252grass3-08 3/7/08 (Revised) (Open this document in 'Page Layout' view!)
Name:
Class days and time:
Please include this on what you hand in!
Graded Assignment 3
Part 1: In your outline there are 6 methods to compare means or medians, methods D1, D2, D3, D4, D5a
and D5b. Methods D6a and D6b compare proportions and method D7 compares variances or standard
deviations. In 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. One of these problems is a chi-squared test.
Note: Look at 252thngs (252thngs) on the syllabus supplement part of the website before you start (and
before you take exams). ). Neatness and clarity of explanation are expected. Note that from now on
neatness means paper neatly trimmed on the left side if it has been torn, multiple pages stapled and
paper written on only one side. This is very similar to Problem D8.
----------------------------------------------------------------------------------------------------------------------------Example: This may seem long but it appears on an old graded assignment 3.
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?”
Solution: You are comparing means before and after the course. You can get away with using means
because the parent distributions are Normal. If  2 is the mean of the second sample, you are hoping that
 2  1 , which, because it contains no equality is an alternate hypothesis. So your hypotheses are
 H 0 : 1   2
 H 0 : 1   2  0
H 0 : D  0
or 
. If D  1   2 , then 
. The important thing to notice

 H 1 : 1   2
 H 1 : 1   2  0
H 1 : D  0
here is that the data are in before and after pairs, so you use Method D4.
-------------------------------------------------------------------------------------------------------------------------------1. Dora Jarr and Daughters is a maker of components for automobile dashboards. When Dora retired, her
company’s stock became publicly traded. A sample of 160 stock analysts were asked whether they rated the
stock as a ‘buy‘in 2007 and again in 2008. 79 analysts rated the stock a ‘buy’ in both 2007 and 2008. 15
analysts recommended it as a ‘buy’ in 2007 but not in 2008. 9 analysts upgraded the stock to a ‘buy’ in
2008. The remaining analysts did not consider the stock a ‘buy’ in either year. Can we say that the
proportion of analysts who favor the stock has fallen?
252grass3-08 3/7/08 (Revised) (Open this document in 'Page Layout' view!)
2. Of a sample of 200 MBA students, 110 are males. Of a sample 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?)
3. We add a sample of 100 CEOs to the data in 2. 80 of them are males. Can we say that there is a
significant difference between the proportions of males in all three groups?
4. 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. If variability is a measure of reliability, can we
say that the new machine is more reliable than the old one?
5. 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 standard deviation of 3.069. 6 of a competitor’s shocks were tested
the same way, and a mean of 10.300 and a standard deviation 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?
6. 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. For Wallaby’s shocks the mean and
standard deviation were now 10.701 with a standard deviation of 3.051. For the competitor the mean was
now 10.422 with a standard deviation 3.043. What method can they now use to compare the average
strength of the shocks?
7. Assume that the situation is identical to problem 5 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?
8. A sample of ten customers are asked to rate their experience with two service firms on a scale of one to
ten. Scores are as follows.
Supervisor
Firm A
Firm B
1
4
7
2
5
6
3
9
6
4
5
7
5
4
5
6
9
8
7
5
4
8
7
6
9
3
5
10
3
6
If we assume that the distribution of results is Normal, what method should we use to see if there is a
difference between average ratings customers give to the firms?
9. Normally in a problem like problem 8, we should not assume an underlying Normal distribution. What
method would we use if we do not assume that the underlying distribution was Normal?
10. 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. Assume
that the severity of the spill is measured by the number of gallons spilled. What method should we use?
11. 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.
12. 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
2
252grass3-08 3/7/08 (Revised) (Open this document in 'Page Layout' view!)
than workers in the first group. Average unemployment rates are computed and variances of employment
rates between communities of each type seem similar.
Part 2: Do problems 1 and 2 in part 1 using a 95% confidence level. Find p-values.
Part 3: (Extra Credit) Invent and solve 4 problems. One each for methods D1 thru D4. Suggestion: Invent
just one problem but change the assumptions so that different methods are needed.
3