Find the critical value or values of $\chi ^ { 2 }$ based on the given information.
-$$\begin{array} { l }
\mathrm { H } _ { 1 } : \sigma \neq 9.3 \
\mathrm { n } = 28 \
\alpha = 0.05
\end{array}$$
A) 16.151, 40.113
B) -40.113, 40.113
C) -14.573, 14.573
D) 14.573, 43.194

Question

Find the critical value or values of $\chi ^ { 2 }$ based on the given information.
-$$\begin{array} { l } 
\mathrm { H } _ { 1 } : \sigma \neq 9.3 \
\mathrm { n } = 28 \
\alpha = 0.05
\end{array}$$
A) 16.151, 40.113
B) -40.113, 40.113
C) -14.573, 14.573
D) 14.573, 43.194

Quizplus · Accepted Answer

We first need to find the degrees of freedom which is given by $df = n-1 = 27$. Then, using a chi-square distribution table, we can find the critical values for a two-tailed test with a significance level of 0.05 and 27 degrees of freedom to be $\chi^2_{0.025,27} = 14.573$ and $\chi^2_{0.975,27} = 43.194$. Therefore, the answer is D.

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