252x0572 11/28/05
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ECO252 QBA2
THIRD HOUR EXAM
Dec 1 2005
Name
Hour of Class Registered
MWF 2, MWF3, TR 12:30, TR2
I. (40 points) Do all the following (2 points each unless noted otherwise). Do not answer question ‘yes’ or
‘no’ without giving reasons. Show your work in questions that are not multiple choice.
1. Turn in your computer problems 2 and 3 marked to show the following: (5 points, 2 point penalty for
not doing.)
a) In problem 2 – what is tested and what are the results?
b) In problem 3 – what coefficients are significant? What is your evidence?
c) In the last graph in problem 3, where is the regression line?
[5]
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 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
(2)
[7]
3. (Sandy) Which of the following is not an assumption required for 1-way ANOVA wth 4 columns..
a) 1   2   3   4 .
b) All of the columns are random samples
c) All of the population have to be Normally distributed.
d)  1   2   3   4
(2)
[9]
4. If we are comparing the means of 5 random samples and find the following:
x1  10 x 2  12 x 3  11 x 4  13 x 5  14
s1  1.0 s 2  1.2 s 3  1.3 s 4  1.5 s 5  1.5
n1  7 n 2  7 n 3  7 n 4  7
The appropriate test statistic is:
x1  x 2  x 3  x 4  x 5
a) D 
s12 s 22 s 32 s 42 s 52




n1 n 2 n3 n 4 n5
b)
c)
d)
e)
n5  7
F with 7 and 4 degrees of freedom
F with 4 and 30 degrees of freedom
F with 4 and 7 degrees of freedom.
 2 with 18 degrees of freedom
f)  2 with 34 degrees of freedom
(2)
[11]
5. If we are doing a 2-way ANOVA and find the following:
Two-way ANOVA: C8 versus C9, C10
Two-way ANOVA: C5 versus C6, C7
Source
Rows
Columns
Interaction
Error
Total
S = 1.955
DF
3
2
6
60
71
SS
32.374
7.861
28.999
229.406
298.639
R-Sq = 23.18%
MS
10.7914
3.9304
4.8331
3.8234
F
2.82
1.03
1.26
P
0.046
0.364
0.288
R-Sq(adj) = 9.10%
The following are significant at the 5% level.
(3)
a) Differences between Row means only
b) Differences between Column means only
c) Both differences between Column means and Interaction
d) Interaction only
d) All are significant at the 5% level
e) None are significant at the 5% level
f) Not enough information.
[14]
6. If we do a 1-way ANOVA and find the following.
One-way ANOVA: C1, C2, C3, C4
Source
Factor
Error
Total
Level
C1
C2
C3
C4
DF
3
68
71
N
18
18
18
18
SS
32.37
266.27
298.64
Mean
11.916
12.436
12.927
13.736
MS
10.79
3.92
F
2.76
P
0.049
Individual 95% CIs For Mean Based on Pooled
StDev
StDev
+---------+---------+---------+--------1.095
(--------*--------)
2.195
(--------*---------)
1.929
(--------*---------)
2.434
(--------*---------)
+---------+---------+---------+--------11.0
12.0
13.0
14.0
Give a 1% Tukey confidence interval (or equivalent test) for 1   3 and explain whether this shows a
significant difference between these two means.
(3)
[17]
Extra Credit – do the same with a Scheffe interval.
(2)
Extra Credit – Do the same for an individual confidence interval for the difference and explain why it is
more likely to show a significant difference than the other two. (2)
2
7. If we do a 1-way ANOVA and find the following: (Sandy 12.50, 12.51)
One-way ANOVA:
Source DF
SS
Factor
?
7.30310
Error
? 101.358
Total 116 108.661
MS
F
1.46062 1.60
0.913131
P
The degrees of freedom for the F test are
(2)
[19]
a) 4, 100
b) 5, 111
c) 4, 111
d) 5, 115.
e) 5, 116
f) 4, 115
8. If we do a 1-way ANOVA and assume that your answer in 7 is correct, pick an appropriate value for
[21]
F with a 10% significance level from the table and explain your results. (2)
9. If we do a simple regression and find the following: (Sandy 13.1, 13.2)
xy  1200 , x  5 , y  10, n  10 ,
x 2  500 . The predicted value of y when x  4 is:


a)
b)
c)
d)
e)
5.2
7.2
8.6
9.6
Answer cant’t be obtained with information given.
10. Assume the following data:
x
y
7
-2
9
-6
5
-1
8
-9
29
-18
Find the following. Show your work!
 x ,  xy , R 2
2
(4)
[25]
(4)
[29]
3
11. The coefficient of determination is defined as
a) Total (squared) variation in y divided by the explained variation.
b) Explained variation in y divided by the total (squared) variation in y
c) Unexplained variation in y divided by the total (squared) variation in y .
d) Sum of the explained and unexplained variation in y divided by the total variation in
[31]
y.
————— 11/28/2005 8:40:25 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > Regress c1 1 c2;
SUBC>
Constant;
SUBC>
Brief 3.
Regression Analysis: Y versus X
The regression equation is
Y = 4.53 + 10.2 X
Predictor
Constant
X
Coef
4.531
10.198
SE Coef
7.217
1.256
T
0.63
8.12
P
0.548
0.000
Analysis of Variance
Source
Regression
Residual Error
Total
Obs
1
2
3
4
5
6
7
8
9
10
X
2.00
7.00
5.00
8.00
5.00
8.00
5.00
3.00
7.00
4.00
Y
DF
1
8
9
22.00
68.00
68.00
96.00
46.00
80.00
52.00
38.00
78.00
48.00
SS
3993.5
484.9
4478.4
MS
3993.5
60.6
F
65.89
P
0.000
Ŷ
24.93
75.92
55.52
86.11
55.52
86.11
55.52
35.12
75.92
45.32
 y  596 ,  x  54 and  x
2
 330
12. From the computer output above, find the following:
a) R 2 (2)
b) s e (2)
c) A 90% confidence interval for 1 (2)
d) A 90% prediction interval for Y when X  5.
(3)
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4
5