n an article in Accounting and Business Research, Carslaw and Kaplan investigate

Question

n 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 equals 27 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?

Explanation / Answer

Solution :-

(a)

Let X be a random variable which is defined as the "audit delay" i.e.the length of time (in days) from a company’s financial year-end to the date of the auditor’s report that affects the market reaction to the report in case of public owner-controlled companies in New Zealand.

Given that, public owner-controlled companies in New Zealand have an audit delay with an assumption that (population standard deviation) equals 27 days,we are to find the size of the random sample of public owner-controlled companies that is needed to make us 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.

Now, here

Probability(the sample mean audit delay is within a margin of error of four days of µ, the population mean audit delay)=95/100

Now , the margin of error can be calculated as follows:-

Margin of error = Critical value * Standard error of the statistic

i.e.   E = zalpha/2 * (/ sqrt(n)) .......(i)

        Now, 100(1-alpha)=95

i.e. alpha = 0.05

i.e. alpha/2 = 0.025

Now, zalpha/2 =1.96 ( where we have assumed the population of the random variables to follow a Normal Distribution)

Therefore, from (i), we can say,

E= 1.96 * (27/sqrt(n))      (assuming the population of the random variables to be normally distributed )....(ii)

Now,according to our problem, critical region is given as:-

    ( X_bar - E , X_bar + E ) = ( X_bar - 4 , X_bar +4 )   ......... (Since sample mean is an unbiased estimator of population mean) ..........(iii)

Now , substituting the value of E from equation (ii) in equation (iii) we get :-

      E = 4

i.e. 1.96 * (27/sqrt(n)) = 4

i.e. n = (1.96 * 27)2 / 42

i.e. n = 175.0329

But,since n indicates the sample size,it has to be an integer; hence n=175.

Therefore, a random sample of 175 public owner-controlled companies is needed to make us 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. (Answer)

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