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 95% 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 .03.The necessary sample size is at least _______.
A)27
B)188
C)211
D)897
E)900

Question

Quizplus · Accepted Answer

To calculate the necessary sample size for estimating a population proportion with a given level of confidence and margin of error, the formula is: $n = \frac{Z^2 \times p(1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the desired level of confidence (for 95% confidence, $Z = 1.96$), $p$ is the estimated proportion (0.30 in this case), and $E$ is the desired margin of error (0.03). Plugging in the values: $n = \frac{1.96^2 \times 0.30(1-0.30)}{0.03^2}$, which calculates to approximately 897. Therefore, the researcher needs a sample size of at least 897 to achieve the desired precision.

A Researcher Wants to Estimate the Percent of the Population