prob5sol - The Hong Kong University of Science and...

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- 1 - The Hong Kong University of Science and Technology ISMT 111 - Business statistics, Fall 2002 Problem Sheet 5 Solutions 1. H 0 : m 1 - m 2 = 0 H 1 : m 1 - m 2 0 Test statistic t = 2 1 2 1 2 1 1 1 ) ( ) ( n n s x x + - - - m m , where s = ) 2 ( ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 - + - + - n n S n S n = 2 6 5 ) 25 . 10920 )( 5 ( ) 25 . 15750 )( 4 ( - + + = 91667 . 13066 Then t = ) 6 1 5 1 ( 91667 . 13066 7940 8230 + - = 4.19. And t α /2, n1 + n2 – 2 = t 0.005, 9 = 3.25. Since t > t 0.005, 9 , reject H 0 at 0.05 level of significance. 2. H 0 : m = $33.99 H 1 : m > $33.99 Test statistic 0 . 2 36 / 0 . 3 99 . 33 99 . 34 = - = z . p -value = P( z > 2) = 0.0228. Reject H 0 if a p -value. Hence, the range is 1 a 0.0228. 3. (a) Person d = A – B 1 6 2 3 3 -5 4 8 5 0 6 8 7 11 8 -1 f8e5 d 3.75 s d 5.44 H 0 : m d
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- 2 - H 1 : m d > 0 Test statistic t = 95 . 1 8 / 44 . 5 75 . 3 / = = n s d d . And t α , n– 1 = t 0.025, 7 = 2.365. Since t < t 0.025, 7 , we cannot reject H 0 . We do not have sufficient evidence to suggest that A charges higher average monthly premium than B. (b) As t 0.025, 7 = 2.365 & t 0.05, 7 = 1.895 0.025 < p-value < 0.05. Hence, the lower bound on the p-value is 0.025 4. (a) H 0 : p = 0.5 H 1 : p > 0.5 p ˆ = 100 55 = 0.55 Test statistic z = 1 100 ) 5 . 0 )( 5 . 0 ( 5 . 0 55 . 0 ˆ = - = - n pq p p . And z α = z 0.05 = 1.645. Since z < z 0.05 , cannot reject H 0 at 0.05 level of significance. (b) Let m 1 be the population average monthly salary among those with one job offer. Let m 2 be the population average monthly salary among those with three jobs offer. H 0 : m 1 - m 2 = 0 H 1 : m 1 - m 2 0 Test statistic z = 1 . 2 30 1500 40 1200 11000 10300 ) ( ) ( 2 2 2 2 2 1 2 1 2 1 2 1 - = + - = + - - - n S n S x x m m . p -value = 2 P( z > 2.1) = 2(0.0179) = 0.0358. Since p -value < a = 0.05, reject H 0 at 0.05 level of significance. 5. (a) Let m 1 be the mean salary per hours of male factory workers. Let m 2 be the mean salary per hours of female factory workers. H 0 : m 1 - m 2 = 1.5 H 1 : m 1 - m
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- 3 - Test statistic t = 2 1 2 1 2 1 1 1 ) ( ) ( n n s x x + - - - m m , where s = ) 2 ( ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 - + - + - n n S n S n = 2319 . 6 2 12 11 ) 6 . 6 )( 1 12 ( ) 8 . 5 )( 1 11 ( 2 2 = - + - + - Then t = 8836 . 1 12 1 11 1 2319 . 6 5 . 1 ) 25 . 35 65 . 41 ( = + - - . And
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prob5sol - The Hong Kong University of Science and...

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