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prob5sol

# 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 = 0

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