Certified public accountants are often required to appear with clients if the IRS audits the client’s tax return. Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advice and support from the accountant if the client were audited. The fee is charged up front like an insurance premium and is less than the amount that would be charged if the client were later audited and then decided to ask the firm for assistance during the audit. A large accounting firm is trying to determine what fee to charge for next year’s returns. In previous years, the actual mean cost to the firm for attending a client audit session was $ 650. To determine if this cost has changed, the firm randomly samples 32 client audit fees. The sample mean audit cost was $ 680 with a standard deviation of $ 75.
a) Develop a 95% confidence interval estimate for the mean audit cost.
b) Based on your confidence interval, what do you think of the claim that the mean cost has changed?