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Lower Your Cholesterol Researcher Francisco Fuentes and his colleagues wanted to determine the most effective diet for reducing LDL cholesterol, the so-called “bad” cholesterol, among three diets: (1) a saturated-fat diet: 15% protein, 47% carbohydrates, and 38% fat (20% saturated fat, 12% monounsaturated fat, and 6% polyunsaturated fat); (2) the Mediterranean diet: 47% carbohydrates, and 38% fat (10% saturated fat, 22% monounsaturated fat, and 6% polyunsaturated fat); and (3) the US National Cholesterol Education Program or NCEP-1 Diet: 10% saturated fat, 12% monounsaturated fat, and 6% polyunsaturated fat. Participants in the study were shown to have the same levels of LDL cholesterol before the study and were randomly assigned to one of the three diets, or treatment groups. After 28 days, their LDL cholesterol levels were recorded. The data in the following table are based on this study.

(a) Why is this study a completely randomized design?

(b) What is the response variable? What is the explanatory variable that is controlled and set at three levels?

(c) The participants were randomly assigned to one of three treatment groups. What is the purpose of randomization in this study?

(d) State the null and alternative hypotheses.

(e) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations.

(f) Are the mean LDL cholesterol levels different at the  level of significance?

(g) Draw boxplots of the LDL cholesterol levels for the three groups to support the analytic results obtained in part (f).

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A study by the Organization for Economic Cooperation and Development (OECD) found that the average annual hours actually worked per worker has decreased in most of Western Europe in the first decade of the 2000s. Suppose an OECD-wide survey is conducted that found that 43% of the responding workers in the survey cited ‘less business, less work’ as the number one reason for this reduction in the annual working hours. Suppose you want to test this figure in the Netherlands to determine whether Dutch workers feel the same way. A random sample of 315 Dutch full-time workers whose work-week has been getting shorter is chosen. They are offered a selection of possible reasons for this reduction and 120 pick ‘less business, less work’. Use techniques presented in this chapter and an alpha of 0.05 to test to determine whether the 43% figure for Western Europe for this reason holds true in the Netherlands.

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Is there a difference in the proportion of construction workers who are under 35 years of age and the proportion of telephone repair people who are under 35 years of age? Suppose a study is conducted in Dundee, Scotland, using random samples of 338 construction workers and 281 telephone repair people. The sample of construction workers includes 297 people below 35 years of age and the sample of telephone repair people includes 192 people under that age. Use these data to construct a 90% confi dence interval to estimate the difference in proportions of people under 35 years of age among construction workers and telephone repair people.

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Crash Data The Insurance Institute for Highway Safety conducts experiments in which cars are crashed into a fixed barrier at 40 mph. The barrier’s deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40 mph. Suppose you want to know if the mean head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles. The researcher wants to determine if the means for head injury for each class of vehicle are different. The following data were collected from the institute’s study.

(a) State the null and alternative hypotheses.

(b) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations.

(c) Test the hypothesis that the mean head injury for each vehicle type is the same at the level of significance.

(d) Draw boxplots of the three vehicle types to support the analytic results obtained in part (c).

 

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