A researcher wants to estimate the proportion of millennials who regularly listen to podcasts (defined as at least two entire podcasts per week). Previous studies indicate that only 18% of millennials listen regularly to podcasts, and this researcher wants to estimate if that figure has increased. For this purpose, the researcher will use a 98% confidence level and wants to estimate the population proportion within 0.01 (i.e., 1 percentage point) of the actual value. The required sample size is at least ___.
A) 47
B) 48
C) 320
D) 321
E) 331

Question

Quizplus · Accepted Answer

The formula for sample size calculation with a 98% confidence level and a margin of error of 0.01 can be expressed as:
n = (Z^2 * p * (1-p)) / E^2
where Z is the z-score corresponding to 98% confidence level (Z = 2.33), p is the estimated population proportion (p = 0.18), and E is the margin of error (E = 0.01).
Substituting these values in the formula, we get:
n = (2.33^2 * 0.18 * 0.82) / 0.01^2
n = 320.47
Since the sample size must be a whole number, we round up to the next integer, which is 321. Therefore, the required sample size is at least 321. The answer is D.

A Researcher Wants to Estimate the Proportion of Millennials Who