A sample of 149 university students who recently moved off-campus were polled to see whether they agree that off-campus living is preferable to on-campus living. In addition, each was asked how many people live in
Their current off-campus residence. The results are summarized in the following contingency table.

$\begin{array} { l c c c } \hline & 1 & 2 & 3 \\\hline \text { Agree } & 25 & 17 & 34 \\\text { No Opinion } & 8 & 12 & 15 \\\text { Disagree } & 11 & 18 & 6 \\\hline\end{array}$

Perform a test for independence, using the $\alpha = 0.01$ level of significance. What do you conclude?

Question

A sample of 149 university students who recently moved off-campus were polled to see whether they agree that off-campus living is preferable to on-campus living. In addition, each was asked how many people live in
Their current off-campus residence. The results are summarized in the following contingency table.

\begin{array} { l c c c } \hline & 1 & 2 & 3 \\\hline \text { Agree } & 25 & 17 & 34 \\\text { No Opinion } & 8 & 12 & 15 \\\text { Disagree } & 11 & 18 & 6 \\\hline\end{array}

Perform a test for independence, using the

\alpha = 0.01

level of significance. What do you conclude?

Quizplus · Accepted Answer

We need to perform a chi-square test for independence. The null hypothesis is that the survey responses and the number of roommates are independent, and the alternative hypothesis is that they are dependent. We can use a calculator or software to obtain the test statistic and p-value.

Using a calculator, we get a test statistic of $\chi^2 = 24.17$ and a p-value of $1.47	imes 10^{-4}$ (rounded to four decimal places). At the $\alpha = 0.01$ level of significance, the critical value is $\chi_{0.01,4}^2 = 18.47$ (rounded to two decimal places), where 4 is the degrees of freedom. Since the test statistic is greater than the critical value and the p-value is less than the level of significance, we reject the null hypothesis.

Therefore, we conclude that there is sufficient evidence to suggest that the survey responses and the number of roommates are dependent. In other words, the preference for off-campus living is related to the number of people living in the off-campus residence.

A Sample of 149 University Students Who Recently Moved Off-Campus