Question

Suppose a clothing store wants to determine the current percentage of customers who are over the age of forty. How many customers should the company survey in order to be 92% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of customers who are over the age of forty?

Answer 1

Answer:

852

Step-by-step explanation:

Given the information in the question, EBP=0.03 since 3%=0.03 and zα2=z0.04=1.751 because the confidence level is 92%. The values of p′ and q′ are unknown, but using a value of 0.5 for p′ will result in the largest possible product of p′q′, and thus the largest possible n. If p′=0.5, then q′=1−0.5=0.5. Therefore,

n=z2p′q′EBP2=1.7512(0.5)(0.5)0.032=851.7

Round the answer up to the next integer to be sure the sample size is large enough. The sample should include 852 customers.