Question

49. Where do young adults live? A survey by the National p9 727 Institutes of Health asked a random sample of young 747 aduilts (aged 19 to 25 years). Where do you live now? That is, where do you stay most often?" Here is the full twoway table (omitting a few who refused to answer and one who reported being homeless) Gender Female Male Tol 923 986 1909 Parents' home Living Another person's home 144 132 location Own place 294 1129 2423 119 246 2488 23664854 (a) Should we use a chi-square test for homogeneity or a Group quarters 127 Total 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). Here is Minitab output from a chi-square test. Chi-square Tests Female, Hale Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Female 923 Male Total 986 1909 Parents' home 978.49930.51 3.147 3.309 Another home 144 132 276 141.47 134.53 0.045 0.048 own place 1294 1129 2423 1241.95 1181.05 2.294 2.181 127 Group 119 246 126.09 119.91 0.007 0.007 Total Chi-sq -11.038, DF 3, P-Value 0.012 2488 2366 4854 e) Cheek that the conditions for carrying out the test are met. (d) Interpret the Pvalue. What conclusion would you draw?

Answer 1

a) Chi square test for independence

b) The null and alternative hypothesis

H0: Living location is independent of gender.

Ha: Living location is not independent of gender.

c) Conditions are met as

1. The sampling is simple random sampling .

2. The variable is under study is catagorical .

3. Expected frequency in each cell is more than 5 .

d) P value = 0.012

Since P value > 0.05 , the result is not significant

We reject the null hypothesis

There is sufficient evidence to conclude that living location is not independent of gender.