A researcher wants to estimate the population proportion with a 90% level of confidence.She estimates from previous studies that the population proportion is no more than .30.The researcher wants the estimate to have an error of no more than .02.The necessary sample size is at least ___.
A)29
B)47
C)298
D)1421
E)1500

Question

Quizplus · Accepted Answer

We use the formula for sample size calculation:

n = (Z^2 * p * (1-p)) / (E^2)

where Z is the z-score for the desired level of confidence (1.645 for 90%), p is the estimated population proportion, and E is the desired margin of error.

Substituting the given values:

n = (1.645^2 * 0.30 * 0.70) / (0.02^2) = 1421

Therefore, the necessary sample size is at least 1421. Option D is the correct choice.

A Researcher Wants to Estimate the Population Proportion with a 90