185323959-Business-Stats-Ken-Black-Case-Answers.pdf

2 shell contracted researchers appear to have

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2. Shell contracted researchers appear to have stratified on age, ethnicity, household location, occupation, and previous employment with Shell. With regard to opinions about Shell as a “premier” company, some strata that might make sense are age, ethnicity, economic class, education, occupation, gender, and geographic location. It is important to Shell that all segments of the U.S. adult population be reached. In order to test to determine the effectiveness of marketing campaigns, Shell needs to recognize that there will likely be differences in the perceptions of young people and those of old people of what a “premier” company should be because of their life experiences and the types of messages that appeal to them. The same thing is true for different ethic groups (different cultural values may appeal to different groups), economic class (the economics of the household may determine what types of “premier” messages appeal to their needs), education (at what level of education should the messages be targeted), occupation (how does Shell impact various occupations differently? eg. environment, reliability of products, availability of products, pricing), gender (often men and women seek different outcomes from firms), and geographic location (state and regional cultures vary and thus consumer messages should be targeted so as to parallel geographic interests).
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Case Notes 17 3. In 1979, p = .12. A new survey of n = 350 resulted in p ˆ = .25. Prob.( p ˆ > .25 n = 350 and p = .12): 350 ) 75 )(. 25 (. 12 . 25 . ˆ - = - = n q p p p z = 5.62 From Table A.5, the area for z = 5.62 is .5000. Prob.( p ˆ > .25) = .5000 - .5000 = . 0000 It is virtually impossible to randomly select 350 people and have 25% declare that Shell is a “premier” company if in the population only 12% believe that Shell is a “premier” company. This is strong statistical evidence that the 12% figure is no longer true and that the actual population figure is greater. This is a nice segue into section 8.3 of chapter 8 in which the sample data can be used to estimate the actual proportion who now believe that Shell is a “premier” company. It also lays the groundwork for the hypothesis testing to come in chapter 9. 4. Prob.( x > 2.0 μ = 1.8, σ = .7, and n = 35): 35 7 . 8 . 1 0 . 2 - = - = n x z σ μ = 1.69 From Table A.5, the area for z = 1.69 is .4545 Prob.( x > 2.0) = .5000 - .4545 = .0455 There is only a 4.55% probability that the sample mean of 2.0 was obtained by chance. It is likely that the population mean is no longer 1.8 and indeed, is now higher. This is a good place for the instructor to mention .05 as a common standard for low probability and begin the groundwork for chapter 9.
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Case Notes 18 Prob.( x > 2.5 μ = 1.8, σ = .7, and n = 35): 35 7 . 8 . 1 5 . 2 - = - = n x z σ μ = 5.92 From Table A.5, the area for z = 5.92 is .5000. Prob.( x > 2.5) = .5000 - .5000 = . 0000 It is virtually impossible to randomly obtain a sample mean of 2.5 or more from a sample of 35 with this standard deviation if the population mean is only 1.8. This is, of course, even more conclusive evidence than obtaining a sample mean of 2.0. A discussion of the .0455 probability above and the .0000 value here may result in a preliminary understanding of the notion of p -value introduced in chapter 9.
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Case Notes 19 Chapter 8 Thermatrix 1. n = 115 For 95% confidence, z = 1.96 Use:
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