252x0571 11/28/05
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ECO252 QBA2 Name
THIRD HOUR EXAM Hour of Class Registered
Dec 1 2005 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 [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
4. If we are comparing the means of 4 random samples and find the following: x
1

10 x
2

12 x
3

11 x
4

13 s
1

2 .
0 s
2

2 .
2 s
3

2 .
3 s
4

2 .
5 n
1

5 n
2

5 n
3

5 n
4

5
The appropriate test statistic is: a)
 2
with 12 degrees of freedom b)
 2 with 19 degrees of freedom
[9] c) F with 5 and 4 degrees of freedom d) F with 3 and 16 degrees of freedom e) f)
F with 4 and 5 degrees of freedom.
D
 s x
1 n
1
1
2

 x s
2
2
2 n
2

 x s
3
2
3 n
3

 x
4 s n
4
2
4
[11]

5. If we are doing a 2-way ANOVA and find the following:
Two-way ANOVA: C8 versus C9, C10
Source DF SS MS F P
Rows 3 8.2963 2.76542 2.95 0.040
Columns 2 3.7183 1.85916 1.98 0.147
Interaction 6 25.8108 4.30180 4.58 0.001
Error 60 56.3071 0.93845
Total 71 94.1325
S = 0.9687 R-Sq = 40.18% R-Sq(adj) = 29.22%
The following are significant at the 1% level. a) Differences between Row means only b) Differences between Column means only
(3) c) Differences between both Row and Column means d) Interaction only e) All are significant at the 1% level f) None are significant at the 1% level g) Not enough information. [14]
6. If we do a 1-way ANOVA and find the following.
One-way ANOVA: C1, C2, C3, C4
Source DF SS MS F P
Factor 3 32.37 10.79 2.76 0.049
Error 68 266.27 3.92
Total 71 298.64
Individual 95% CIs For Mean Based on Pooled
StDev
Level N Mean StDev +---------+---------+---------+---------
C1 18 11.916 1.095 (--------*--------)
C2 18 12.436 2.195 (--------*---------)
C3 18 12.927 1.929 (--------*---------)
C4 18 13.736 2.434 (--------*---------)
+---------+---------+---------+---------
11.0 12.0 13.0 14.0
Give a 1% Tukey confidence interval (or equivalent test) for
  
4
and explain whether this shows a significant difference between these two means.
Extra Credit – do the same with a Scheffe interval. (2)
(3) [17]
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 MS F P
Factor ? 6.76792 0.615264 0.636
Error ? 162.448 0.966951
Total 179 169.216
The degrees of freedom for the F test are a) 10, 168 b) 11, 158 c) 10, 158 d) 11, 168. e) 9, 178 f) 10, 178
(2)
8. If we do a 1-way ANOVA and assume that your answer in 7 is correct, pick an appropriate value for
F with a 10% significance level from the table and explain your results. (2) [21]
9. If we do a simple regression and find the following: (Sandy 13.1, 13.2)
 xy

1150 , a) 10 x

5 , y

10 , n

20 ,
 x
2 
550 .
The predicted value of y when x

6 is: b) 11 c) 12 d) 13 e) Answer can’t be obtained with information given. (4)
10. Assume the following data: x y
[25]
4
3
7
2
0
5
2 1
16 8
Find the following. Show your work!
 x
2
,
 xy , R
2
(4) [29]
3

11. The percentage of the total (squared) variation of the y variable around its mean accounted for by the x variable is measured by the a) Coefficient of Correlation b) Coefficient of Explanation c) Coefficient of Determination d) Standard error of the estimate s e
(2) [31]
————— 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 = 12.5 + 5.10 X
Predictor Coef SE Coef T P
Constant 12.464 2.465 5.06 0.001
X 5.0990 0.6282 8.12 0.000
Analysis of Variance
Source DF SS MS F P
Regression 1 998.38 998.38 65.89 0.000
Residual Error 8 121.22 15.15
Total 9 1119.60
Obs X Y Y
ˆ
1 0.00 11.00 12.46
2 5.00 34.00 37.96
3 3.00 34.00 27.76
4 6.00 48.00 43.06
5 3.00 23.00 27.76
6 6.00 40.00 43.06
7 3.00 26.00 27.76
8 1.00 19.00 17.56
9 5.00 39.00 37.96
10 2.00 24.00 22.66
 y

298,
 x

34 and
 x
2 
= 154
12. From the computer output above, find the following: a) R
2
(2) b) s e
(2) c) A 95% confidence interval for d) A 95% confidence interval for

0
(2)
Y when X

5 .
(3) [40]
4

5