The following MINITAB output presents a confidence interval for a proportion.
$\begin{array}{crrcc}
\hline \text { Variable } & \mathrm{X} & \mathrm{N} & \text { Sample p } & 95 \% \mathrm{CI} \
\mathrm{x} & 117 & 159 & 0.735849 & (0.667319,0.804379) \
\hline
\end{array}$
Use the information in the display to construct a $98 \%$ confidence interval for $p$.
A) (0.655, 0.817)
B) (0.678, 0.793)
C) (0.667, 0.804)
D) (0.646, 0.826

Question

Quizplus · Accepted Answer

The 95% confidence interval is (0.667319, 0.804379). To construct a 98% confidence interval, we can use the formula:sample proportion +/- 2.326 * sqrt((sample proportion * (1 - sample proportion)) / sample size)Plugging in the values from the output, we get:0.735849 +/- 2.326 * sqrt((0.735849 * (1 - 0.735849)) / 159)= 0.735849 +/- 0.076= (0.659849, 0.811849)Therefore, the 98% confidence interval is (0.659849, 0.811849), which is closest to option A.

The Following MINITAB Output Presents a Confidence Interval for a Proportion