Mathematics, 11.04.2020 16:17 isabellawest2
Suppose an automotive repair company wants to determine the current percentage of customers who keep up with regular vehicle maintenance. How many customers should the company survey in order to be 95% confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion of customers who keep up with regular vehicle maintenance?
385
Given the information in the question, EBP=0.05 since 5%=0.05 and zα2=z0.025=1.96 because the confidence level is 95%. 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=1.962(0.5)(0.5)0.052 =384.2
Round the answer up to the next integer to be sure the sample size is large enough. The sample should include 385 customers.
Answers: 1
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