A researcher wants to estimate the percent of the population that uses the radio to stay informed on local news issues.The researcher wants to estimate the population proportion with a 90% level of confidence. He estimates from previous studies that no more than 30% of the population stay informed on local issues through the radio.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

To find the necessary sample size, we use the formula:
n = ((Z^2 * p * q) / E^2)
where Z is the z-score for the level of confidence, p is the estimated proportion, q is 1-p, and E is the desired margin of error.
For a 90% level of confidence, the z-score is 1.645.
p is estimated to be no more than 0.30.
So, q = 1-0.30 = 0.70.
The error of no more than 0.02 means that E = 0.02.
Plugging in these values, we get:
n = ((1.645^2 * 0.30 * 0.70) / 0.02^2) = 1420.71
Rounding up, the necessary sample size is at least 1421. Therefore, the best choice is D) 1421.

A Researcher Wants to Estimate the Percent of the Population