Gender diversity of board of directors. The gender diversity of a large corporation’s board of directors was studied in Accounting & Finance (December 2015). In particular, the researchers wanted to know whether firms with a nominating committee would appoint more female directors than firms without a nominating committee. One of the key variables measured at each corporation was the percentage of board directors who are female. In a sample of 491 firms with a nominating committee, the mean percentage was 7.5%; in an independent sample of 501 firms without a nominating committee, the mean percentage was 4.3%.

a. To answer the research question, the researchers compared the mean percentage of female board directors at firms with a nominating committee with the corresponding percentage at firms without a nominating committee using an independent samples test. Set up the null and alternative hypotheses for this test.

b. The test statistic was reported as z =