A study of first-year college students asked separate random samples of students from private and public universities the following question: “How many miles is this university from your permanent home?” Students had to choose from the following options: 5 or fewer, 6 to 10, 11 to 50, 51 to 100, 101 to 500, or more than 500.27 Here is the two-way table summarizing the responses:

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).

Here is Minitab output from a chi-square test.

Chi-Square Test: Public, Private

Expected counts are printed below observed counts

Chi-Square contributions are printed below expected counts

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

d. Interpret the P-value. What conclusion would you draw?

Transcribed Image Text:

Public Private Total 5 or less 1951 1028 2979 1869.6 1109.4 3.54 5.97 6 to 10 2688 1285 3973 2493.4 1479.6 15.19 25.59 11 to 50 10971 5527 16498 10354 6144.1 36.77 61.98 51 to 100 6765 2211 8976 5633.2 3342.8 227.4 383.2 101 to 500 15177 6195 21372 13413 7959.2 232 391 Over 500 5811 9486 15297 9600.2 5696.8 1496 2520.4 Total 43363 25732 69095 Chi-Sq = 5398.7, DF = 5, P-Value = 0.0000 %3D