5 Suppose that 20 out of 50 females and 10 out of 40 males are depressed in a

Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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5. Suppose that 20 out of 50 females and 10 out of 40 males are depressed in a sample. Determine whether the frequency of depression is related to sex (30 pts). Solution. This was an in-class example we studied. Let us formulate this problem in terms of categorical data. Model specification (10 pts). Let p 11 and p 21 be the respective proportions of depression in females and males. p 12 and p 22 are the respective proportions of non-depression in females and males. We are interested in testing H 0 : p 11 = p 21 , p 12 = p 22 . 4 pts will be deducted if you do not clearly specify what these p ij ’s are. Inference setup (10 pts). Under H 0 , we compute the expected number of elements in each cell and compute the χ 2 test statistic value. Actual computation (10pts). Then the cutoff value χ 2 α, 1 for α -level test can be computed from N (0 , 1) . Note that α = P ( χ 2 1 > χ 2 α, 1 ) = P ( Z 2 > χ 2 α, 1 ) = 2 P ( Z > χ α, 1 ) . So χ 2 α, 1 = Z 2 α/ 2 . For α = 0 . 05 , χ 2 α, 1 = 1 . 96 2 . For this problem, pnorm or qnorm values will be given. 2

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