Teacher Salaries. The National Education Association collects data on teacher salaries and publishes results in Estimates of School Statistics Database. Independent samples of 100 secondary school teachers and 125 elementary school teachers yielded the data, in thousands of dollars, on annual salaries as presented on the WeissStats site.

a. Obtain histograms, boxplots, and normal probability plots of the two samples.

b. Based on your results from part (a), given the choice between using a pooled t-test or a Mann–Whitney test, which would you choose? Explain your answer.

c. Use both the pooled t-test and the Mann–Whitney test to decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that the average salary of secondary school teachers exceeds that of elementary school teachers. Compare the results of the two tests.

Extending the Concepts and Skills Normal Approximation for M. The Mann–Whitney table, Table VI, stops at n1 = 10 and n2 = 10. For larger samples, a normal approximation can be used.

Normal Approximation for M Suppose that the two distributions of the variable under consideration have the same shape. Then, for samples of sizes n1 and n2,

μM = n1(n1 + n2 + 1)/2,

σM = √

n1n2(n1 + n2 + 1)/12, and M is approximately normally distributed for n1 ≥ 10 and n2 ≥ 10.

Thus, for sample sizes of 10 or more, the standardized variable z = M − n1(n1 + n2 + 1)/2

√

n1n2(n1 + n2 + 1)/12 has approximately the standard normal distribution.