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

To determine the sample size, we use the formula:

n = (Z^2 * P * Q) / E^2

Where:
Z = value from the standard normal distribution for the desired confidence level (98% = 2.33)
P = estimated population proportion (0.18)
Q = 1 - P (0.82)
E = desired margin of error (0.01)

Plugging in these values, we get:

n = (2.33^2 * 0.18 * 0.82) / 0.01^2
n = 320.78

Since we need a whole number for the sample size, we round up to 321. Therefore, the best choice is D) 321.

A Researcher Wants to Estimate the Proportion of Millennials Who