252x0431 4/12/04
(Page layout view!)
ECO252 QBA2 Name
THIRD HOUR EXAM Hour of Class Registered ____
Apr 16 2004
I. (30+ points) Do all the following (2 points each unless noted otherwise). Do not answer question ‘yes’ or ‘no’ without giving reasons.
1. Turn in your computer problems 2 and 3 marked as requested in the Take-home. (5 points, 2 point penalty for not doing.)
2. (Dummeldinger) As part of a study to investigate the effect of helmet design on football injuries, head width measurements were taken for 30 subjects randomly selected from each of 3 groups (High school football players, college football players and college students who do not play football – so that there are a total of 90 observations) with the object of comparing the typical head widths of the three groups. If the researchers are reluctant to assume that the data in each of these three groups comes from a Normally distributed population, they should use the following method. a. The Kruskal-Wallis test. b. One-way ANOVA c. The Friedman test d. Two-Way ANOVA
3. Assume that the researchers ignore your advice, whether right or wrong, in problem 2. If one-way
ANOVA is used, how many degrees of freedom apply to the Within sum of squares? [9]
4. (Berenson et al.) In a study of drive-through times at fast food chains, the following was recorded (in seconds). n
1
 n
2
 n
3
 n
4
 n
5

20 , x
.
1

150 , x
.
2

167 , x

.
3

169 , x
.
4

171 , x
.
5

172 , where 1 =
Wendy’s, 2 = McDonald’s, 3 = Checkers, 4 = Burger King, 5 = Long John Silver’s.
H
0
:

1
 
2
 
3
 
4
 
5
One-Way ANOVA
Source DF SS MS F Statistic p Value
Between 4 ???? ???? ???? 3.24067E-08
Within 95 12407 130.6 ????
Total 99
You do not need to fill in any of the omitted data. Does the ANOVA show a significant difference between drive through times? Why? (2) [11]
5. From the above ANOVA and the means given above, do the mean time times for McDonald’s and
Long John Silver’s differ significantly? Use a Tukey method. (5)

252x0431 4/12/04
Exhibit 1: A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges ( Y ) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a company is the company’s sales revenue (
X ) -- measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model. The analyst took the Minitab output home to check out, but it fell into a puddle and all that he (or I) can read is below.
The regression equation is
Y = -2700 + 20.00 X
Predictor Coef Stdev t-ratio p
Constant -2700.0 ---- --- 0.600
X 20.000 ---- --- 0.034 s = 65.00 R-sq = ---- R-sq(adj) = ----
6.
Referring to Exhibit 1, interpret the estimate of

0
, the Y -intercept of the line. a) All companies will be charged at least $2,700 by the bank. b) There is no practical interpretation since a sales revenue of $0 is a nonsensical value. c) About 95% of the observed service charges fall within $2,700 of the least squares line. d) For every $1 million increase in sales revenue, we expect a service charge to decrease
$2,700.
7.
Referring to Exhibit 1, interpret the p value for testing whether a) There is sufficient evidence (at the

1
exceeds 0.

= 0.05 level) to conclude that sales revenue ( X ) is a useful linear predictor of service charge ( Y ). b) There is insufficient evidence (at the

= 0.10 level) to conclude that sales revenue ( X ) is a useful linear predictor of service charge ( Y ). c) Sales revenue ( X ) is a poor predictor of service charge ( Y ). d) For every $1 million increase in sales revenue, we expect a service charge to increase
$0.034.
8.
Referring to Exhibit 1, a 95% confidence interval for

1
is (15, 30). Interpret the interval. a) We are 95% confident that the mean service charge will fall between $15 and $30 per month. b) We are 95% confident that the sales revenue ( X ) will increase between $15 and $30 million for every $1 increase in service charge ( Y ). c) We are 95% confident that average service charge ( Y ) will increase between $15 and $30 for every $1 million increase in sales revenue ( X ). d) At the

= 0.05 level, there is no evidence of a linear relationship between service charge ( Y ) and sales revenue ( X ). [22]
2

