Use the given data to find the minimum sample size required to estimate the population proportion.
-Margin of error: $0.09$; confidence level: $95 \%$; from a prior study, $\hat { \mathrm { p } }$ is estimated by the decima equivalent of $87 \%$.
A) 5
B) 48
C) 54
D) 162

Question

Quizplus · Accepted Answer

The minimum sample size $ n $ can be calculated using the formula: $ n = \left( \frac{Z^2 \cdot \hat{p} \cdot (1-\hat{p})}{E^2} \right) $, where $ Z $ is the Z-score for the confidence level (1.96 for 95%), $ \hat{p} = 0.87 $, and $ E = 0.09 $. Plugging in these values gives $ n \approx 54 $.

Use the Given Data to Find the Minimum Sample Size 0.090.090.09

Use the Given Data to Find the Minimum Sample Size $0.09$