Question

4. 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 92 U.S. firms is selected. Of these, 28 firms have a chief marketing officer on their top management team. The test is conducted at a significance level of a.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: Ho: p s 0.42; Ha: p>0.42 O Ho: p-0.42; Hai p 0.42 Ho: p-0.42; Ha: p # 0.42 Ho: p 2 0.42; Ha: p< 0.42 If the null hypothesis is true, the sampling distribution of the sample proportion p can be approximated by a and a standard deviation of with a mean The test statistic is

Answer 1

To Conduct he hypothesis tat, the ni and altemnave hypoteses ane dinulated us Alteinakve hypotheses myla. P(I-P) o the given data we have n- 92 then23 92 Consider h. 72. o. 2u36

Now 0.30-o42 =-2.33 2 ha xesecha ole i P-value : 2p(2オー2.332)ー00191

USin Value we seject Ho be cause Pvbe is le thanos