# AP-Statistics-Exam ```Statistics Assignment
Full-Length Practice Exam
Page 1 of 23
Multiple-Choice Section (90 minutes)
Choose the one best answer for each of the following questions.
It's important to stay within the time limit to see how you'd do under real test conditions. If
you can't finish all the questions in 90 minutes, go back later and do the problems you
weren't able to finish.
1. A five-number summary of a univariate data set is determined to be
[10, 15, 25, 45, 85]. These data are to be used to construct a (modified)
boxplot. Which of the following statements are true?
I.
The mean is probably greater than the median.
II. There is at least one outlier.
III. The data are skewed to the right.
A.
I only
B.
II only
C.
III only
D. I and III only
E.
I, II, and III
2. You have a rather strange die: Three faces are marked with the letter A, two
faces with the letter B, and one face with the letter C. You roll the die until you
get a B. What is the probability that the first B appears on the first or the
second roll?
A.
.333
B.
.704
C.
.556
D. .037
E.
.296
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Statistics Assignment
Full-Length Practice Exam
Page 2 of 23
3. You are going to construct a 95% confidence interval for the difference
between two independent sample means. There are 12 subjects in one sample
and 11 in the other. You think that the two populations have the same standard
deviation, and so decide to use a pooled estimator of the population variance.
How many degrees of freedom would you use for this t procedure?
A.
21
B.
23
C.
10
D. 12
E.
22
ˆ = 19.41 + .17 x . What is the
4. The regression line for this bivariate data set is y
residual for the point with an x-value of 68?
x
y
A.
30.97
B.
3.03
C.
34
56
28
45
25
68
34
49
30
58
32
63
36
66
23
62
29
D. –30.97
E.
–3.03
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Statistics Assignment
Full-Length Practice Exam
Page 3 of 23
5. Which of these distributions has the largest standard deviation? Assume that
the range is the same for each histogram shown here.
A.
B.
C.
D.
E.
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Statistics Assignment
Full-Length Practice Exam
Page 4 of 23
6. Randomization is important in experiments because:
A.
it makes treatment and control groups equal in size.
B.
it ensures that there are enough subjects in all treatment groups.
C.
D. it controls for any bias the experimenter may have.
E.
it helps ensure that treatment and control groups are as alike as possible.
7. You have a rather strange die: Three faces are marked with the letter A, two
faces with the letter B, and one face with the letter C. If you were to roll this
die, what is the probability that at least one of the first two rolls would be a B?
A.
5/9
B.
1/3
C.
1/9
D. 4/9
E.
7/9
8. You want to see if a coin is fair. You flip it 5 times and count the number of
heads. If H is the number of heads obtained in five flips of the coin, what is the
P-value of the test when H equals 4?
A.
5/32
B.
6/32
C.
7/32
D. 8/32
E.
9/32
9. You are going to construct a 99% t confidence interval for a population mean
based on a sample of size 22. What is the critical value of t (t*) you will use to
construct the interval?
A.
2.819
B.
2.845
C.
2.080
D. 2.831
E.
2.518
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Statistics Assignment
Full-Length Practice Exam
Page 5 of 23
10. Franny is told that the z-score for her SAT test score was 1.2 compared to all
twelfth-grade girls who took the test. Which of the following best describes
what this means?
A.
Only 1.2% of the twelfth-grade girls taking this test had scores higher than Franny.
B.
Franny's score is 1.2 points higher than the average score for all twelfth-grade girls
who took the SAT.
C.
Franny received 1,200 on the SAT.
D. Franny's score is 1.2 standard deviations above the mean of twelfth-grade girls who
took the SAT.
E.
Franny's score is 1.2 times greater than the average score for all twelfth-grade girls
who took the SAT.
11. A double-blind experimental design is:
A.
one in which neither the experimenter nor the subject are aware of which treatment
B.
one whose purpose is to standardize responses of the various treatment groups.
C.
one in which the subject is unaware of whether they are receiving the treatment or
not, but the researcher is aware.
D. one in which groups are matched on a specific set of criteria so as to eliminate any
obvious differences between the groups.
E.
another way to describe an experiment in which no placebo is used.
12. Sometimes t procedures are referred to as robust. Which of the following best
describes what this means?
A.
