z-Based Confidence Intervals for a Population Mean

In an article in Accounting and Business Research, Carslaw and Kaplan investigate factors that influence "audit delay" for firms in New Zealand. Audit delay, which is defined to be the length of time (in days) from a company's financial year-end to the date of the auditor's report, has been found to affect the market reaction to the report. This is because late reports often seem to be
associated with lower returns and early reports often seem to be associated with higher returns. Carslaw and Kaplan investigated audit delay for two kinds of public companies—owner-controlled and manager-controlled companies. Here, a company is considered to be owner controlled if 30 percent or more of the common stock is controlled by a single outside investor (an investor not part of the management group or board of directors). Otherwise, a company is
considered manager controlled. It was felt that the type of control influences audit delay. To quote Carslaw and Kaplan:
Large external investors, having an acute need for timely information, may be expected to pressure the company and auditor to start and to complete the audit as rapidly as practicable.

a) Suppose that a random sample of 100 public owner-controlled companies in New Zealand is found to give a mean audit delay of xbar = 82.6 days, and assume that s equals 33 days. Calculate a 95 percent confidence interval for the population mean audit delay for all public owner-controlled companies in New Zealand.

b) Suppose that a random sample of 100 public manager-controlled companies in New Zealand is found to give a mean audit delay of xbar = 93 days, and assume that s equals 37 days. Calculate a 95 percent confidence interval for the population mean audit delay for all public manager-controlled companies in New Zealand.

c) Use the confidence intervals you computed in parts a and b to compare the mean audit delay for all public owner-controlled companies versus that of all public manager-controlledcompanies. How do the means compare? Explain.