4. Hypothesis tests about a population proportion Aa Aa A firm\'s corporate stra

Question

4. Hypothesis tests about a population proportion Aa Aa 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 92 U.S. firms is selected. Of these, 28 firms have a chief marketing officer on their top management team. The test is conducted at a significance level of -.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: Ho: p = 0.42; Hai p 0.42 O Ho: p 0.42; Ha: p 0.42 Ho: p = 0.42; Hai p 0.42 If the null hypothesis is true, the sampling distribution of the sample proportion p can be approximated by a and a standard deviation of with a mean t-distribution with 92 degrees of freedom t-distribution with 91 degrees of freedom binomial distribution normal distribution

Explanation / Answer

a)

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.42
Ha:   p   =/=   0.42 [ANSWER, OPTION D]

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b)

First blank: NORMAL DISTRIBUTION
Second blank: 0.42
Third blank: 0.0515
Fourth blank: -2.25 [ANSWERS]

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Details:

As we see, the hypothesized po =   0.42      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.304347826      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.051457031      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.247548501      
          
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c)

As alpha = 0.05, 2 tailed,

OPTION D: Reject Ho when z < -1.96 or z > 1.96 [ANSWER]

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d)

First blank: 0.0244
Second blank: Rejected
Third blank: -2.25 < -1.960
Fourth blank: Rejected
Fifth blank: 0.0244 < 0.05
Sixth blank: Can conclude [ANSWER]

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