They are not affected by extreme values.
B.
They can be used in many different situations, unlike less robust measures.
C.
They are still useable even when the assumptions necessary for their use are
violated.
D. They do not require that samples be drawn from normal populations.
E.
They can be used even if the population standard deviation is unknown.
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Statistics Assignment
Full-Length Practice Exam
Page 6 of 23
13. A Statistics teacher decides to give A's only to students who score in the top
15% on the final exam. The scores are normally distributed with a mean of 78
and a standard deviation of 7 (this is also the population standard deviation).
To the nearest integer value, what is the lowest score a student could earn and
A.
79
B.
80
C.
82
D. 83
E.
85
14. From the data in this table, what is P(B | E)?
C
D
E
Total
A.
12/35
B.
12/55
C.
23/70
A
B
Total
23
15
12
50
32
15
23
70
55
30
35
120
D. 35/70
E.
23/35
15. Which of the following are true statements?
I.
An observational study differs from an experiment in that only experiments
have distinct groups upon which measurements are made.
II. A sample survey is one type of experiment.
III. Experiments, but not observational studies, can point to cause-and-effect
relationships.
A.
I only
B.
II only
C.
III only
D. II and III only
E.
I, II, and III
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Statistics Assignment
Full-Length Practice Exam
Page 7 of 23
16. Consider the following set of sample data: 21, 24, 25, 32, 35, 31, 29, 28. Which
of the following will give a 95% confidence interval for the mean of the
population from which this sample was drawn?
A.
28.125 &plusmn; 1.96 (4.61/ 8 )
B.
28.125 &plusmn; 2.365(4.31/ 8 )
C.
28.125 &plusmn; 2.306(4.61/ 8 )
D. 28.125 &plusmn; 2.365(4.61/ 8 )
E.
28.125 &plusmn; 2.306(4.31/ 8 )
17. Which of the following are necessary in order to use a normal approximation
to the sampling distribution of a sample proportion?
I.
The population from which the sample was drawn must be at least 10 times
larger than the sample.
II. The population from which the samples are drawn must be normal.
III. The sample must be a simple random sample from the population.
A.
I only
B.
II only
C.
III only
D. I and III only
E.
II and III only
18. What are the mean and median of the data presented in the table below?
Value
15
18
19
23
27
A.
21.7, 23
B.
21.7, 19
C.
21.7, 20
Relative
Frequency
.15
.10
.20
.25
.30
Cumulative
Frequency
.15
.25
.45
.70
1.00
D. 20.4, 23
E.
20.4, 19
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Statistics Assignment
Full-Length Practice Exam
Page 8 of 23
19. A population is strongly skewed to the left with a mean of 18 and a standard
deviation of 4. You draw samples of size 4 from this population and calculate
the mean of each sample. Which of the following shows the mean, standard
deviation, and shape of the sampling distribution of the sample mean?
A.
18; 4; skewed to the left
B.
18; 2; approximately normal according to the Central Limit Theorem
C.
18; 2; skewed to the right
D. 18; 2; skewed to the left
E.
18; 4; approximately normal according to the Central Limit Theorem.
20. What is the &quot;five-number summary&quot; of the data given in the table below?
Value
15
18
19
23
27
Relative
Frequency
.15
.10
.20
.25
.30
Cumulative
Frequency
.15
.25
.45
.70
1.00
A. 15-18-19-23-27
B. 15-18-19-23-23
C. 15-18-23-27-27
D. 15-18-18-23-27
E. 15-19-23-23-27
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Statistics Assignment
Full-Length Practice Exam
Page 9 of 23
21. Given the tree diagram shown here, what is P(A | E)?
C
A
B
D
E
.7
.3
.3
C
.1
D
E
A.
7/11
B.
3/4
C.
4/7
.4
.3
.5
.4
D. 3/10
E.
.21
22. Researchers conduct a study to determine whether an online statistics course
is superior to an in-class course in terms of success on the AP Exam. They
compare the scores of 150 students, 75 of whom took each type of course. The
online students did better, on average, so the researchers publish an article
recommending that students who want to do well on the AP Exam should
consider the online course rather than a course at their school. Which of the
following statements is true?
A.
The results of this study are meaningless because this was an observational study
and not an experiment.
B.
