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 σ equals 23 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 percent confident that formula15_2.mml the sample mean audit delay, is within a margin of error of four days of µ, the population mean audit delay?

(b) 99 percent confident that formula15_2.mml the sample mean audit delay, is within a margin of error of four days of µ?

Answer 1

To estimate the mean audit delay of public owner-controlled companies in New Zealand, the formula n = (Z * σ / E)^2 is used to determine the required sample size. For a 95% confidence level and a margin of error of 4 days, a sample size of 157 companies is needed. For a 99% confidence level, a sample size of 302 companies is required.

Step-by-step explanation:

To determine the sample size needed to estimate the mean audit delay of public owner-controlled companies in New Zealand, we can use the formula:
n = (Z * σ / E)^2

Where:
n = sample size
Z = Z-score (corresponding to the desired confidence level)
σ = standard deviation of the population mean audit delay
E = margin of error

(a) 95% confidence level:
Z = 1.96 (corresponding to a 95% confidence level)
E = 4 days
σ = 23 days

Substituting the values into the formula:
n = (1.96 * 23 / 4)^2 = 156.1024

Rounding up to the next whole number, a sample size of 157 public owner-controlled companies is needed.

(b) 99% confidence level:
Z = 2.57 (corresponding to a 99% confidence level)
E = 4 days
σ = 23 days

Substituting the values into the formula:
n = (2.57 * 23 / 4)^2 = 301.4641

Rounding up to the next whole number, a sample size of 302 public owner-controlled companies is needed.