1. A simple random sample of 50 customers is selected from an account receivable

portfolio and the sample mean account balance is $1000. The population

standard deviation is known to be $200.

a. Construct a 95% confidence interval for the mean account balance of the

population.

b. What is the margin of error for estimating the mean account balance at the

95% confidence level?

c. Construct a 95% confidence interval for the mean account balance of the

population if the sample mean account balance is obtained from a random

sample of 100 instead of 50.

d. Based on the answer from a. and c., describe the effect of a

larger sample size on the length of the confidence interval at the same

confidence level?

4. In a survey, the planning value for the population proportion is p* = 0.38. How

large should the sample size for the survey be if the desired level of confidence is

95% and the desired margin of error is 0.045?