Self-selection is not a factor when comparing the performance of the two groups.
C.
This is an example of the placebo effect.
D. Though there is a relationship between the type of course and performance, this
study does not show that there is a cause-and-effect relationship.
E.
There is too much sampling error in this type of study to be able to make
conclusions.
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Statistics Assignment
Full-Length Practice Exam
Page 10 of 23
23. The table below gives (in seconds) the time required for six right-handed
people to complete a test of dexterity, first with their left hand, then with their
right. You want to perform a t test to see if there is a significant difference
between the times required for the left and right hands. The appropriate
number of degrees of freedom for this test is:
Alice
Bob
Carrie
Doug
Eleanor
Frank
A.
6
B.
12
C.
11
Left Hand
23
Right Hand
19
19
17
26
20
22
18
18
20
19
20
D. 10
E.
5
24. Two variables are related so that the slope of their regression line is 6, and so
that sy = 4.2 and s x = .35 . What is r, the correlation coefficient for the two
variables?
A.
1/12
B.
72
C.
.6
D. .5
E.
.54
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Statistics Assignment
Full-Length Practice Exam
Page 11 of 23
25. All 32 seniors at a High School took both the AP Exam in Statistics and the AP
Exam in Calculus. Their mean score on the Statistics exam was 2.57 with a
standard deviation of .7. Their mean score on the Calculus exam was 2.78 with
a standard deviation of .64. If we combine these tests into a single score, the
correct mean and standard deviation are:
A.
5.35; .7 +.64
B.
5.35,
.7 + .64
C.
5.35,
.72 + .642
D. 5.35, .72 + .642
E.
The mean is 5.35, but you cannot determine the standard deviation from this
information.
26. You want to research a new pill you hope will relieve the effects of arthritis in
persons over 50 years of age. You divide your volunteers into two groups: one
consisting of people aged 50-60 and one consisting of people over 60. You
further divide each of those groups by gender. The members of each of these
four groups are randomly assigned to treatment and control groups with the
treatment group receiving the new pill and the control group receiving the
placebo. The basic design of this study is:
A.
double-blind, blocked by age and gender.
B.
comparative randomized, blocked by age, gender, and type of medication.
C.
randomized and stratified.
D. completely randomized.
E.
comparative randomized, blocked by age and gender.
27. The final exam scores in freshman English at a large high school are normally
distributed with a mean of 84% and a standard deviation of 14. If 450 students
took the exam, approximately how many students scored between 70% and
80%?
A.
103
B.
125
C.
.2289
D. 99
E.
95
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Statistics Assignment
Full-Length Practice Exam
Page 12 of 23
28. You want to construct a 95% confidence interval for the proportion of patients
who will experience adverse reactions to a new medication. Because side
effects can be rather severe, you desire a margin of error of no more than .05.
You have no idea, prior to doing the research, of what the true proportion
might be. What is the minimum number of subjects you will need in your
study?
A.
384
B.
385
C.
19.6
D. 1537
E.
390
29. A binomial event is observed 50 times. The probability of the event being
successful is .3. Let X equal the count of successes of the event during the 50
trials. What are &micro; X and σ X ?
A.
15; 3.24
B.
.3; .15
C.
15; 10.5
D. .15; 3.24
E.
15; 3.87
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Statistics Assignment
Full-Length Practice Exam
Page 13 of 23
30. You want to obtain a simple random sample of size 30 of all students in the
junior class. Assume there are 150 boys and 150 girls in the class. Which of the
following methods will produce such a sample?
I.
Number the students from 1 to 300. Randomly select one of the first 10
students, then take every tenth student on the list after that.
II. Number the students from 1 to 300. Use a random number generator to
select 30 numbers from 1 to 300. Your sample consists of the students
whose names correspond to the generated numbers.
III. Number the boys from 1 to 150 and number the girls from 151 to 300.
Randomly select 15 boys by using a random number generator to pick 15
numbers from 1 to 150. Then select 15 girls by using a random number
generator to pick 15 numbers from 151 to 300.
A.
I only
B.
II only
C.
III only
D. II and III only
E.
I, II, and III
31. A study found that the hours students spend watching television and their
grade point averages (GPAs) have a correlation of r = –.71. Given this
information, which of the following statements is most accurate?
A.
