Late payment of medical claims can add to the cost of health care. An article reported that the mean time from the date of service to the date of payment for one insurance company was 41.4 days during a recent period. Suppose that a sample of 100 medical claims is selected during the latest time period.The sample mean time from the date of service to the date of payment was 39.6 days, and the sample standard deviation was 7.4 days.
(a) Using the 0.05 level of significance, is there evidence that the population mean has changed from 41.4 days?
(b) What is your answer in(a)if you use the 0.01 level of significance?
(c) What is your answer in(a)if the sample mean is 38.2 days and the sample standard deviation is 10.7 days?
(d) Because the sample size is 100, do you need to be concerned about the shape of the population distribution when conducting the t-test in (a)? Explain.