In an article in Accounting and Business Research, Carslaw and Kaplan study the effect of control (owner versus manager control) on audit delay (the length of time from a company's financial year-end to the date of the auditor's report) for public companies in New Zealand. Suppose a random sample of 100 public owner-controlled companies in New Zealand gives a mean audit delay of 1 = 82.6 days, while a random sample of 100 public manager-controlled companies in New Zealand gives a mean audit delay of 2 = 93 days. Assuming the samples are independent and that σ1, = 32.83 and σ2 = 37.18:
a Let µ1 be the mean audit delay for all public owner-controlled companies in New Zealand, and let µ2 be the mean audit delay for all public manager-controlled companies in New Zealand. Calculate a 95 percent confidence interval for µ1 - µ2. Based on this interval1 can we be 95 percent confident that the mean audit delay for all public owner-controlled companies in New Zealand is less than that for all public manager-controlled companies in New Zealand? If so1 by how much?
b. Consider testing the null hypothesis H0: µ1 - µ1 = 0 versus Ha: µ1 - µ2 < 0. Interpret (in writing) the meaning (in practical terms) of each of H0 and Ha.
c. Use a critical value to test the null hypothesis H0: µ1 - µ2 = 0 versus Ha: µ1 - µ2 < 0 at the .05 level of significance. Based on this test what do you conclude about how µ1 and µ2 compare? Write your conclusion in practical terms.
d. Find the p-value for testing H0: µ1 - µ2 = 0 versus Ha: µ1 - µ2 < 0. Use the p-value to test H0 versus Ha by setting a equal to .101 .051 .0251 .01. and .001. How much evidence is there that µ1 is less than µ2?