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 _______ ( ans options: normal distribution, t-distribution of 96 degree freedom, t-distribution of 97 degree freedom, binomial distribution) with a mean _______ (ans options: of 31, that is unknown, of 0.42, of 0.3196) and a standard deviation of ________ (ans options : z=-2.00, t=-2.00, z=-31, z=31, t=2.00) . 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 _______ ( ans options:
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.
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