A sample of 149 university students who recently moved off-campus were polled to see whether $\begin{array}{lccc}
\hline & 1 & 2 & 3 \
\hline \text { Agree } & 25 & 17 & 34 \
\text { No Opinion } & 8 & 12 & 15 \
\text { Disagree } & 11 & 18 & 6 \
\hline
\end{array}$

Perform a test for independence, using the $\alpha = 0.01$ level of significance. What do you conclude?
A) Reject $H _ { 0 }$. It appears that the survey responses and the number of roommates are dependent.
B) Do not reject $H _ { 0 }$. There is insufficient evidence to conclude that the survey responses and the number of roommates are dependent.

Question

A sample of 149 university students who recently moved off-campus were polled to see whether $\begin{array}{lccc}
\hline & 1 & 2 & 3 \
\hline \text { Agree } & 25 & 17 & 34 \
\text { No Opinion } & 8 & 12 & 15 \
\text { Disagree } & 11 & 18 & 6 \
\hline
\end{array}$

Perform a test for independence, using the $\alpha = 0.01$ level of significance. What do you conclude?
A) Reject $H _ { 0 }$. It appears that the survey responses and the number of roommates are dependent.
B) Do not reject $H _ { 0 }$. There is insufficient evidence to conclude that the survey responses and the number of roommates are dependent.

Quizplus · Accepted Answer

To test for independence, a chi-square test is used. The null hypothesis $H_0$ states that there is no association between the survey responses and the number of roommates (they are independent). The alternative hypothesis $H_a$ suggests that there is an association (they are dependent). Without calculating the exact chi-square statistic and p-value here, if the decision is to reject $H_0$, it means the test found sufficient evidence to conclude that the survey responses and the number of roommates are dependent, indicating an association between these two variables.

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