HW12 - Solution to HW12: Problem 1: a) It appears that...

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Solution to HW12: Problem 1: a) It appears that brand A and B might have the same mean, or perhaps B and C, but it appears that brand A and C have different means. b) By rule of thumb, ratio of the largest variance to the smallest variance is 2 1.619835 1 . 1 4 . 1 2 2 < = , so we are okay to pool. c) : H : H a 3 2 1 0 = = μ they are not equal. 32 . 10 20 20 10 8 . 10 20 2 . 10 20 6 . 9 10 3 2 1 3 3 2 2 1 1 = + + × + × + × = + + + + = n n n X n X n X n X 2 3 3 2 2 2 2 1 1 Trt ) ( ) ( ) ( SS X X n X X n X X n + + = 2 2 2 10.32) - (10.8 20 10.32) - (10.2 20 10.32) - (9.6 10 × + × + × = 0.08 1 = with 2 1 3 = = df 75.44 ) 1 ( ) 1 ( ) 1 ( SS 2 3 3 2 2 2 2 1 1 = + + = s n s n s n E 47 3 3 2 1 = + + = n n n df 3.195056 F 3.139979 47 / 2 / 0.05,2,47 = < = = SSE SS F Trt We fail to reject the null hypothesis and conclude there is no significant evidence of inequality between two means. d) 0.1178672 44 . 75 08 . 10 08 . 10 2 = + = + = = Trt SS SSE SSE SST SSE R e) A and C are significant different as they have the largest difference in mean. In fact, if you test the equality of A and C , you will reject the null hypothesis.
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HW12 - Solution to HW12: Problem 1: a) It appears that...

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