Chapter 9
Hypothesis Tests
Case Problem 1: Quality Associates, Inc.
1. The hypothesis testing results are shown below:
Sample 1
Sample 2
Sample 3
Sample 4
Sample Size
30
30
30
30
Mean
11.959
12.029
11.889
12.081
Standard Deviation
0.220
0.220
0.207
0.206
Level of Significance (alpha)
0.010
0.010
0.010
0.010
Critical Value (lower tail)
-2.576
-2.576
-2.576
-2.576
Critical Value (upper tail)
2.576
2.576
2.576
2.576
Hypothesized value
12
12
12
12
Standard Error
0.040
0.040
0.038
0.038
Test Statistic
-1.027
0.713
-2.935
2.161
p-value
0.304
0.476
0.003
0.031
Only sample 3 leads to the rejection of the hypothesis H0: µ = 12. Thus, corrective action is
2. The sample standard deviations for all four samples are in the .20 to .22 range. It appears that the
process population standard deviation assumption of .21 is good.
3. With = .01, z.005 = 2.576. Using the standard error of the mean
xn=/
=0.0383, the upper
and lower control limits are computed as follows:
Upper Control Limit = 12 + 2.576 (0.0383) = 12.0987
4. Increasing the level of significance will cause the null hypothesis to be rejected more often. While
this may mean quicker corrective action when the process is out of control, it also means that there
will be a higher error probability of stopping the process and attempting corrective action when the
Case Problem 2: Ethical Behavior of Business Students at Bayview University
1. The following questions were used to obtain data regarding three types of cheating:
During your time at Bayview, did you ever present work copied off the internet as your own?
During your time at Bayview, did you ever copy answers off another student’s exam?
During your time at Bayview, did you ever collaborate with other students on projects that were
supposed to be completed individually?
Using the data provided we can compute the proportion of all students, male students, and female
But, to estimate the percentage of students that have engaged in some form of cheating, we need to
count how many students answered yes to one or more of the above questions. One of the easiest
ways is to do this is to add another column to the data set whose cell values will be “No” if the
student answered no to each of the above questions and “Yes” if the student answered yes to one or
more of the questions. There are a number of ways to obtain the values in this new column. One of
All Business Students
Copied
from Internet
Percent
Copied
on Exam
Count
Percent
No
82.22
No
72
80.00
Yes
17.78
Yes
18
20.00
n
N
90
Collaborated
on Individual
Project
Percent
Cheated
Count
Percent
No
67.78
No
53
58.89
Yes
32.22
Yes
37
41.11
n
N
90
These results show that 16 of the 90 business students (17.78%) presented work copied off the
Male Students
Copied
from Internet
Percent
Copied
on Exam
Count
Percent
No
85.42
No
39
81.25
Yes
14.58
Yes
9
18.75
n
N
48
Collaborated
on Individual
Project
Percent
Cheated
Count
Percent
No
62.50
No
27
56.25
Yes
37.50
Yes
21
43.75
n
N
48
For the 48 male students, 14.58% presented work copied off the internet as their own; 18.75%
copied answers off another student’s exam; and 37.50% collaborated with other students on projects
Female Students
Copied
from Internet
Percent
Copied
on Exam
Count
Percent
No
78.57
No
33
78.57
Yes
21.43
Yes
9
21.43
n
N
42
Collaborated
on Individual
Project
Percent
Cheated
Count
Percent
No
73.81
No
26
61.90
Yes
26.19
Yes
16
38.10
n
N
42
For the 42 female students, 21.43% presented work copied off the internet as their own; 21.43%
copied answers off another student’s exam; and 26.19% collaborated with other students on projects
Additional Comments
• The proportion of students involved in some type of cheating is higher for male students
(.4375) than for female students (.3810).
• The most common form of cheating involved collaborating on projects that were supposed
2. 95% confidence intervals for the proportion of students that were involved in some type of cheating
follow.
All Business Students
.4111p=
Margin of error =
.025
(1 ) .4111(1 .4111)
1.96 .1017
90
pp
zn
−−
==
95% Confidence interval: .4111
.1017 or .3094 to .5128
.4375p=
.3810p=
Margin of error =
.025
(1 ) .3810(1 .3810)
1.96 .1469
42
pp
zn
−−
==
95% Confidence interval: .3810
.1469 or .2341 to .5279
3. The Chronicle of Higher Education reported that the proportion of business students who admitted
to some form of cheating was .56. Since we are interested in testing to see if the population
proportion of business students at Bayview who admitted to some form of cheating is less than
business students at other universities, we are looking for evidence that p, the population proportion,
is less than .56. Thus, the appropriate hypothesis test is
0: .56
: .56
a
Hp
Hp
We will use α = .05.
.4111p=
and
00
(1 ) .56(1 .56) .0523
90
p
pp
n
−−
= = =
admitted to some form of cheating was .47. Since we are interested in testing to see if the population
proportion of business students at Bayview who admitted to some form of cheating is less than non-
business students at other universities, we are looking for evidence that p, the population proportion,
is less than .47. Thus, the appropriate hypothesis test is
0: .47
: .47
a
Hp
Hp
We will use α = .05.
.4111p=
and
00
(1 ) .47(1 .47) .0526
90
p
pp
n
−−
= = =
type of cheating is much less than the proportion for business students at other universities.
Nonetheless, the fact that approximately 41% of all Bayview business students are involved in some
type of cheating still indicates a serious problem for the college. The dean needs to take additional
steps to deal with the problem of cheating in the college. Possible steps the dean might consider
include the following:
• Form a committee of students and faculty to investigate how students and faculty can work
together to reduce the extent of cheating.
• Require course outlines to include a statement regarding the expectations of the instructor
regarding cheating incidents and how they will be dealt with.
• Sponsor seminars where business executives can talk about the importance of ethical