252grass3 10/15/03 (Open this document in 'Page Layout' view!)
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Graded Assignment 3
In your outline there are 6 methods to compare means or medians, methods D1, D2, D3, D4, D5a and D5b.
Method D6 compares proportions and method D7 compares variances or standard deviations. In all the
following cases, identify H 0 and H 1 and identify which method to use. If the hypotheses involve a mean,
state the hypotheses in terms of both  and D  1   2 . If the hypotheses involve a proportion, state
them in terms of both p and p  p1  p 2 . If the hypotheses involve standard deviations or variances,
state them in terms of both  2 and
 12
 22
or
 22
 12
. All the questions involve means, medians, proportions or
variances. (Most problems are highly edited versions of problems in McClave, et. al.)
Note: Look at 252thngs ( 252thngs) in the syllabus supplement before you start (and before you take
exams).
1. Of 200 MBA students, 110 are males. Of 500 managers, 300 are males. Is there a significant difference
between the fraction of males in the population of MBA students and the population of managers? (What
are H 0 and H 1 and what is the identifier of the method you would use?)
2. You have two machines that plop fruit into bottles, a new one and an old one. A sample of weights of 10
bottles from the old machine is taken, the average weight is 971.375 grams with a standard deviation of
15.250 grams. A sample of weights is taken from the new machine and the average weight turns out to be
971.374 grams with a standard deviation of 11.001 grams. Is the new machine more reliable than the old
one?
3. The Wallaby Shock Absorber company takes 6 of its own shock absorbers and tests them for durability
by driving different cars 20000 miles with them. The mean and variance of the strength of the shock was
recorded giving a mean of 10.716 and a variance of 3.069. 6 of a competitor’s shocks were tested the same
way, and a mean of 10.3 and a variance of 3.304 were found. The manufacturer wants to compare the
means, and assumes an underlying Normal distribution, but needs to find out first whether to use method D2
or D3. What should the manufacturer do to decide?
4. The manufacturer in the previous example never did decide what to do. Instead Wallaby continued the
experiment by testing 120 of its own shocks and 90 of the competitors. What method can they now use to
compare the average strength of the shocks?
5. Assume that the situation is identical to problem 3 above, but that an analysis of the data indicates that
the distribution of strengths is highly skewed to the right. What method should be used now to compare the
strength of the shocks?
6. A group of supervisors are given the exams on management skills before and after taking a course in
management. Scores are as follows.
Supervisor
Before
After
1
63
78
2
93
92
3
84
91
4
72
80
5
65
69
6
72
85
7
91
99
8
84
82
9
71
81
10
80
87
11
68
93
If we assume that the distribution of results is Normal. What method should we use to answer the question
“Has the course improved the scores of the managers?”
7. What method would we use in problem 6 above if we assumed that the underlying distribution was not
Normal?
8. We have data for 15 recent oil spills caused by fire and 15 oil spills caused by collision. We want to
show that the spills caused by collision are worse than those caused by fire, and we have evidence that the
variability of the spills caused by collision is far larger than the variability of spills caused by fire. What
method should we use?
9. Students are asked to rate the reality shows produced by ABC and Fox on a scale of 1 to 10. Analysis
of the data set, which can be considered ordinal data, indicates that the distribution is not symmetrical. A
random sample of 30 ratings of Fox shows and 25 ratings of ABC show is given and the researcher wants
to prove that Fox produces better shows.
10. Unemployment rates are found for 20 urban communities and 10 university communities in
Pennsylvania. The researcher wants to show that workers in the second group of communities are better off
than workers in the first group. Average unemployment rates are computed and variances of employment
rates between communities of each type seem similar.
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