A teacher finds that final grades in the statistics department are distributed as: A, 25\%; B, 25\%; C, $40 \%$; D, $5 \% ; F , 5 \%$. At the end of a randomly selected semester, the following grades were recorded. Find the rejection region used to determine if the grade distribution for the department is different than expected. Use $\alpha = 0.01$.
$\begin{array}{l|lllll}
\text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Number } & 36 & 42 & 60 & 8 & 14
\end{array}$

A) $\chi ^ { 2 } 13.277$
B) $\chi ^ { 2 } 9.488$
C) $\chi ^ { 2 } 7.779$
D) $\chi ^ { 2 } 11.143$

Question

A teacher finds that final grades in the statistics department are distributed as: A, 25\%; B, 25\%; C, $40 \%$; D, $5 \% ; F , 5 \%$. At the end of a randomly selected semester, the following grades were recorded. Find the rejection region used to determine if the grade distribution for the department is different than expected. Use $\alpha = 0.01$.
$\begin{array}{l|lllll}
\text { Grade } & \text { A } & \text { B } & \text { C } & \text { D } & \text { F } \
\hline \text { Number } & 36 & 42 & 60 & 8 & 14
\end{array}$

A) $\chi ^ { 2 } > 13.277$
B) $\chi ^ { 2 } > 9.488$
C) $\chi ^ { 2 } > 7.779$
D) $\chi ^ { 2 } > 11.143$

Quizplus · Accepted Answer

The rejection region for a chi-square test is determined by the chi-square critical value, which depends on the significance level ($\alpha$) and the degrees of freedom. For a significance level of 0.01 and 4 degrees of freedom (since there are 5 categories - 1), the critical value from chi-square distribution tables is greater than 13.277.

A Teacher Finds That Final Grades in the Statistics Department 40%40 \%40%

A Teacher Finds That Final Grades in the Statistics Department $40 \%$