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.

(a) Suppose that a random sample of 107 public owner-controlled companies in New Zealand is found to give a mean audit delay of x⎯⎯x¯ = 82.10 days, and assume that σ equals 35 days. Calculate a 95 percent confidence interval for the population mean audit delay for all public owner-controlled companies in New Zealand. (Round your answers to 3 decimal places.)

The 95 percent confidence interval is [ , ]

(b) Suppose that a random sample of 107 public manager-controlled companies in New Zealand is found to give a mean audit delay of x⎯⎯x¯ = 93 days, and assume that σ equals 39 days. Calculate a 95 percent confidence interval for the population mean audit delay for all public manager-controlled companies in New Zealand. (Round your answers to 3 decimal places.)

The 95 percent confidence interval is [ , ]

(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-controlled companies. How do the means compare?

Mean audit delay for public owner-controlled companies appears to be (Click to select)shorterlonger and there is (Click to select)noa smalla large amount of overlap of the intervals.

Answer 1

a) Consider X : Audit delay for public owner -controlled companies in New Zealand.

From the information

n = sample size = 107

Xbar = sample mean = 82.10

Sigma = population standard deviation = 35

Let : Mean audit delay for public owner -controlled companies in New Zealand.

Since population standard deviation is known. We used normal distribution to find confidence interval for population mean.

(1-alpha)*100% confidence interval for population mean is

Alpha: level of significance = 0.05

From normal probability table

Z_alpha/2= Z _0.025 = 1.96

Hence 95% confidence interval for mean audit delay for public owner -controlled companies in New Zealand is

= ( 75.4494, 88.7506)

The 95 percent confidence interval is [ 75.4494, 88.7506].

b) Consider Y : Audit delay for public manager -controlled companies in New Zealand.

From the information

n = sample size = 107

Ybar = sample mean = 93

Sigma = population standard deviation = 39

Let : Mean audit delay for public manager -controlled companies in New Zealand.

Since population standard deviation is known. We used normal distribution to find confidence interval for population mean.

(1-alpha)*100% confidence interval for population mean is

Alpha: level of significance = 0.05

From normal probability table

Z_alpha/2= Z _0.025 = 1.96

Hence 95% confidence interval for mean audit delay for public manager-controlled companies in New Zealand is

=(85.6103,100.3987)

The 95 percent confidence interval is [ 85.6103, 100.3987].

c) Length of confidence interval in (a) = 88.7506 - 75.4494 = 13.3012

Length of confidence interval in (b) = 100.3987 - 85.6103 = 14.7794

Mean audit delay for public owner-controlled companies appears to be shorter than mean audit delay for public manager-controlled companies and there is a small large amount of overlap of the intervals.