Use the given data to find the minimum sample size required to estimate the population proportion.
-Margin of error: 0.04; confidence level: 95%; from a prior study, $\hat { p }$ is estimated by the decimal equivalent of 60%.
A) 1441
B) 996
C) 519
D) 577

Question

Quizplus · Accepted Answer

Using the formula for the minimum sample size needed to estimate a population proportion,

n = $\frac {z^2 * \hat {p} * (1 - \hat {p})}{E^2}$

where z is the z-score associated with the desired confidence level, $\hat {p}$ is the estimated population proportion from prior studies, and E is the margin of error.

Plugging in the given values, we get:

n = $\frac {(1.96)^2 * 0.6 * (1 - 0.6)}{0.04^2}$

n ≈ 577, so the minimum sample size required is approximately 577. Therefore, the answer is D.

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

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