö ç çè æ + m - m - - = 2 1 2 2 1 2 1 1 1 ) ( ) ( n n s x x t p = ÷ø ö çè æ + - - 12 1 12 1 275 0 ) 71 74 ( = .44, p-value = .6617 (Excel). There is not enough evidence to infer that the population means differ. 210 13.7 Rejection region: = - < n a , 2 / t t = - 22 , 025 . t -2.074 or = > n a , 2 / t t = 22 , 025 . t 2.074 ÷ ÷ø
ö ç çè æ + m - m - - = 2 1 2 2 1 2 1 1 1 ) ( ) ( n n s x x t p = ÷ø ö çè æ + - - 12 1 12 1 652 , 41 0 ) 71 74 ( = .036, p-value = .9716 (Excel). There is not enough evidence to infer that the population means differ. 13.8 The value of the test statistic decreases and the p-value increases. 13.9 Rejection region: = - < n a , 2 / t t = - 289 , 025 . t -1.960 or = > n a , 2 / t t = 289 , 025 . t 1.960 ÷ ÷ ø ö ç ç è æ + m - m - - = 2 2 2 1 2 1 2 1 2 1 ) ( ) ( n s n s x x t = ÷ø ö çè æ + - - 150

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225 150 324 0 ) 71 74 ( = 1.57, p-value = .1179 (Excel). There is not enough evidence to infer that the population means differ. 13.10 The value of the test statistic increases and the p-value decreases. 13.11 Rejection region: = - < n a , 2 / t t = - 22 , 025 . t -2.074 or = > n a , 2 / t t = 22 , 025 . t 2.074 ÷ ÷ø ö ç çè æ + m - m - - = 2 1 2 2 1 2 1 1 1 ) ( ) ( n n s x x t p = ÷ø ö çè æ + - - 12 1 12 1 275 0 ) 71 76 ( = .74, p-value = .4676 (Excel). There is not enough evidence to infer that the population means differ. 13.12 The value of the test statistic increases and the p-value decreases.
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## This note was uploaded on 06/06/2011 for the course ADMS 2320 taught by Professor Rochon during the Spring '08 term at York University.

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Chapter 13 - 209 Chapter 13 For all exercises in Chapters 13 and 14 we employed the F-test of two variances at the 5 significance level to decide

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