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15 SM_Ch13

# 15 SM_Ch13 - Chapter 13 13.1a Equal-variances estimator 1 1...

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Chapter 13 13.1a Equal-variances estimator + ± - α 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 + ± - α 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 + ± - α 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 μ - μ = 0 ) ( : H 2 1 1 μ - μ 0 a Equal-variances test statistic Rejection region: = - < ν α , 2 / t t = - 22 , 025 . t –2.074 or = ν α , 2 / t t = 22 , 025 . t 2.074 + μ - μ - - = 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 ( 0 ) 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: = - < ν α , 2 / t t = - 22 , 025 . t –2.074 or = ν α , 2 / t t = 22 , 025 . t 2.074 + μ - μ - - = 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 ( 0 ) 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. 25

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d Equal-variances test statistic Rejection region: = - < ν α , 2 / t t = - 298 , 025 . t –1.960 or = ν α , 2 / t t = 298 , 025 . t 1.960 + μ - μ - - = 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 ( 0 ) 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: = - < ν α , 2 / t t = - 22 , 025 . t –2.074 or = ν α , 2 / t t = 22 , 025 . t 2.074 + μ - μ - - = 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 ( 0 ) 71 76 ( 2 2 = .72, p-value = .4796. There is not enough evidence to infer that the population means differ. g The value of the test statistic increases and the p-value decreases. 13.3 a Unequal-variances estimator 1 n ) n / s ( 1 n ) n / s ( ) n / s n / s ( 2 2 2 2 2 1 2 1 2 1 2 2 2 2 1 2 1 - + - + = ν = 64.8 (rounded to 65, approximated by 70 = ν ) + ± - α 2 2 2 1 2 1 2 / 2 1 n s n s t ) x x ( = (63 – 60) ± 1.667 + 45 7 50 18 2 2 = 3 ± 4.59 b Unequal-variances estimator 1 n ) n / s ( 1 n ) n / s ( ) n / s n / s ( 2 2 2 2 2 1 2 1 2 1 2 2 2 2 1 2 1 - + - + = ν = 63.1 (rounded to 63, approximated by 60 = ν ) + ± - α 2 2 2 1 2 1 2 / 2 1 n s n s t ) x x ( = (63 – 60) ± 1.671 + 45 15 50 41 2 2 = 3 ± 10.38 c The interval widens.
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15 SM_Ch13 - Chapter 13 13.1a Equal-variances estimator 1 1...

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