ECON227-2007 final

ECON227-2007 final - FACULTY OF ARTS FINAL EXAMINATION ECON...

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Unformatted text preview: FACULTY OF ARTS FINAL EXAMINATION ECON 227D sec 001 Economic Statistics Examiner: Prof. K. MacKenzie Monday April 16, 2005 Associate Examiner: Prof. J. Kurien 2 p.m. — 5 p.m. INSTRUCTIONS: Answer in exam book. Calculators are allowed. Statistics tables allowed. No notes or texts allowed. Dictionaries are allowed. Legal sized crib sheets allowed You may keep the exam. Answer all 7 questions. All questions have the same value. This exam comprises 8 pages, including the cover page. ECON 227 sec 001 1. In November 2001 a popular chain of coffee shops launched its prepaid debit card. The card, which can be for any amount from $5 to $500, can be used at any of the locations of the chain. The card was so popular when it was first released that many stores ran out, and by mid-2002 more than 5000000 of the cards had been activated. Suppose a study of 25 randomly-selected customers is taken. prmmmnsweaflwdflwamomfiofmepmpmdcmdflhdr%m&flwrmmbmof days a month when they make a purchase at the chain, the number of cups of coffee drunk per day, and their income (in $10005). The data are given below, followed by some MINITAB printouts. Amount age days cups income 5 25 4 1 20 25 30 12 5 35 10 27 10 4 30 5 42 8 5 30 15 29 11 8 25 50 25 12 5 60 10 50 8 3 30 15 45 6 5 35 5 32 16 7 25 5 23 10 1 20 20 40 18 5 40 35 35 12 3 40 40 28 10 3 50 15 33 12 2 30 200 40 15 5 80 15 37 3 l 30 40 51 10 8 35 5 20 8 4 25 30 26 15 5 35 100 38 19 10 45 30 27 12 3 35 25 29 14 6 35 25 34 10 4 45 50 30 6 3 55 15 22 8 5 30 ECON 227 sec 001 MODELI The regression equation is amount = ~ 83.83 + 0.2369 age + 1.190 days + 1.422 cups + 2.4065 income Predictor Coef StDev T P Constant —83.83 22.49 -3.73 0.001! age 0.2369 0.5759 0.41 0.685 days 1.190 1.474 0.81 0.429 cups 1.422 2.631 0.54 0.595 income 2.4065 0.3597 6.69 0.000 S = 22.15 R—Sq = 75.5% Analysis of Variance Source DF 88 MS F P Regression 4 30175.0 7543.8 15.38 0.000 Residual Error 20 9811.0 490.5 Total 24 39986.0 3 MODELH The regression equation is amount = — 77.32 + 1.068 days + 1.762 cups + 2.4350 income Predictor Coef StDev T P Constant —77.32 15.67 -4.93 0.000 days 1.068 1.415 0.75 0.459 cups 1.762 2.448 0.72 0.480 income 2.4350 0.3460 7.04 0.000 S = 21.71 R—Sq = 75.3% Analysis of Variance Source DF SS MS F P Regression 3 30092 10031 21.29 0.000 Residual Error 21 9894 471 Total 24 39986 ECON 227 sec 00] MODELHI The regression equation is amount = — 73.08 + 2.821 cups + 2.5042 income Predictor Coef StDeV T P Constant —73.08 14.48 —5.04 0.000 cups 2.821 1.986 1.42 .0.170 income 2.5042 0.3303 7.58 0.000 S = 21.49 R—Sq = 74.6% Analysis of Variance Source DE SS MS F P Regression 9r +*‘k*~k +**** **~k~k* Residual Error ** ***** *** Total 24 39986 Answer the following questions, justifying the answers wherever possible from numbers found in the printouts. Are all three models significant for predicting the amount? é Use MODEL II to predict the amount of the card of a 32—year—old customer who goes to the chain 7 days a month, drinks 5 cups of coffee a day, and earns $45000 a year. Fill out the missing numbers, in the Analysis—of—variance table in MOD indicated by asterisks, 3L III. What proportion of the variation in amounts is explained by the regression in MODEL 11? Is this a significant reduction from the coefficient of determination in MODEL 1? Give a 95% CI contribution of (confidence interval)for the marginal ‘income’ in MODEL 111. What is the standard error of the estimate in MODEL 111? ECON 227 sec 001 2. Use the same data set as for question 1. a) A simple—regression model, MODEL IV, is to be calculated by regressing “amount’ on " Find the OLS equation income’. either using statistics buttons on your calculator or with a formula using the following partial computations: Zx=920 2x2=38200 ny=40275 Zyi=64950 Zy=790 7c = 36.8 SA. 21345362405 y = 31.6 s), = 4081768408 b) Fill out the analysis—of—variance table for this regression. c) Find a 95% PI (prediction interval) for the amount on the card of a customer with income $45000. d) Calculate the standard error of the regression coefficient. 