A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the critical value $$\chi _ { 0 } ^ { 2 }$$ to determine if there is enough evidence to conclude that the number of minutes spent online per day is
Related to gender. Use $$\alpha$$ = 0.05. $$\begin{array} { l | c c c c }
& { \text { Minutes spent online per day } } \
\hline \text { Gender } & 0 - 30 & 30 - 60 & 60 - 90 & 90 + \
\text { Male } & 25 & 35 & 75 & 45 \
\text { Female } & 30 & 45 & 45 & 15
\end{array}$$
A)7.815
B)9.348
C)11.345
D)6.251

Question

A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the critical value $$\chi _ { 0 } ^ { 2 }$$ to determine if there is enough evidence to conclude that the number of minutes spent online per day is
Related to gender. Use $$\alpha$$ = 0.05. $$\begin{array} { l | c c c c } 
& { \text { Minutes spent online per day } } \
\hline \text { Gender } & 0 - 30 & 30 - 60 & 60 - 90 & 90 + \
\text { Male } & 25 & 35 & 75 & 45 \
\text { Female } & 30 & 45 & 45 & 15
\end{array}$$
A)7.815
B)9.348
C)11.345
D)6.251

Quizplus · Accepted Answer

The critical value for a chi-square test is determined by the degrees of freedom (df) and the significance level ($\alpha$). The degrees of freedom for a chi-square test of independence are calculated as $(r-1)(c-1)$, where $r$ is the number of rows and $c$ is the number of columns in the contingency table. In this case, there are 2 rows (Male, Female) and 4 columns (0-30, 30-60, 60-90, 90+), so $df = (2-1)(4-1) = 1*3 = 3$. At a significance level of $\alpha = 0.05$ and $df = 3$, the critical value from the chi-square distribution table is 7.815.

A Researcher Wants to Determine Whether the Number of Minutes χ02\chi _ { 0 } ^ { 2 }χ02​

A Researcher Wants to Determine Whether the Number of Minutes $\chi _ { 0 } ^ { 2 }$