f07mid2soln - Stat 571 Second Midterm Exam 1(a df= 10(13 1...

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Stat 571 Second Midterm Exam November 20, 2007 1(a) df= 10+(13 - 1) - 2 = 20 since one zero is dropped in the second sample. With a 2-sided test . 02 < p < . 05 and we conclude that the two groups have different variances (reject “ σ 1 = σ 2 ”). (b) Using the t-test that does not require equal variance we get s 2 ¯ y 1 - ¯ y 2 = 8 . 06 2 10 + 2 . 05 2 13 = 6 . 82 and t = (90 . 30 - 86 . 65) / 6 . 82 = 1 . 398. Using df= 9 and a 2-sided test we get . 10 < p < . 20. We fail to reject “ μ 1 = μ 2 ”: there is no significant difference between the average size of the two Lyrebird species. 2(a) the Mann-Whitney test p-value is 0 . 028 because the ranks do not change. The t-test p-value is smaller than 0 . 006 because only ¯ y 1 - ¯ y 2 changes (increases). Sample sizes (4) and variability ( s 1 and s 2 ) stay the same. So t increases and the p-value decreases. (b) Data set 3 (top). Since the ranks are the same in data set 3 and in data set 1, the p-value from Mann- Whitney test is 0 . 028, which is < . 05. With data set 4 the rank sums would be 23 and 13, and 13 is too big to get significance at the .
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