1 e) Show that (X,y) satisfies the OLS line equation, at least for this particular set of data. 3. Use the same data set as for questions 1 and 2. a) Test at the 5% level whether the variances of the variables ‘amount’ and ‘income’ are significantly different. b) Test whether the means of the variables ‘amount’ and ‘income’ are significantly different. c) Give a 90% CI (confidence interval) for the mean amount on the debit cards. d) At least how many customers would be needed to establish a 96% CI for the mean income of customers if the margin of error desired is five—hundred dollars? f) Test whether the standard deviation in ‘income’ is significantly greater than 30. ECON 227 sec 001 “HHUNINGd The remaining questions on the examination do not refer to the data set above. 4. A random sample 0: Economics undergraduate students at MacMillan University yielded the following data: b) From Not from Total Montreal Montreal ___[ Female 488 112 _ 600 312 88 r 400 800 200 I 1000 Test whether the proportion of female students significantly exceeds 57%. Use the p-value method. Test whether the proportion of female students in the group from Montreal is significantly greater than the proportion of female students in the group not from Montreal. 3 What is the standard error of the sample proportion of female students in the group from Montreal? From Not from Montreal Montreal 488 112 88 200 Test whether the incidence of being from Montreal depends significantly on whether the student is female or male. Suppose by bad luck the random sample in this question is untypical of MacMillan undergraduate Economics students, so that the conclusion drawn in part a) is wrong. Is the error of Type I or Type H? U: ECON 227 sec 001 c) How large a sample would be needed to form a 99% CI for the proportion of dissatisfied students if the required margin of error is to be i 0.008 ? 6. The table below gives the holdings in Eurelian bonds of a randomly-selected group of Eurelians in different fields. Blue Collar White Collar Entertaignent Total East 12000 15000 9000 _ 12500 48500 Eurelia * Central 13500 16200 10800 14000 54500 Eurelia I 16000 i9600 12000 50100 "47200 29400' 38500 153100 a a) Test whether the mean holdings are significantly different in the different fields after the effect of the region (East, Central, West) has been removed. b) Form a 90% CI (confidence interval) for the difference in mean holdings between Blue and White collar Eurelians. 7. a) A large group of Eurelians has been polled concerning political preferences. It is suspected that there is virtually a tie amongst the three major political parties in Eurelia. Here are the results of the poll: Recidivist Party _‘_Party Party preferred preferred 340 Atavist Party preferred Test whether there is a significant difference in party preferences in Eurelia. ECON 227 sec 001 b) Another hypothesis test is performed on the data in part a). Let p stand for the proportion of Atavist Party supporters in the Eurelian population. The alternative hypothesis for the test is 1-10 : p :t l . What is the p-value 3 for this test? \- I have a textbook in which the value listed in the t tables for 150 degrees of freedom in the column headed 0.025 is 1,976. If I look in the tables of the F distribution with numerator df equal to 1 and denominator df equal to 150, what number should appear on the 0.05 page? ...
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ECON227-2007 final - FACULTY OF ARTS FINAL EXAMINATION ECON...

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