252grass3-061 10/27/06 (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.
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   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: 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
:



H
:




0
2
2
 1 1
 1 1
H 1 : D  0
here is that the data are in before and after pairs, so you use Method D4.
1. West Chester University plays 11 football games a year. Though it is a questionable practice, these 11
games can be regarded as a random sample taken from an infinite number of games that they might have
played. Statistics can be computed from them like proportion of games won or the mean and standard
deviation of touchdowns or completed passes per game. At Christmas 2007, you look at these statistics and
assert that the team did significantly better in 2007 than it did in 2006.
a. The statistic you wish to use is completed passes. If x1 is a column listing the number of passes
completed in each game in 2006 in random order and x 2 is a column listing the number of passes
completed in each game in 2007 in random order and you consider these as independent random samples
and wish to compare the mean passes completed per game and to get results that verify your statement, what
are your hypotheses? What is your method?
b. Your roommate, Gigglebutz, says that you have done this all wrong, because the distributions
have not been shown to be Normal. You do the test described in section 6.3 of the text and sadly agree with
Gigglebutz that the distributions are probably not Normal. What is your test and method now?
c. Gigglebutz is still not satisfied and points out that these are not independent random samples and
what you should do is rearrange all your data so that each column represents a year and each row an
opponent. Any school that was not played in both years should be dropped from your data. What is your test
and method now?
2. Standard deviation is often a measure of reliability. A manufacturer is providing a connector and is
getting complaints that the connector is often too large or too small for the intended use. A sample of 250
connectors produced by the process in current use is taken. Then a new process is tried and a sample of 45
connectors is taken. Find the hypotheses and method to show that the new process produces a more reliable
product.
3. (Dummeldinger pg 148) We are interested in attitudes about sexual discrimination. Various groups were
asked if they believed sexual discrimination is a problem in the United States.   .05 
a. Out of 50 men 11 believed that sexual discrimination is a problem. Out of 40 women 19 said
that sexual discrimination is a problem. Is there a significant difference between male and female attitudes?
b. A group of 100 men are picked from upper levels of a group of large American firms. They are
asked if sexual discrimination is a problem in the United States. 38 said ‘yes.’ They are then sent to a
program on mentoring female executives where they discuss, among other things, what problems seem to be
peculiar to young female executives. Afterwards the men are asked the same question. This time 41 said
‘yes.’ Assuming that these 100 men are representative of all exectutives who are trained to mentor female
executioves, has the training increased the proportion that believe there is a problem?
c. Random samples (each 100 people) of male 1) high school gradutes, 2) college graduates and 3)
peple with MBAs are asked the same question. Out of the first group 35 said ‘yes.’ Out of the second group
38 said ‘yes.’ Out of the third group 39 said ‘yes.’ Is there a significant difference between the attitudes of
the three groups.
Extra credit: (Place answers at the end of the assignment)
d. You have enough information to do two of the three problems above. What
additional information do you need?
e. Do one of the three problems. State your conclusion clearly.
2
4. (Dummeldinger) A researcher a random sample of n graduates of MBA programs, which included
n1 women and n 2 men. Their starting salaries were recorded. Use 1 and/or  1 for population parameters
for women and  2 and/or  2 for women. Choose hypotheses and methods for the following.   .10 
a. n1  n 2  150 . The researcher wants to show that men have a higher mean starting salary than
women.
b. n1  18 and n2  12 . The researcher wants to compare the dispersion of men’s and women’s
salaries. The researcher has no prior opinion as to which is more variable.
c. n1  18 and n2  12 and the null hypothesis in 4b) has not been rejected. Dummeldinger gives
the following data.
x1  48266 .70
and
x 2  55000 .0
. The researcher wants to show that men have a
s1  13577 .63
s 2  11741 .25
higher mean starting salary than women.
Extra credit: (Place answers at the end of the assignment)
d. Do problem 4c. (Hint: before you start move the decimal point so that the sample
means and standard deviations are in thousands.) State your conclusion clearly.
5. (Dummeldinger) In order to find the effect of membership in a fraternity or sorority on grades, 250
students who had joined fraternities of sororities were picked as a random sample.
a. GPA’s were recorded for each student for the semester before ( x1 column) and the semester
after they joined ( x 2 column). Mean GPAs were compared. Choose hypotheses and method.
b. Dummeldinger says that a 95% confidence interval for the difference between the means was
0.24 to 1.02. What is your conclusion?)
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