420Pr4 - 1 There is some evidence that drinking moderate...

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1. There is some evidence that drinking moderate amounts of wine helps prevent heart attacks. The table below gives data on yearly wine consumption (liters of alcohol from drinking wine, per person) and yearly deaths from heart disease (deaths per 100,000 people) in 19 developed nations. (Data from M. H. Criqui, University of California, San Diego, reported in the New York Times , December 28, 1994.) Country Alcohol from wine Heart disease deaths Country Alcohol from wine Heart disease deaths Australia 2.5 211 Netherlands 1.8 167 Austria 3.9 167 New Zealand 1.9 266 Belgium 2.9 131 Norway 0.8 227 Canada 2.4 191 Spain 6.5 86 Denmark 2.9 220 Sweden 1.6 207 Finland 0.8 297 Switzerland 5.8 115 France 9.1 71 United Kingdom 1.3 285 Iceland 0.8 211 United States 1.2 199 Ireland 0.7 300 West Germany 2.7 172 Italy 7.9 107 Σ x = 57.5, Σ y = 3,630, Σ x 2 = 287.39, Σ y 2 = 777,726, Σ x y = 8,381.4, Σ ( x x ) 2 = 113.3768421, Σ ( y y ) 2 = 84,204.94737, Σ ( x x ) ( y y ) = – 2,604.126316. a) Find the equation of the least-squares regression line. b) Compute the correlation coefficient. c) Describe the form of the relationship. Is there a linear pattern? How strong is the relationship? Is the direction of the association positive or negative? Explain in simple language what this says about wine and heart disease. d) Test H 0 : ρ = 0 vs. H a : < 0 at a 1% level of significance. e) Do you think these data give good evidence that drinking wine causes a reduction in heart disease deaths? Why?
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f) Test H 0 : ρ = 0.60 vs. H a : < – 0.60 at a 1% level of significance. What is the p-value of this test? 2. A researcher investigates the relationship between a teacher’s experience and students’ performance on the standard test, Michigan Educational Assessment Plan (MEAP). The results are shown by the scatter plot below. The researcher concludes: “Since the correlation coefficient r is close to zero, there seems to be no relationship between Experience and Student Performance .” Can you offer a reasonable criticism of his argument and his conclusion? Teacher’s Experience vs. Student’s Performance on the MEAP 3. In a college health fitness program, let X denote the weight in kilograms of a male freshman at the beginning of the program and let Y denote his weight change during a semester. Assume that X and Y have a bivariate normal distribution with μ X = 75, σ X = 9, μ Y = 2.5, σ Y = 1.5, ρ = – 0.6. (The lighter students tend to gain weight, while the heavier students tend to lose weight.) a) What proportion of the students that weigh 85 end up losing weight during the semester? That is, find P ( Y < 0 | X = 85 ).
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420Pr4 - 1 There is some evidence that drinking moderate...

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