According to a Bureau of Labor Statistics report released on March 25, 2015, statisticians earn an average of $84,010 a year and accountants and auditors earn an average of $73,670 a year (www.bls. gov). Suppose that these estimates are based on random samples of 2000 statisticians and 1800 accountants and auditors. Further, assume that the sample standard deviations of the annual earnings of these two groups are $15,200 and $14,500, respectively, and the population standard deviations are unknown but equal for the two groups.
a. Construct a 98% confidence interval for the difference in the mean annual earnings of the two groups, statisticians and accountants and auditors.
b. Using a 1% significance level, can you conclude that the average annual earnings of statisticians is higher than that of accountants and auditors?