A sports statistician is interested in determining if there is a relationship between the number of home team and visiting team losses and different sports. A random sample of 526 games is selected and the results are given below. Find the critical value $\chi _ { 0 } ^ { 2 }$ to test the claim that the number of home team and visiting team losses is independent of the sport. Use $\alpha = 0.01$.
$\begin{array} { l | c c c c }
& \text { Football } & \text { Basketball } & \text { Soccer } & \text { Baseball } \
\hline \text { Home team losses } & 39 & 156 & 25 & 83 \
\text { Visiting team losses } & 31 & 98 & 19 & 75
\end{array}$

A) 11.345
B) 12.838
C) 7.815
D) 9.348

Question

A sports statistician is interested in determining if there is a relationship between the number of home team and visiting team losses and different sports. A random sample of 526 games is selected and the results are given below. Find the critical value $\chi _ { 0 } ^ { 2 }$ to test the claim that the number of home team and visiting team losses is independent of the sport. Use $\alpha = 0.01$.
$\begin{array} { l | c c c c } 
& \text { Football } & \text { Basketball } & \text { Soccer } & \text { Baseball } \
\hline \text { Home team losses } & 39 & 156 & 25 & 83 \
\text { Visiting team losses } & 31 & 98 & 19 & 75
\end{array}$

A) 11.345
B) 12.838
C) 7.815
D) 9.348

Quizplus · Accepted Answer

The degrees of freedom for the chi-square test of independence is (r - 1)(c - 1) = (4 - 1)(2 - 1) = 3. Using a chi-square distribution table with 3 degrees of freedom and a significance level of 0.01, the critical value is 11.345.

A Sports Statistician Is Interested in Determining If There Is χ02\chi _ { 0 } ^ { 2 }χ02​

A Sports Statistician Is Interested in Determining If There Is $\chi _ { 0 } ^ { 2 }$