A sociologist randomly selects 675 females 15 to 19 years old and asks each to d

Question

A sociologist randomly selects 675 females 15 to 19 years old and asks each to disclose her family structure at age 14 and whether she has abused drugs. Use the results in the table to answer the questions below. Structure 1 Structure 2 Structure 3 Structure 4 Had abused drugs 69 67 70 62 Had not abused drugs 82 106 68 151 Compute the expected values of each cell under the assumption of independence. Structure 1 Structure 2 Structure 3 Structure 4 Had abused drugs Had not abused drugs (Round to three decimal places as needed.) Compute the chi-square test statistic. X_0^2 = (Do not round until the final answer. Then round to three decimal places as needed.) Test whether family structure and drug history of 15- to 19-year-old females are independent at the alpha = 0.05 level of significance. X_0^2 is less than or equal to X_alpha^2, so do not reject H_0. X_0^2 is greater than X_alpha^2, so do not reject H_0. X_0^2 is less than or equal to X_alpha^2, so reject H_0. X_0^2 is greater than X_alpha^2, so reject H_0.

Explanation / Answer

a)

b)X2 =19.324

critical value = 7.815

c) option D

Observed O structure 1 structure 2 structure 3 structure 4 Total had abused 69 67 70 62 268 had not abused 82 106 68 151 407 Total 151 173 138 213 675 Expected E=rowtotal*column total/grand total structure 1 structure 2 structure 3 structure 4 Total had abused 59.953 68.687 54.791 84.569 268 had not abused 91.047 104.313 83.209 128.431 407 Total 151 173 138 213 675 chi square =(O-E)^2/E structure 1 structure 2 structure 3 structure 4 Total had abused 1.365 0.0415 4.2217 6.0230 11.651 had not abused 0.899 0.027 2.780 3.966 7.672 Total 2.264 0.069 7.002 9.989 19.3236

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