9. Hypothesis tests about a population proportion A firm's corporate strategy is driven largely by its top management team. One method of gauging the influence of marketing on corporate strategy is to measure the proportion of firms with a chief marketing officer on their top management team. Over the 5-year period from 2000 to 2004, 42% of firms had a chief marketing officer on their top management team. [Source: Pravin Nath and Vijay Mahajan, "Chief Marketing Officers: A Study of Their Presence in Firms'Top Management Teams," Journal of Marketing, 70 (2007).] To test the hypothesis that the influence of marketing on corporate strategy today is different from its influence in the 2000-2004 period, a random sample of 97 U.S. firms is selected. Of these, 31 firms have a chief marketing officer on their top management team. The test is conducted at a significance level of a = 0.05. Let p be the true proportion of firms with a chief marketing officer currently on their top management team. To conduct the hypothesis test, the null and alternative hypotheses are formulated as: O Ho: p 2 0.42; H1: p 0.42 O Ho: p = 0.42; Hi: p = 0.42 O Ho: p = 0.42; H1: p = 0.42 If the null hypothesis is true, the sampling distribution of the sample proportion P can be approximated by a with a mean and a standard deviation of The test statistic is