Question

Suppose a bank manager has developed a new system to reduce customer wait time at branches for teller services. She obtains a sample of 100 customer wait times, and calculates the sample mean wait time to be 5.65 minutes. She knows that the population standard deviation is 1.20 minutes. Suppose the bank manager wants to ensure that the margin of error of her 95% confidence interval is no more than 0.20 minutes. How large a sample should she obtain?

C.I. = [5.41, 5.89] with an MOE of 0.2352

Answer 1

Solution :

Given that,

Population standard deviation = = 1.20

Margin of error = E = 0.20

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size = n = (Z_/2* / E) ²

n = (1.96 * 1.20/ 0.20)²

n = 138.30

n = 139

Sample size = 139