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 81 U.S. firms is selected. Of these, 32 firms have a chief marketing officer on their top management team. The test is conducted at a significance level of = 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:

H: p = 0.42; Haa: p 0.42

H: p 0.42; Haa: p > 0.42

H: pp= 0.42'; Haa: pp 0.42

H: p 0.42; Haa: p < 0.42

If the null hypothesis is true, the sampling distribution of the sample proportion ppcan be approximated by a _______ with a mean _______ and a standard deviation of _______ . The test statistic is _____________ .

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 81 U.S. firms is selected. Of these, 32 firms have a chief marketing officer on their top management team. The test is conducted at a significance level of = 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:

H: p = 0.42; Haa: p 0.42

H: p 0.42; Haa: p > 0.42

H: pp= 0.42'; Haa: pp 0.42

H: p 0.42; Haa: p < 0.42

If the null hypothesis is true, the sampling distribution of the sample proportion ppcan be approximated by a with a mean and a standard deviation of .

The test statistic is ______ .

Use the Distributions tool to develop the rejection region. According to the critical value approach (with = 0.05), when do you reject the null hypothesis?

Reject H if t -1.990 or if t 1.990

Reject H if z -1.960 or if z 1.960

Reject H if z -1.645 or if z 1.645

Reject H if z -1.960

Use the provided Distributions tool to determine the p-value. The p-value is ________ .

Using the critical value approach, the null hypothesis is ______ , because _______ . Using the p-value approach, the null hypothesis is ________ , because _______ . Therefore, you ______ conclude that the influence of marketing on corporate strategy today is different from its influence in the 2000-2004 period.