The following MINITAB output presents a confidence interval for a population mean.
$\begin{array}{crrrcc}
\hline \text { Variable } & \mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } & 99 \% \mathrm{CI} \
\mathrm{x} & 23 & 139.9598 & 34.2443 & 7.1404 & (119.824,160.096) \
\hline
\end{array}$

Find the critical value $t _ { \alpha / 2 }$ for a $98 \%$ confidence interval.
A) $2.820$
B) $2.508$
C) $2.500$
D) $2.807$

Question

The following MINITAB output presents a confidence interval for a population mean.
$\begin{array}{crrrcc}
\hline \text { Variable } & \mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } & 99 \% \mathrm{CI} \
\mathrm{x} & 23 & 139.9598 & 34.2443 & 7.1404 & (119.824,160.096) \
\hline
\end{array}$

Find the critical value $t _ { \alpha / 2 }$ for a $98 \%$ confidence interval.
A) $2.820$
B) $2.508$
C) $2.500$
D) $2.807$

Quizplus · Accepted Answer

The critical value $t _ { \alpha / 2 }$ for a $98 \%$ confidence interval with $N-1 = 22$ degrees of freedom (since $N = 23$) is approximately $2.508$, which is found in t-distribution tables or using statistical software for the $99 \%$ confidence level (since $100\% - 98\% = 2\%$, and we split this into two tails, leading to $1\%$ in each tail).

The Following MINITAB Output Presents a Confidence Interval for a Population