Question

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. Suppose that public owner-controlled companies in New Zealand have an audit delay with an assumption that the population standard deviation equals 24 days. How large a random sample of public owner- controlled companies is needed to make us... (Round up your final answers to the next whole number.) (a) 95% confident that the sample mean audit delay, is within a margin of error of four days of u, the population mean audit delay? D companies (b) 99% confident that the sample mean audit delay, is within a margin of error of four days of u? companies

Answer 1

Solution :

Given that,

Population standard deviation = $\sigma$ = 24

Margin of error = E =

a) At 95% confidence level the z is,

$\alpha$ = 1 - 95%

$\alpha$ = 1 - 0.95 = 0.05

$\alpha$/2 = 0.025

Z_$\alpha$/2 = 1.96

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [ 1.96 *24 / 4 ]²

n = 138.29

Sample size = n = 139 companies

b) At 99% confidence level the z is,

$\alpha$ = 1 - 99%

$\alpha$ = 1 - 0.99 = 0.01

$\alpha$/2 = 0.005

Z_$\alpha$/2 = 2.576

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [ 2.576 *24 / 4 ]²

n = 238.88

Sample size = n = 239 companies