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 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: p̄ p̄ = 0.42'; Haa: p̄ p̄ ≠ 0.42 H₀: p ≥ 0.42; Haa: p < 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 z ≤ –1.960 Reject H₀ if z ≤ –1.960 or if z ≥ 1.960 Reject H₀ if t ≤ –1.985 or if t ≥ 1.985 Reject H₀ if z ≤ –1.645 or if z ≥ 1.645 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 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 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: p̄ p̄ = 0.42'; Haa: p̄ p̄ ≠ 0.42
H₀: p ≥ 0.42; Haa: p < 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 z ≤ –1.960
Reject H₀ if z ≤ –1.960 or if z ≥ 1.960
Reject H₀ if t ≤ –1.985 or if t ≥ 1.985
Reject H₀ if z ≤ –1.645 or if z ≥ 1.645
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 that,
The random variable is the number of chief marketing officers on the top management team.
The population proportion is
The sample size is 97
The favorable outcomes are 31
The sample proportion is as follows,
is the sample size
The level of significance is
The test statistic is as follows,
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