1.
Alex gives an exam in one of the classes he teaches.
The maximum possible score
is 70.
Alex then groups the students by the number of missed lectures, and then
obtains a random sample from each of the three groups:
students who did not miss
any of the lectures,
students who missed just a few lectures,
and students who
missed a lot of lectures. The results are shown in the table below.
Lectures Missed
None
A Few
A Lot
64
48
52
57
59
45
67
50
50
70
55
57
54
62
60
62
54
60
n
i
7
5
6
i
y
62
54.8
53
s
i
2
31
34.7
28
a)
Does the data suggest that at the
average exam scores for these
three groups are not the same?
State the null and alternative
hypotheses, construct an ANOVA
table and state your conclusion at
α
= 0.05
and
α
= 0.01.
b)
Use a 95% confidence level and
Scheffé’s multiple comparison
procedure to compare the average
exam score for students who did not
miss any of the lectures with the average exam scores for those who missed just a few
lectures and those who missed a lot of lectures.
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The grade point averages of students participating in college sports programs at
Anytown State University are compared.*
Football
Basketball
Hockey
3.2
2.6
2.4
2.4
1.9
3.8
3.1
2.6
3.7
3.3
2.8
2.3
1.8
2.5
2.1
1
y
= 2.5
2
1
s
= 0.220
2
y
= 3.3
2
2
s
= 0.235
3
y
= 2.3
2
3
s
= 0.145
a)
At
α
= 0.05, can one conclude that there is a difference in the mean GPA of
the three groups?
Specify the null and the alternative hypotheses.
Show the
calculations leading to your conclusion in the form of an ANOVA table.
b)
Construct a 95% confidence interval for the difference between the average
GPA for Basketball and the average GPA for Hockey.
c)
Use a 95% confidence level and Scheffé’s multiple comparison procedure to
compare the average GPA for Basketball with the average GPA for Hockey.
d)
Use a 95% confidence level and Scheffé’s multiple comparison procedure to
compare the average GPA for Basketball with the average GPA for Football
and Hockey.
e)
Use a 95% confidence level and Tukey’s pairwise comparison procedure to
compare the average GPA for Basketball with the average GPA for Hockey.
____________
*
The data does
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 Spring '08
 Stepanov
 Statistics, Normal Distribution, Regression Analysis, Statistical hypothesis testing, average GPA

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