252x0631 11/15/06
ECO252 QBA2
THIRD EXAM
Nov 30and Dec 1, 2006
TAKE HOME SECTION
Name: _________________________
Student Number: _________________________
Class days and time : _________________________
Please Note: Computer problems 2 and 3 should be turned in with the exam (2). In problem 2, the 2 way
ANOVA table should be checked. The three F tests should be done with a 5% significance level and you
should note whether there was (i) a significant difference between drivers, (ii) a significant difference
between cars and (iii) significant interaction. In problem 3, you should show on your third graph where the
regression line is. Check what your text says about normal probability plots and analyze the plot you did.
Explain the results of the t and F tests using a 5% significance level. (2)
III Do the following. Note: Look at 252thngs (252thngs) on the syllabus supplement part of the website
before you start (and before you take exams). Show your work! State H 0 and H 1 where appropriate.
You have not done a hypothesis test unless you have stated your hypotheses, run the numbers and
stated your conclusion. (Use a 95% confidence level unless another level is specified.) Answers without
reasons or accompanying calculations usually are not acceptable. Neatness and clarity of explanation
are expected. This must be turned in when you take the in-class exam. Note that from now on
neatness means paper neatly trimmed on the left side if it has been torn, multiple pages stapled and
paper written on only one side. Because so much of this exam is based on student numbers, there is a
penalty for failing to state your correct student number.
1) Bassett et al. give the following numbers for the year and the number of pensioners in the United
Kingdom. Pensioners are in millions. The 2000 number is a bit shaky, so subtract the last digit of your
student number divided by 10 from the 12.00 that you see there. Label your answer to this problem with a
version number. (Example: Good ol’ Seymour’s student number is 123456, so the 12.000 becomes 12.000 0.6 = 11.400 and he labels it Version 6.) 'Pensioners' is the dependent variable and 'Year' is the independent
variable, so what you are going to get is a trend line. If you don’t know what dependent and independent
variables are, stop work until you find out.
1
2
3
4
5
6
7
8
Year
1966
1971
1975
1976
1977
1978
1979
2000
Pensioners
6.679
7.677
8.321
8.510
8.637
8.785
8.937
12.000
Bassett et. al. strongly suggest that you change the base year to something other than the year zero. They
recommend that you subtract 1970 from every number in the ‘Year’ column, so that 1966 becomes -4 and
2000 becomes 30. This will make your computations easier.
a. Compute the regression equation Y  b0  b1 x to predict the number of pensioners in each year. (3).You
may check your results on the computer, but let me see real or simulated hand calculations.
b. Compute R 2 . (2)
c. Compute s e . (2)
d. Compute s b1 and do a significance test on b1 (2)
e. Use your equation to predict the number of pensioners in 2005 and 2006. Using the 2006 number, create
a prediction interval for the number of pensioners for that year. Explain why a confidence interval for the
number of pensioners is inappropriate. (3)
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252x0631 11/15/06
f. Make a graph of the data. Show the trend line clearly. If you are not willing to do this neatly and
accurately, don’t bother. (2)
g. What percent rise in pensioners did the equation predict for 2006? What percent rise does it predict for
2050? The population of the United Kingdom grew at roughly 0.31% a year over the last quarter of the 20th
century. Can you intelligently guess what is wrong? (1)
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2) The Lees in their text ask whether experience makes a difference in student earnings and present the
following data for student earnings versus years of work experience. To personalize these data, take the
second to last digit of your student number call it a . Clearly label the problem with a version number based
on your student number. Then take your a , multiply it by 0.5 and add it to the 13 in the lower left corner. .
(Example: Good ol’ Seymour’s student number is 123456, so the 13 becomes 13 + 0.5(5) = 13 + 2.5 = 15.5
and he labels it Version 5.) Each column is to be regarded as an independent random sample.
Years of Work Experience
1
2
3
16
19
24
21
20
21
18
21
22
13
20
25
a) State your null hypothesis and test it by doing a 1-way ANOVA on these data and explain whether the
test tells us that experience matters or not. (4)
b) Using your results from a) present two different confidence intervals for the difference between earnings
for those with 1 and 3 years experience. Explain (i) under what circumstances you would use each interval
and (ii) whether the intervals show a significant difference. (2)
b) What other method could we use on these data to see if years of experience make a difference? Under
what circumstances would we use it? Try it and tell what it tests and what it shows. (3)
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c) (Extra Credit) Do a Levene test on these data and explain what it tests and shows. (4)
3) (Abronovic) A group of 4 workers produces defective pieces at the rates shown below during different
times of the day. Personalize the data by subtracting the last digit of your student number from the 14 in the
lower right corner. Use the number subtracted to label this as a version number. (Example: Good ol’
Seymour’s student number is 123456, so the 13 becomes 14 - 6 =8 and he labels it Version 8.)
Time
Worker’s Name
Apple
Plum
Pear
Melon
Early
10
11
8
12
Morning
Late
9
8
7
10
Morning
Early
12
13
11
11
Afternoon
Late
13
14
10
14
Afternoon
Sum of Row 1 = 41, SSQ of Row 1 = 429, Sum of Column 1 = 44, SSQ of Column 1 = 494,
Sum of Row 2 = 34, SSQ of Row 2 = 294, Sum of Column 2 = 46, SSQ of Column 2 = 550,
Sum of Row 3 = 47, SSQ of Row 3 = 555, Sum of Column 3 = 36, SSQ of Column 3 = 334,
a) Do a 2-way ANOVA on these data and explain what hypotheses you test and what the conclusions are.
(6)
b) Using your results from a) present two different confidence intervals for the difference between numbers
of defects for the best and worst worker and for the defects from the best and second best times. Explain
which of the intervals show a significant difference and why. (3)
c) What other method could we use on these data to see if years of experience make a difference while
allowing for cross-classification? Under what circumstances would we use it? Try it and tell what it tests
and what it shows. (3)
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