Where do young adults live? A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):25 Female Male Parents’ home 923 986 Another person’s home 144 132 Own place 1294 1129 Group quarters 127 119

(a) Should we use a chi-square test for homogeneity or a chi-square test for independence in this setting?

Justify your answer.

(b) State appropriate hypotheses for performing the type of test you chose in part (a).

Minitab output from a chi-square test is shown below.

Chi-Square Test: Female, Male Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Female Male Total 1 923 986 1909 978.49 930.51 3.147 3.309 2 144 132 276 141.47 134.53 0.045 0.048 3 1294 1129 2423 1241.95 1181.05 2.181 2.294 4 127 119 246 126.09 119.91 0.007 0.007 Total 2488 2366 4854 Chi-Sq = 11.038, DF = 3, P-Value = 0.012

(c) Check that the conditions for carrying out the test are met.

(d) Interpret the P-value in context. What conclusion would you draw?