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 approximate sample size is at least _______.
A)29
B)47
C)298
D)1421
E)1500

Question

Quizplus · Accepted Answer

The sample size can be calculated using the formula for estimating a population proportion: $n = \frac{Z^2 \times p(1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (for 90% confidence, $Z \approx 1.645$), $p$ is the estimated proportion (0.30), and $E$ is the margin of error (0.02). Plugging in the values: $n = \frac{1.645^2 \times 0.30 \times (1-0.30)}{0.02^2} \approx 1421$.

A Researcher Wants to Estimate the Percent of the Population