Question: You are supervising an audit to decide whether or not any errors in the recording of account transactions are "material errors." Each account has a reported balance, whose accuracy can be verified only by careful and costly investigation; the account's error is defined as the difference between the reported balance and the actual balance. Note that the error is zero for any account that is correctly reported. In practical terms, for this situation involving 12,000 accounts, the total error is material only if it is at least $5,000. The average error amount for 250 randomly selected accounts was found to be $0.25, and the standard deviation of the error amount was $193.05. You may assume that your reputation as an auditor is on the line, so you want to be fairly certain before declaring that the total error is not material.
a. Find the estimated total error based on your sample and compare it to the material amount.
b. Identify the null and research hypotheses for a one-sided test of the population mean error per account and explain why a one-sided test is appropriate here.
c. Find the appropriate one-sided 95% confidence interval statement for the population mean error per account.
d. Find the t-statistic.
e. Which hypothesis is accepted as a result of a one-sided test at the 5% level?
f. Write a brief paragraph explaining the results of this audit.