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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 mid2002 more than 5000000 of the cards had
been activated. Suppose a study of 25 randomlyselected customers is taken.
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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 pvalue 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 randomlyselected
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 110 : p :t l . What is the pvalue 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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