Dec. 10, 2009 ECON 240A-1 L. PhillipsFinalAnswer all 5 questions. No talking or communicating.1. (30) In 1994, the chief executive officers, CEO’s, of the major tobacco companiestestified 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 accordingto 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 FactorSUMMARYGroups Count Sum Average VarianceNicotine-Group 1 50 776.17 15.5234 3.715655551Nicotine-Group 2 50 669.27 13.3854 3.592629429Nicotine-Group 3 50 503.82 10.0764 3.82519902ANOVASource ofVariation SS df MS F P-value F critBetween Groups 753.172233 2 376.5861167 101.47392772.06E-28 3.057621Within Groups 545.540716 147 3.711161333Total 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,Dec. 10, 2009 ECON 240A-2 L. PhillipsFinalNicotine = 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 itsaverage 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? Group1e. 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 VariablesDependent Variable: NICOTINEMethod: Least SquaresSample: 1 150Included observations: 150Variable Coefficient Std. Error t-Statistic Prob. GROUP1 2.138000 0.385287 5.549103 0.0000GROUP3 -3.309000 0.385287 -8.588392 0.0000C 13.38540 0.272439 49.13166 0.0000R-squared 0.579937 Mean dependent var 12.99507Adjusted R-squared 0.574222 S.D. dependent var 2.952320S.E. of regression 1.926437 Akaike info criterion 4.169019Sum squared resid 545.5407 Schwarz criterion 4.229232Log likelihood -309.6764 F-statistic 101.4739Durbin-Watson stat 2.085378 Prob(F-statistic) 0.0000002. (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 ifDec. 10, 2009 ECON 240A-3 L. PhillipsFinalthe 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 CanadiansJob Finance HealthFamily Life OtherAmerica 266 347 153 164 92 1022Canada 315 276 187 128 79 985581 623 340 292 171 2007.a. Under the assumption of independence, fill in the expected numbers inTable 2-2. You can round to the nearest whole number.Table 2-2: Expected number under independenceJob Finance HealthFamily Life OtherAmerica 296 317 173 149 87Canada 285 306 167 143 84b. Fill in the contribution to chi-square in Table 2-3, rounded to the nearestwhole 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 χ2 .Table 2-3: Contribution to Chi-SquareJob Finance HealthFamily Life OtherAmerica 3 3 2 2 0Canada 3 3 2 2 0Total χ2 = __20______c. What are the two primary factors that Americans stress about more than expected under independence between countries? Finance and family lifed. What are the two primary factors that Canadians stress about more than expected under independence between countries? Job and healthDec. 10, 2009 ECON 240A-4 L. PhillipsFinale. 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, withyour risk level α = 0.05, and draw in and label your total chi-square statistic.0.000.050.100.150.200 5 10 15 20CHIDENSITYFigure 2-4: Chi-Square Distribution for ____ Degrees of F reedom3. (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
View Full Document
Unlocking...