Question

7. 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 Họ: p > 0.42; Hệ: p < 0.42 o Ho: p < 0.42; H: p > 0.42 o Họ: P = 0.42; HT: P + 0.42 o Ho: p = 0.42; Hệ: 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 Select a Dist... - Distributions 0 1 2 3 Use the Distributions tool to develop the rejection region. According to the rejection region method (with a = 0.05), when do you reject the null hypothesis? Reject Ho if zs -1.960 Reject Ho if z s -1.960 or if z 2 1.960 Reject Ho if z s -1.645 or if z > 1.645 Reject Ho if t s -1.985 or if t > 1.985 Use the provided Distributions tool to determine the p-value. The p-value is Using the rejection region method, the null hypothesis is , because . Using the p-value approach, the null hypothesis is , because Therefore, you infer that the influence of marketing on corporate strategy today is different from its influence in the 2000-2004 period.

Answer 1

Solution:

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 о Но: р s 0.42; Hj: р > 0.42 o Ho: p = 0.42; H1: § + 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 normal distribution with a mean Mean = µ = p= 0.42 and a standard deviation of 0.0501 0.42 p(1- p) O =. 0.42(1-0.42) = 0.0501 The test statistic is 97 -2.00 п p-p 0.3196- 0.42 = -2.00 p(1– p) 0.0501

Use the Distributions tool to develop the rejection region. According to the rejection region method (with a = 0.05), when do you reject the null hypothesis? 3 -1.960 Reject Ho if z s -1.960 or if z > 1.960 Reject Ho if z Reject Ho if z s -1.645 or if z 2 1.645 Reject Ho if t s -1.985 or if t 2 1.985 0.0451 Use the provided Distributions tool to determine the p-value. The p-value is Using the rejection region method, the null hypothesis is rejected z statistic falls in rejection . Using the p-value approach, the null hypothesis is rejected region because because "p-value less than 0.05 strategy today is different from its influence in the 2000-2004 period. Therefore, you_can infer that the influence of marketing on corporate