Dec 10 2009 ECON 240A 1 Final L Phillips 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 Nicotine Group 1 Nicotine Group 2 Nicotine Group 3 ANOVA Source of Variation Count 50 50 50 SS Sum 776 17 669 27 503 82 df Between Groups Within Groups 753 172233 545 540716 2 147 Total 1298 71295 149 Average 15 5234 13 3854 10 0764 Variance 3 715655551 3 592629429 3 82519902 MS F 376 5861167 3 711161333 101 4739277 P value 2 06E28 F crit 3 057621 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 Dec 10 2009 ECON 240A 2 Final L Phillips 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 d Which group had the highest nicotine content Group1 e These two techniques look different Can you spot something that is identical between the two statistical reports the tabular result and the regression The F statistic is the same for both techniques Table 1 2 Regression of Tobacco Leaf Nicotine Content by Group Indicator Variables Dependent Variable NICOTINE Method Least Squares Sample 1 150 Included observations 150 Variable Coefficient Std Error t Statistic Prob GROUP1 GROUP3 C 2 138000 3 309000 13 38540 0 385287 0 385287 0 272439 5 549103 8 588392 49 13166 0 0000 0 0000 0 0000 R squared Adjusted R squared S E of regression Sum squared resid Log likelihood Durbin Watson stat 0 579937 0 574222 1 926437 545 5407 309 6764 2 085378 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion F statistic Prob F statistic 12 99507 2 952320 4 169019 4 229232 101 4739 0 000000 2 30 The American Psychological Association estimates that 60 of absences from work are due to stress related issues costing US companies over 57 billion per year Stress contributes to rising health care costs Employee sponsored health insurance premiums have been increasing at double digit rates for example 11 4 in 2004 Stress related issues include worries about one s job finance health family life and other factors A survey of 1023 Americans and 985 Canadian adults asked them to report their primary source of stress in an attempt to see if Dec 10 2009 ECON 240A 3 Final L Phillips the factors causing stress might vary from country to country The results of the survey are reported in Table 2 1 Table 2 1 The Primary Source of Stress from a Survey of Americans and Canadians Job America Canada 266 315 581 Finance 347 276 623 Health 153 187 340 Family Life 164 128 292 Other 92 79 171 1022 985 2007 a Under the assumption of independence fill in the expected numbers in Table 2 2 You can round to the nearest whole number Table 2 2 Expected number under independence America Canada Job 296 285 Finance 317 306 Health 173 167 Family Life 149 143 Other 87 84 b Fill in the contribution to chi square in Table 2 3 rounded to the nearest whole number and report the total chi square statistic In this case rounding to the nearest whole number in parts a and b causes less than a 2 error in total 2 Table 2 3 Contribution to Chi Square America Canada Job 3 3 Finance 3 3 Health 2 2 Family Life 2 2 Other 0 0 Total 2 20 c What are the two primary factors that Americans stress about more than expected under independence between countries Finance and family life d What are the two primary factors that Canadians stress about more than expected under independence between countries Job and health Dec 10 2009 ECON 240A 4 Final L Phillips e How many degrees of freedom are there for the total chi square statistic 4 In Figure 2 4 illustrate i e draw in and label the critical chi square statistic for the appropriate degrees of freedom with your risk level 0 05 and draw in and label your total chi square statistic F igure 2 4 Chi Square Distribution for Degrees of F reedom 0 20 Chi Sq critival 5 9 49 DENSITY 0 15 0 10 0 05 Total Chi Square 20 0 00 0 5 9 49 10 15 20 20 CHI 3 30 In Thursday s discussion accompanying your presentations I mentioned the current upsurge in food stamp recipients in the US California is one of the states that is currently lagging in enrolling people eligible for food stamps California also has an interesting history with regard to relative expenditures on food stamps The California Statistical Abstract 2008 reports total value of food stamp benefits issued since fiscal year 1970 71in Table E 18
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