About 71% of students' GPAs depend on hours spent watching television.
B.
About half of the variation in GPAs can be explained by hours spent watching
television.
C.
A student could improve his/her GPA by watching less television.
D. There is a cause-and-effect relationship between watching television and success in
school.
E.
For each decrease in one hour of television watching, there will be a corresponding
increase of .7 in a student's GPA.
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Statistics Assignment
Full-Length Practice Exam
Page 14 of 23
χ2
32. You conduct a
test for independence to see if political affiliation is related
to gender in a medium-sized Midwestern town. The test is based on data from a
survey asking respondents to indicate their preference for one of four political
2
parties. Your X value is 5.21. What P-value is associated with this value?
A.
.05 &lt; p &lt; .10
B.
p &gt; .25
C.
.15 &lt; p &lt; .20
D. .025 &lt; p &lt; .05
E.
.02 &lt; p &lt; .025
33. Two variables appear to be exponentially related. A researcher takes the
natural logarithm of each y-value and computes the equation for the regression
of ln y on x. The resulting equation is ln y = 2.35 + 4.48x. To the nearest
integer, what is the predicted value of y when x equals .65?
A.
5.262
B.
182,810
C.
172
D. 188
E.
193
34. You have a table of random single-digit numbers that has an equal number of
every digit from zero to nine. If you start at the first digit on the table and
begin moving to the right, what is the probability that you do not land on an
even number (2, 4, 6, or 8) until the fifth digit?
A.
.4
B.
.0768
C.
.05184
D. .01024
E.
.031104
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Statistics Assignment
Full-Length Practice Exam
Page 15 of 23
35. It is appropriate to use a matched pairs experimental design when:
A.
both treatment and control groups are similar.
B.
each subject is to receive both treatments.
C.
you need a special technique for establishing a control group.
D. a comparative randomized design is not feasible.
E.
you need a control for confounding variables.
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Statistics Assignment
Full-Length Practice Exam
Page 16 of 23
36. Use this computer output to determine r, the correlation coefficient between
Method 1 and Method 2.
Descriptive Statistics
Variable
METHOD 1
METHOD 2
Variable
METHOD 1
METHOD 2
N
12
12
Mean Median
64.42 66.50
63.25 63.50
Min
52.00
53.00
Max
74.00
73.00
Q1
57.25
55.75
TrMean
64.70
63.30
StDev
7.10
7.28
SEMean
2.05
2.10
Q3
70.25
69.75
Regression Analysis
The regression equation is
Predictor
Constant
METHOD 2
s = 6.892
A.
.241
B.
.380
C.
.058
Coef
40.98
0.3705
R-sq =
Stdev
18.17
0.2856
t-ratio
p
2.25 0.048
1.30 0.224
D. .145
E.
.027
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Statistics Assignment
Full-Length Practice Exam
Page 17 of 23
37. Which of the following gives a 99% confidence interval for the slope of the
regression line from this computer output?
Descriptive Statistics
Variable
METHOD 1
METHOD 2
Variable
METHOD 1
METHOD 2
N
12
12
Mean Median
64.42 66.50
63.25 63.50
Min
52.00
53.00
Max
74.00
73.00
Q1
57.25
55.75
TrMean
64.70
63.30
StDev
7.10
7.28
SEMean
2.05
2.10
Q3
70.25
69.75
Regression Analysis
The regression equation is
Predictor
Constant
METHOD 2
s = 6.892
Coef
40.98
0.3705
R-sq =
A.
40.98 &plusmn; 3.169(.286)
B.
.371 &plusmn; 3.055(.286)
C.
.371 &plusmn; 3.169(6.892)
Stdev
18.17
0.2856
t-ratio
p
2.25 0.048
1.30 0.224
D. .371 &plusmn; 3.055(40.98)
E.
.371 &plusmn; 3.169(.286)
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Statistics Assignment
Full-Length Practice Exam
Page 18 of 23
38. Look at the scatterplot pictured here. Regarding the point marked A, which of
these are true?
I. A is better described as an influential point rather than an outlier.
II. Removing A from the scatterplot would cause the correlation to increase.
III. Removing A from the scatterplot would cause the slope of the regression
line to decrease significantly.
A.
I only
B.
I and II only
C. II only
D.
