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 α = 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: H₀: p = 0.42; Haa: p ≠ 0.42 H₀: p ≤ 0.42; Haa: p > 0.42 H₀: p̄ p̄ = 0.42'; Haa: p̄ p̄ ≠ 0.42 H₀: p ≥ 0.42; Haa: p < 0.42 If the null hypothesis is true, the sampling distribution of the sample proportion p̄ p̄ can 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 α = 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: H₀: p = 0.42; Haa: p ≠ 0.42 H₀: p ≤ 0.42; Haa: p > 0.42 H₀: p̄ p̄ = 0.42'; Haa: p̄ p̄ ≠ 0.42 H₀: p ≥ 0.42; Haa: p < 0.42 If the null hypothesis is true, the sampling distribution of the sample proportion p̄ p̄ can 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 α = 0.05), when do you reject the null hypothesis? Reject H₀ if t ≤ -1.990 or if t ≥ 1.990 Reject H₀ if z ≤ -1.960 or if z ≥ 1.960 Reject H₀ if z ≤ -1.645 or if z ≥ 1.645 Reject H₀ 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.
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 α = 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:
H₀: p = 0.42; Haa: p ≠ 0.42
H₀: p ≤ 0.42; Haa: p > 0.42
H₀: p̄ p̄ = 0.42'; Haa: p̄ p̄ ≠ 0.42
H₀: p ≥ 0.42; Haa: p < 0.42
If the null hypothesis is true, the sampling distribution of the sample proportion p̄ p̄ can 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 α = 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:
H₀: p = 0.42; Haa: p ≠ 0.42
H₀: p ≤ 0.42; Haa: p > 0.42
H₀: p̄ p̄ = 0.42'; Haa: p̄ p̄ ≠ 0.42
H₀: p ≥ 0.42; Haa: p < 0.42
If the null hypothesis is true, the sampling distribution of the sample proportion p̄ p̄ can 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 α = 0.05), when do you reject the null hypothesis?
Reject H₀ if t ≤ -1.990 or if t ≥ 1.990
Reject H₀ if z ≤ -1.960 or if z ≥ 1.960
Reject H₀ if z ≤ -1.645 or if z ≥ 1.645
Reject H₀ 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.
Given Information:
42% of firms had a chief marketing officer on their top management team.
A random sample of 81 U.S. firms is selected. Of these, 32 firms have a chief marketing officer on their top management team.
Significance level α = 0.05
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
