A survey of students at a college was asked if they lived at home with their parents, rented an apartment, or owned their own home. The results are shown in the table below sorted by gender. At $\alpha = 0.05$, test the claim that living accommodations are independent of the gender of the student.
$\begin{array}{r|lll}
& \text { Live with Parent } & \text { Rent Apartment } & \text { Own Home } \
\hline \text { Male } & 20 & 26 & 19 \
\text { Female } & 18 & 28 & 26
\end{array}$

A) Reject the null hypothesis. There is sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.
B) Reject the null hypothesis. There is not sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.
C) Fail to reject the null hypothesis. There is sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.
D) Fail to reject the null hypothesis. There is not sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.

Question

A survey of students at a college was asked if they lived at home with their parents, rented an apartment, or owned their own home. The results are shown in the table below sorted by gender. At $\alpha = 0.05$, test the claim that living accommodations are independent of the gender of the student.
$\begin{array}{r|lll} 
& \text { Live with Parent } & \text { Rent Apartment } & \text { Own Home } \
\hline \text { Male } & 20 & 26 & 19 \
\text { Female } & 18 & 28 & 26
\end{array}$

A) Reject the null hypothesis. There is sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.
B) Reject the null hypothesis. There is not sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.
C) Fail to reject the null hypothesis. There is sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.
D) Fail to reject the null hypothesis. There is not sufficient evident to warrant rejection of the claim that living accommodation and gender are independent.

Quizplus · Accepted Answer

The chi-square test for independence would be used here. After calculating the expected frequencies and the chi-square statistic, if the p-value is greater than 0.05, we fail to reject the null hypothesis, indicating that there is not sufficient evidence to suggest that living accommodations are dependent on gender.

A Survey of Students at a College Was Asked If α=0.05\alpha = 0.05α=0.05

A Survey of Students at a College Was Asked If $\alpha = 0.05$