According to a report in The New York Times, in the United States, accountants and auditors earn an average of $70,130 a year and loan officers earn $67,960 a year (Jessica Silver Greenberg, The New York Times, April 22, 2012). Suppose that these estimates are based on random samples of 1650 accountants and auditors and 1820 loan officers. Further assume that the sample standard deviations of the salaries of the two groups are $14,400 and $13,600, respectively, and the population standard deviations are equal for the two groups.
a. Construct a 98% confidence interval for the difference in the mean salaries of the two groups—accountants and auditors, and loan officers.
b. Using a 1% significance level, can you conclude that the average salary of accountants and auditors is higher than that of loan officers?