252grass3-071 3/08/07 (Open this document in 'Page Layout' view!)
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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. Method E1 is a
chi-squared test that compares multiple proportions. Method F1 is analysis of variance (ANOVA), which
compares multiple means. If the hypotheses involve two means, state the hypotheses in terms of both 
and D  1   2 . If the hypotheses involve two proportions, state them in terms of both p and
p  p1  p 2 . If the hypotheses involve two 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 that Problem D8 is a similar assignment to that below.
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.
----------------------------------------------------------------------------------------------------------------------------Example: This may seem long but it appears on a previous graded assignment 3.
A group of supervisors are given 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?” What are our hypotheses?
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.
In most of these problems you have to define what you mean by group or sample one and group 2. For
example in problem 3 you will probably let x1 be earnings of corporate lawyers and x 2 be the earnings of
private practice lawyers.
1. You have profit rates, x1 , for a sample of the European operations of 20 pharmaceutical firms. You also
have profit rates, x 2 , for the American operations of the same 20 firms. You believe that they are normally
distributed and you wish to see whether the European firms were more profitable than the American firms.
2. You have a sample of 15 US cities, with a typical salary for a corporate lawyer and a typical salary for a
lawyer in private practice. You wish to compare the earnings of the two types of lawyers. You do not
believe that the underlying distribution is Normal.
3. You have a sample of the earnings of 43 randomly chosen corporate lawyers and another independent
sample of salaries of 43 lawyers in private practice. You wish to show that the average corporate lawyer
makes more than the average lawyer in private practice. You believe that the parent (underlying)
distribution is normal and you think that you know the population variances for each group.
4. You find out that you were wrong about the variances in problem 3 and have to recompute the variances
of the salaries for each of the two groups in Problem 3 from the samples that you had gathered. First you
wish to compare the reliability of earnings for the two groups.
5. Your null hypothesis in Problem 4 was rejected and you, once again, are trying to show that corporate
lawyers make more than lawyers in private practice.
6. Royal Crown Cola recruits a panel of 115 men and 56 women. The entire group is polled to see if they
like the current formulation of Royal Crown better than Coca Cola. Then they are asked to compare a new
formulation of Royal Crown against Coca Cola. Our data consists of the number of each panel member and
whether 1) each member liked Royal Crow better than Coke originally and 2) whether each member liked
Royal Crown Better than Coke with the new formulation for Royal Crown. Has the new formulation
improved the sales prospects of Royal Crown?
7. Using the panel above and only the new formulation, the numbers of men and women who preferred
Royal Crown is tabulated separately and the data is examined to see if gender plays a role in preferences.
8. In addition to the 115 men and the 56 women, the Royal Crown people find 45 monsters to tell them
whether they prefer the new formulation of RC to Coke. We wish to compare the preferences of the three
groups.
9. A group of 25 male accountants with working wives was asked to rate their job satisfaction on a 1 to 10
scale. Another group of 20 male accountants whose wives do not work were also asked to rate their
satisfaction. We want to test whether the satisfaction of accountants with working wives is below that of
those whose wives do not work and do not want to use a method that assumes an underlying Normal
distribution.
Part 2. Do problems 6 and 7 using the following data.
Men
Women
Liked 1st, liked 2nd
12
8
Liked 1st, didn’t
3
3
like 2nd
Didn’t like 1st ,
5
3
liked 2nd
Didn’t like 1st ,
95
42
didn’t like 2nd
Total
115
56
Part 3. (Extra Credit) Invent and solve 4 problems. One each for methods D1 thru D4.
2