252x0431 4/12/04
Exhibit 2: The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the color and shape of the box's logo on the approval rating of the cereal. He combined 4 colors and 3 shapes to produce a total of 12 designs. Each logo was presented to 2 different groups (a total of 24 groups) and the approval rating for each was recorded and is shown below. The manager analyzed these data using the

=
0.05 level of significance for all inferences.
COLORS
SHAPES Red Green Blue Yellow
Circle
Square
Diamond
54
44
34
36
46
48
67
61
56
58
60
60
36
44
36
30
34
38
45
41
21
25
31
33
Source
Analysis of Variance df SS
Colors 3
Shapes 2
2711.17
579.00
Interaction __ 150.33
Error ___ 150.00
23 3590.50
MS F
903.72 72.30
289.50 23.16 p
0.000
0.000
Total
9.
Referring to Exhibit 2, fill in the first 5 missing numbers (not the missing p-value). (3)
10.
Referring to Exhibit 2, assume that your degrees of freedom are correct and find the 5% value of F on the table that would be used to test if the interaction is significant. What is your conclusion and why? (3) [28]
3

252x0431 4/12/04
Exhibit 3 (Mendenhall, et al.) : The president of a local company has asked the vice presidents of the firm to provide an analysis of the business climate of 4 states that may be considered for the location of a manufacturing facility. Each VP rates the state’s business climate on a 1-10 scale with 10 as outstanding and 1 as unacceptable.
State
Vice President
Abel
Baker
Charley
Dogg
Easy
Arkansas
8.5
7.5
9.0
8.0
7.0
Colorado
8.0
8.0
6.0
6.0
5.5
Illinois
3.5
6.0
4.0
7.0
4.5
Iowa
6.0
5.5
7.0
4.0
7.5
11.
Referring to Exhibit 3, assume that the underlying distribution is not Normal. Do an appropriate analysis. a)Tell what test you are going to use.(1) b) State your null hypothesis. (1) c) Perform the test and state your conclusion. (4) d) On the basis of your results, should business climate be considered in locating the facility? Why? (1) [35]
4

252x0431 4/8/04 ECO252 QBA2
Third EXAM
Apr 16, 2004
TAKE HOME SECTION
Name: _________________________
Student Number: _________________________
Class days and time : _________________________
Please Note: computer problems 2 and 3 should be turned in with the exam. In problem 2, the 2 way
ANOVA table should be completed. 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.
II. Do the following: (23+ points). Assume a 5% significance level. Show your work!
1. (Albright, Winston, Zappe) Boa Constructors, an international construction company with offices in
Texas, the Cayman Islands, Belarus, Bosnia and Iraq, conducts an employee empowerment program and after a few months asks random samples of its employees in each office to rate the program on a 1- 10 scale.
Assume that each column below represents a random sample taken in one office. Assume that the underlying distribution is Normal and test the hypothesis

