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 = 5.51 with a corresponding p-value of .0001. Interpret this result if α = .05.

c. Do the population percentages for each type of firm need to be normally distributed for the inference, part b, to be valid? Why or why not?

d. To assess the practical significance of the test, part b, construct a 95% confidence interval for the difference between the true mean percentages at firms with and without a nominating committee. Interpret the result.