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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 RSq 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 RSq = 95.6654%
Analysis of Variance Source DF SS Regression * +****** Residual Error
Total ** kkitic‘kk *zkk‘kskki: T
w0.44
10.56 5.38
0.69
1.32 MS
****+* kinkk9: (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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