8.24 Gender diversity of board of directors. The gender diver- @ sity 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 nom- inating committee would appoint more female directors than firms without a nominating committee. One of the key variables measured at each corporation was the percent- age of board directors who are female. In a sample of 491 rms with a nominating committee, the mean percentage was 7.5%; in an independent sample of 501 firms with- out 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 cor- responding p-value of .0001. Interpret this result if or = .05. c. Do the population percentages for each type of rm need to be normally distributed for the inference, part b, to be valid? Why or why not? :1. To assess the practical significance of the test, part b, construct a 95% confidence interval for the differ- ence between the true mean percentages at firms with and without a nominating committee. Interpret the result. [Hint Use the difference between the sample means and the value of the test statistic to solve for the standard error of the difference between the sample means]