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 $a = 0.05$ test the claim that living accommodations are independent of the gender of the student.
$\begin{array} { r | l l l }
& \text { Live with Parent } & \text { Rent Apartment } & \text { Own Home } \
\hline \text { Male } & 20 & 26 & 19 \
\text { Female } & 18 & 28 & 26
\end{array}$
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 $a = 0.05$ test the claim that living accommodations are independent of the gender of the student.
$\begin{array} { r | l l l } 
& \text { Live with Parent } & \text { Rent Apartment } & \text { Own Home } \
\hline \text { Male } & 20 & 26 & 19 \
\text { Female } & 18 & 28 & 26
\end{array}$
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

To determine if living accommodations are independent of the gender of the student, a chi-square test for independence is used. Without calculating the exact chi-square value and comparing it to the critical value or p-value (since no calculations are provided), the correct approach when there is not enough evidence to show a significant association between two categorical variables is to fail to reject the null hypothesis. The null hypothesis in this context states that there is no association (they are independent) between living accommodations and gender. The choice that correctly reflects this outcome is the one stating there is not sufficient evidence to warrant rejection of the claim that living accommodation and gender are independent.

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

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