Use the given data to find the minimum sample size required to estimate the population proportion.
-Margin of error: 0.09; confidence level: 90%; from a prior study, $\hat{p}$ is estimated by 0.17.
A) 48
B) 144
C) 42
D) 4

Question

Quizplus · Accepted Answer

The minimum sample size $ n $ can be calculated using the formula: $ n = \left( \frac{Z \cdot \sqrt{\hat{p}(1-\hat{p})}}{E} \right)^2 $, where $ Z $ is the Z-score for the confidence level (1.645 for 90%), $ \hat{p} $ is the estimated proportion (0.17), and $ E $ is the margin of error (0.09). Plugging in these values gives $ n \approx 48 $.

Use the Given Data to Find the Minimum Sample Size p^\hat{p}p^​

Use the Given Data to Find the Minimum Sample Size $\hat{p}$