A confidence interval was used to estimate the proportion of statistics students who are female.A random sample of 72 statistics students generated the following 90% confidence interval: (0.438,0.642).Using the information above,what total size sample would be necessary if we wanted to estimate the true proportion to within $\pm$0.08 using 95% confidence?
A)105
B)150
C)420
D)597

Question

Quizplus · Accepted Answer

To estimate the true proportion to within ±0.08 with 95% confidence, we use the formula for the sample size in estimating a proportion: $n = \left(\frac{Z_{\alpha/2} \cdot \sqrt{p(1-p)}}{E}\right)^2$, where $Z_{\alpha/2}$ is the Z-score for the desired confidence level (1.96 for 95%), $p$ is the estimated proportion (we can use the midpoint of the given interval, $(0.438+0.642)/2 = 0.54$), and $E$ is the desired margin of error (0.08). Plugging in the values: $n = \left(\frac{1.96 \cdot \sqrt{0.54(1-0.54)}}{0.08}\right)^2 \approx 150$.

A Confidence Interval Was Used to Estimate the Proportion of Statistics