II and III only
E.
III only
39. The IQs of students at a very prestigious technical university are normally
distributed with a mean of 124 and a standard deviation of 8. What is the
probability that a person selected at random from this population will have an
IQ below 100?
A.
.023
B.
.0013
C.
.005
D. .9987
E.
0
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Statistics Assignment
Full-Length Practice Exam
Page 19 of 23
40. A survey of 40 people finds that 22 prefer Sugar Crunchies breakfast cereal to
Honey Yummies. Another completely independent survey finds that 24 of 50
people surveyed prefer Sugar Crunchies to Honey Yummies. For a significance
test of the hypothesis H0 : p1 = p2 , where p1 is the proportion favoring Sugar
Crunchies from the first survey population, and p2 is the proportion from the
second survey population, what is the standard error of the difference between
the proportions?
A.
B.
1 &ouml;
&aelig; 22 &ouml;&aelig; 24 &ouml;&aelig; 1
+
&ccedil;
&divide;&ccedil;
&divide;&ccedil;
&divide;
&egrave; 40 &oslash;&egrave; 50 &oslash;&egrave; 40 50 &oslash;
23 &ouml;
22 &ouml; &aelig; 23 &ouml;&aelig;
&aelig; 22 &ouml;&aelig;
&divide;
&divide;&ccedil;1 −
&divide; &ccedil;
&divide;&ccedil;1 −
&ccedil;
50 &oslash;
40 &oslash; &egrave; 50 &oslash;&egrave;
&egrave; 40 &oslash;&egrave;
+
50
40
C.
1 &ouml;
&aelig; 46 &ouml;&aelig; 44 &ouml;&aelig; 1
+
&ccedil;
&divide;&ccedil;
&divide;&ccedil;
&divide;
&egrave; 90 &oslash;&egrave; 90 &oslash;&egrave; 40 50 &oslash;
D.
1 &ouml;
&aelig; 22 &ouml;&aelig; 24 &ouml;&aelig; 1
+
&ccedil;
&divide;&ccedil;
&divide;&ccedil;
&divide;
&egrave; 90 &oslash;&egrave; 90 &oslash;&egrave; 40 50 &oslash;
E.
23 &ouml;
22 &ouml; &aelig; 23 &ouml;&aelig;
&aelig; 22 &ouml;&aelig;
&divide;
&divide;&ccedil;1 −
&divide; &ccedil;
&divide;&ccedil;1 −
&ccedil;
50 &oslash;
40 &oslash; &egrave; 50 &oslash;&egrave;
&egrave; 40 &oslash;&egrave;
+
90
90
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Statistics Assignment
Full-Length Practice Exam
Page 20 of 23
Free-Response Section (90 minutes)
provided, then send your corrected work back to your instructor. You'll be scored on
whether you did the work, not on how many questions you answered correctly.
Questions 1-5 should take about 10-15 minutes each. Question 6 is an &quot;Investigative Task,&quot;
and should take about 20-30 minutes. You should do all you can in no more than 90
minutes.
It's important to stay within the time limit to see how you'd do under real test conditions.
Read over all the questions first, and do the questions you feel most confident about. Then
go back and do the questions you're less confident about. Stop at 90 minutes, and then use
If you can't finish all the questions in 90 minutes, go back later and do the problems you
weren't able to finish.
1. You draw samples of size n from the population of all pennies in circulation. The random
variable of interest is the mean age of the pennies in the sample (current year pennies
are considered to be zero years old). The distribution of ages of pennies (starting at 0) is
known to be skewed markedly to the right. That is, there are more recently minted
pennies than older pennies in the population. One scholar claims that the mean age of
all pennies in circulation is 7.4 years with a standard deviation of 3.3 years. Assume that
this scholar is correct. Discuss the mean, standard deviation, and shape of the sampling
distribution of sample means of the ages of pennies for each of the given sample sizes.
Where possible, give precise values.
A. n = 5
B. n = 15
C. n = 40
2. A sports car manufacturer paints its cars silver, white, black, and red in the following
proportions:
Color:
Proportion:
Silver
.2
White
.3
Black
.1
Red
.4
We know that 40% of these cars are manufactured with tan leather upholstery while the
remaining 60% are manufactured with gray leather.
A. