A researcher wants to determine if the number of minutes spent watching television per day is independent ofgender. A random sample of 315 adults was selected and the results are shown below. Find the critical value $x _ { 0 } ^ { 2 }$ to determine if there is enough evidence to conclude that the number of minutes spent watching televisior per day is related to gender. Use $\alpha = 0.05$.
$\text { Gender } $$\quad $$ \text { Minutes spent watching TV per day } $
$\begin{array} { l | c c c c }
\hline & 0 - 30 & 30 - 60 & 60 - 90 & 90 - \text { over } \
\text { Male } & 25 & 35 & 75 & 45 \
\text { Female } & 30 & 45 & 45 & 15
\end{array}$

A) 7.815
B) 9.348
C) 11.345
D) 6.251

Question

A researcher wants to determine if the number of minutes spent watching television per day is independent ofgender. A random sample of 315 adults was selected and the results are shown below. Find the critical value $x _ { 0 } ^ { 2 }$ to determine if there is enough evidence to conclude that the number of minutes spent watching televisior per day is related to gender. Use $\alpha = 0.05$.
$\text { Gender } $$\quad $$ \text { Minutes spent watching TV per day } $ 
$\begin{array} { l | c c c c } 
\hline & 0 - 30 & 30 - 60 & 60 - 90 & 90 - \text { over } \
\text { Male } & 25 & 35 & 75 & 45 \
\text { Female } & 30 & 45 & 45 & 15
\end{array}$

A) 7.815
B) 9.348
C) 11.345
D) 6.251

Quizplus · Accepted Answer

The critical value $x^2_0$ for a chi-square test with $(r-1)(c-1)$ degrees of freedom at a significance level of $\alpha = 0.05$ is found using the chi-square distribution table. Here, $r = 2$ (rows for male and female) and $c = 4$ (columns for different time intervals), so the degrees of freedom $df = (2-1)(4-1) = 3$. Looking up the critical value for $df = 3$ and $\alpha = 0.05$ in the chi-square distribution table gives 7.815.

A Researcher Wants to Determine If the Number of Minutes x02x _ { 0 } ^ { 2 }x02​

A Researcher Wants to Determine If the Number of Minutes $x _ { 0 } ^ { 2 }$