1
 
2
 
3
 
4
 
5
. Data is on the next page. a) Note that office 2, the ‘head’ office in the Cayman Islands, has a smaller sample than the rest. You can help by adding a seventh measurement, the third to last digit of your student number (If it’s a zero, use 10).
For example, Seymour Butz’s student number is 976500 and he will have a second column that reads 7, 6,
10, 3, 9, 10, 5. This should not change the results by much. Find the sample variance of this column. (2) b) Test the hypothesis (6) Show your work – it is legitimate to check your results by running these problems on the computer, but I expect to see hand computations for every part of them. c) Compare means two by two, using any one appropriate statistical method, to find out which were happiest. Actually, we really want to test if the programs worked significantly better in the first two offices, which are English-speaking, than the other three, which are not. Citing numbers from your comparison results, is this correct? (3) d) (Extra Credit) Now we find out that this was not a random sample and that each row represents a separate job description. If this changes your analysis, redo the analysis. In order to fill out the data from the Cayman
Islands, use the last two digits in your student number. For example, Seymour Butz’s student number is
976500 and he will have a second column that reads 7, 6, 10, 3, 9, 10, 5, 10, 10 (5) e) (Extra Credit) What if you found out that each column in the data in b) was a random sample from a non-
Normal distribution? If this changes your analysis, redo the analysis. (5) f) Run Levene’s test on the data in b) . You may do this by computer. There will be lots of output, but just look at the 2 or 3 lines from Levene’s test. What does it test for and what is the conclusion ? (2)
Hint: If you put your data in the first 5 columns of Minitab with a column number above them, the following should be of interest.
MTB > AOVOneway c1-c5.
MTB > Stack c1-c5 c11;
#Does a 1-way ANOVA
# Stacks the data in c12, col.no. in c12.
SUBC> Subscripts c12;
SUBC> UseNames.
MTB > rank c11 c13
MTB > Unstack (c13);
SUBC> Subscripts c12;
#Puts the ranks of the stacked data in c13
SUBC> After;
SUBC> VarNames.
MTB > %Vartest c11 c12
#Unstacks the data in the next 5 available
# columns. Uses IDs in c12.
#Does a bunch of tests, including Levene’s
On stacked data in c11 with IDs in c12.
5

252x0431 4/8/04
If you remember what you did in Computer Problem 2, you should be able to add row numbers in an unused column and run a 2-way ANOVA.
Ratings of Program
Office
Row 1 2 3 4 5
1 8 7 7 5 6
2 2 6 5 3 6
3 9 10 5 6 6
4 8 3 5 9 6
5 3 9 4 6 3
6 10 10 3 5 4
7 9 5 5 8
8 6 5 6 6
9 8 3 3 2
Sum of column 1 = 63.000
Sum of squares of column 1 =
503.00
Sum of column 3 = 42.000
Sum of squares of column 3 =
208.00
Sum of column 4 = 48.000
Sum of squares of column 4 =
282.00
Sum of column 5 = 47.000
Sum of squares of column 5 =
273.00
2. (Keller, Warrack) A dealer records the odometer reading and selling price in thousands of a sample of
100 3-year old Ford Tauruses (well equipped and in excellent condition) sold at auction. Unfortunately, he missed one car in his initial computations. The 101 st car has an odometer reading of 16.000 (in thousands) and sold at 14.800 plus the last three digits of your student number divided by 1000. For example, Seymour
Butz’s student number is 976500, so he thinks the car sold at $14.800 + $0.500 = 15.300 (thousands). The column sums are given below without the 101 st car, so you should find it easy to adjust these sums for the
101 st car.
Row Odometer Price
1 37.388 14.646
2 44.758 14.122
3 45.833 14.016
. .. ..
. .. ..
. .. ..
98 33.190 14.518
99 36.196 14.712
100 36.392 14.266 sumy 1482.28 sumx 3600.95 smxsq 133977 smxy 53107.6 smysq 21997.3
Note that these sums can’t be used directly, but they should help you to get the corrected numbers.
‘Price’ is the dependent variable and ‘Odometer’ is the independent variable. If you don’t know what that means, don’t do the problem until you find out. Show your work – it is legitimate to check your results by running the problem on the computer, but I expect to see hand computations that show clearly where you got your numbers for every part of this problem.
 a. Compute the regression equation Y
  b
0
 b x to predict the ‘Price’ on the basis of ‘Odometer’. (2) b. How much does the equation predict that a car with an odometer reading of 35000 miles will sell for? If the answer isn’t reasonable compared to the prices shown above, find your mistake and fix it. (1) c. Compute R
2
. (2) d. Compute s e
. (2) e. Compute s b
0
and do a significance test on b
0
(1.5) f . Compute s b
1
and do a confidence interval for b
1
(1.5) g. Do an ANOVA table for the regression. What conclusion can you draw from this table about the relationship between advertising expenditures and sales? Why? (2) h. Do a prediction interval for the selling price of the car in b. Explain the difference between this and a confidence interval and why this is the appropriate interval to use here. (3) [73]
6