# Chapter 19 - Chapter 19 19.1 H 0 The two population...

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Chapter 19 19.1 : H 0 The two population locations are the same : H 1 The location of population 1 is different from the location of population 2 5 . 232 2 ) 1 15 15 ( 15 2 ) 1 n n ( n ) T ( E 2 1 1 = + + = + + = 11 . 24 12 ) 1 15 15 )( 15 )( 15 ( 12 ) 1 n n ( n n 2 1 2 1 T = + + = + + = σ a T ) T ( E T z σ - = = 11 . 24 5 . 232 250 - = .73, p-value = 2P(Z > .73) = 2(1 – .7673) = .4654. b T ) T ( E T z σ - = = 11 . 24 5 . 232 275 - = 1.76, p-value 2P(Z > 1.76) = 2(1 – .9608) = .0784. c The value of the test statistic increases and the p-value decreases. 19.2 : H 0 The two population locations are the same : H 1 The location of population 1 is to the right of the location of population 2 Rejection region: 05 . z z z = α = 1.645 065 , 1 2 ) 1 40 30 ( 30 2 ) 1 n n ( n ) T ( E 2 1 1 = + + = + + = 26 . 84 12 ) 1 40 30 )( 40 )( 30 ( 12 ) 1 n n ( n n 2 1 2 1 T = + + = + + = σ a T ) T ( E T z σ - = = 26 . 84 065 , 1 205 , 1 - = 1.66, p-value P(Z > 1.66) = 1 – .9515 = .0485. There is enough evidence to infer that the location of population 1 is to the right of the location of population 2. b T ) T ( E T z σ - = = 26 . 84 065 , 1 065 , 1 - = 0, p-value = P(Z > 0) = .5. There is not enough evidence to infer that the location of population 1 is to the right of the location of population 2. c The value of the test statistic decreases and the p-value increases. 19.3 : H 0 The two population locations are the same : H 1 The location of population 1 is to the left of the location of population 2 Rejection region: T L T = 19 Sample 1 Rank Sample 2 Rank 75 5 90 9 60 1 72 3 73 4 103 10 66 2 82 8 81 7 78 6 101

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1 T = 19 2 T = 36 There is enough evidence to infer that the location of population 1 is to the left of the location of population 2. 19.4 : H 0 The two population locations are the same : H 1 The location of population 1 is different from the location of population 2 Rejection region: T U T = 127 or T L T = 83 Sample 1 Rank Sample 2 Rank 15 4.0 8 2.0 7 1.0 27 18.0 22 14.0 17 7.0 20 .5 25 16.0 32 20.0 20 11.5 18 9.5 16 5.0 26 17.0 21 13.0 17 7.0 17 7.0 23 15.0 10 3.0 30 19.0 18 9.5 1 T = 118 2 T = 92 There is not enough evidence to infer that the location of population 1 is different from the location of population 2. 19.5 : H 0 The two population locations are the same : H 1 The location of population 1 is to the left of the location of population 2 1 2 3 4 5 6 7 8 9 10 A B C D E Wilcoxon Rank Sum Test Rank Sum Observations New 623.5 25 Leading 651.5 25 z Stat -0.2716 P(Z<=z) one-tail 0.3929 z Critical one-tail 1.6449 P(Z<=z) two-tail 0.7858 z Critical two-tail 1.96 a z = –.27, p-value = .3929. There is not enough evidence to infer that the new beer is less highly rated than the leading brand. b The printout is identical to that of part a.
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Chapter 19 - Chapter 19 19.1 H 0 The two population...

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