ECON227-2006 final

ECON227-2006 final - FACULTY OF ARTS FINAL EXAMINATION ECON...

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Unformatted text preview: FACULTY OF ARTS FINAL EXAMINATION ECON 227D]. (01) e (02) ECONOMIC STATISTICS Examiner: Prof. Ken MacKenzie Thursday, April 27, 2006 Associate Examiner: Prof. John Kurien 09:00—12:00 ENSTRUCTION: Closed book, 8 1/2 X 14" crib sheet allowed, statistics tables allowed, calculators allowed, dictionaries allowed. Answer all 6 questions. All questions have the same value. This exam comprises 6 pages (does not include cover page, fiust the number of pages with questions). ECON 227 1. Data have been collected on nutrition for a suitably random sample of twelve popular dry cereals. For a standard serving of each cereal measurements were made of the numbers of units of protein, carbohydrates, fat, vitaminA, and calories. Brand Protein Carbo Fat Calories VitA Life 6 19 l l 10 0 Grape Nuts 3 23 0 100 25 Super Sugar Crisp 2 26 0 1 10 25 Special K 6 21 0 110 25 Rice Krispies 2 25 0 110 25 Raisin Bran 3 28 1 120 25 Product 19 2 24 0 110 lOO Wheaties 3 23 l l 10 25 Total 3 23 i 110 100 Puffed Rice 1 13 0 50 0 Sugar Corn Pops 1 26 0 l 10 25 Sugar Smacks 2 25 O 110 25 a) Predict the number of calories of another cereal with 5 units of protein, 23 carbohydrate units, 1 fat unit, and 25 units of vitamin A. Use MODEL 1. l3) What proportion of the variation in calories is explained by the regression reiationship in i) MODEL I ? ii) MODEL 11 ? c) Is the increase in R2 significant from MODEL I to MODEL 11 ? Justify your answer numerically from the printouts. d) Give a 90% confidence interval for the marginal contribution of a unit of carbohydrates based on the results in MODEL 1. e) Find the missing numbers in the analysis—of—variance table for MODEL 11. f) Find Pearson’s correlation coefficient for the Carbo and Fat data, and determine whether these two variables are significantly correlated. ECON 227 MODEL I The regression equation is Calories m Predictor Coef StDev Constant 16.71 17.74 Carbo 3.6630 0.7889 Fat 9.726 6.071 VitA 0.02410 0.09612 8 = 9.868 R-Sq e 77.7403% Analysis of Variance Source DF SS Regression 3 2720.91 Residual Error 8 779.09 Total 11 3500.00 MODEL 11 The regression equation is T .94 .64 .60 .25 OI—‘nbO MS 906.97 97.39 Calories: —4.082+ 3.9805Carbo+ 5.215Protein+ Predictor Coef StDev Constant "4.082 9.217 Carbo 3.9805 0.3768 Protein 5.2150 0.9693 Fat 2.208 3.187 vita 0.06052 0.04585 8 = 4.655 R-Sq = 95.6654% Analysis of Variance Source DF SS Regression * +****** Residual Error Total ** k-kitic‘k-k *zk-k‘ksk-ki: T w0.44 10.56 5.38 0.69 1.32 MS ****+* kink-k9: (3000 2.20 00000 16.71 + 3.663 Carbo + 9.726 Fat + 0.0241 VitA P .374 .002 .148 .808 9.31 0.005 8Fat+0.06052VitA P .671 .000 .001 .511 .228 F P 38.62 0.000 ECON 227 2. Regress Calories on VitA either using statistics functions on the calculator or using formulas and the following partial computations: Zx=400 Zy=1260 Zfizzsooo 232344000 2392135800. a} Find the OLS line equation b) Test whether the number of units of vitamin A is significant for predicting the number of calories in a standard serving. C) Regardless of your conclusion in b) form a 95% confidence interval for the mean number of calories in standard servings with 25 units of vitamin A. Use the simple- regression model of this question. d) What is the standard error of the estimate in this model? e) Show that the point (3;?) satisfies the OLS equation. 3. a) Test whether the variances of Carbo and VitA are significantly different. b) Test whether the mean of VitA is significantly greater then the mean of Carbo. c) What are the technical requirements for performing the tests you used in parts a) and b) ? d) Estimate the standard error of the difference in sample means for Carbo and VitA. f) Test whether the mean of VitA significantly exceeds 23. ECON 227 4. A random sample of working citizens of Eurelia and Begonia was selected, and the following cross—tabulation was done. d) Eurelia Begonia Self — employed 180 240 notself — employed 820 960 Give a 95% confidence interval for the proportion of those self—employed amongst working citizens in Eurelia. How large a sample would be needed in order to form a 99% confidence interval for the proportion of those self— employed amongst the working citizens of Begonia? The margin of error desired is 0.011. Is the proportion of those self—employed significantly higher in Begonia than in Eurelia? Use the pmvalue method to perform this test. For the test in c), if the choice of sample is unlucky and leads to the wrong conclusion, would the error be of Type I or Type II ? ECON 227 S. In Eurelia there are three categories of bicycle license, with different fees for each. The table below is based on a random sample of 262 Eurelian bicycle—license holders. License Fee $25 $30 $27 Female 28 32 24 Male 36 44 40 Other 1 8 24 16 a) Does the type of license bought depend significantly on whether the Eurelian is Female, Male, or Other? b) How large a sample would be needed in order to establish a 90% confidence interval for the mean amount paid by Eurelians in the Other category? o) Is the mean amount paid by men significantly different from the mean amount paid by women? d) Test whether the incidence of license buying is about the same for Females, Males, and Others. ECON 227 6. Independent random samples of office workers in Halifax (H), Montreal (M), and Toronto (T) were selected and the office workers’ fitness indexes were measured. The data are shown below. (Hg: ff If If If AJ 44 A! A! 44 A4 T T T T T T bufim 40 44 42 48 48 32 38 41 48 52 3O 32 25 41 46 44 a) Test whether the mean indexes are about the same in all three cities, or whether at least one is significantly different. b) Form a 95% confidence interval for the difference in the mean indexes of Montreal (M) and Toronto (T). c) The p—value for the test in part a) was worked out on MINITAB, but unfortunately the printer wasn't working too well, so it was hard to see whether the p—value is 0.212 or 0.012. Which is it? Justify your answer. ...
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ECON227-2006 final - FACULTY OF ARTS FINAL EXAMINATION ECON...

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