final2009240Akey

# final2009240Akey - Dec 10 2009 ECON 240A-1 Final L Phillips...

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Dec. 10, 2009 ECON 240A- 1 L. Phillips Final Answer all 5 questions. No talking or communicating. 1. (30) In 1994, the chief executive officers, CEO’s, of the major tobacco companies testified before a subcommittee of the US Congress. One issue was whether tobacco companies deliberately added highly addictive nicotine to cigarettes. The CEO’s argued that variation in nicotine content in cigarettes was due to weather. They stated that a small tobacco leaf contained as much nicotine as a large leaf but more of the small leaf was used to make a cigarette, and hence cigarettes made from small leaves had more nicotine in them. To investigate this question, a plant scientist ran an experiment, watering 50 tobacco plants in group 1 according to normal rainfall, watering 50 plants in group 2 at 67% of normal rainfall, and watering 50 plants in group 3 at 33% of normal rainfall. The scientist found that indeed, plants receiving more water had significantly larger leaves. Then he investigated the contention by the CEO’s that different size leaves had the same nicotine content. He ran analysis of variance and reported the following results in Table 1-1. Table1-1: Table of One-Way ANOVA for Nicotine Content By Group (leaf Size) Anova: Single Factor SUMMARY Groups Count Sum Average Variance Nicotine-Group 1 50 776.17 15.5234 3.715655551 Nicotine-Group 2 50 669.27 13.3854 3.592629429 Nicotine-Group 3 50 503.82 10.0764 3.82519902 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 753.172233 2 376.5861167 101.4739277 2.06E- 28 3.057621 Within Groups 545.540716 147 3.711161333 Total 1298.71295 149 a. Were the cigarette company executives correct about different sized leaves having the same nicotine content? Explain No, Group 1 has 50% more nicotine per leaf than Group 3, and the F-statistic shows that the averages for the 3 groups are significantly different. b. Do you think the scientist’s experiment was sufficiently statistically significant to be convincing? Explain. Yes. Large F with a very small probability of being that large by chance. The tobacco companies hired an economist that ran the following regression of nicotine content against a constant and two dummy variables, Group1, and Group3,

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Dec. 10, 2009 ECON 240A- 2 L. Phillips Final Nicotine = c + b*Group1 +d*Group3 + e, with the results on the next page in Table 1-2.. The economist argued that since the coefficient on one group, group 1, was positive and the coefficient on the other group, group 3, was negative, the meaning of the regression result was unclear, calling the scientist’s study into question. c. Was the economist right or just trying to lie with statistics? Explain. Just trying to lie with statistics. The group 2 dummy was omitted so its average is picked up by the intercept, and the coefficient on the group 1 dummy is the difference between the group 1 average and the group 2 average which is positive, etc.
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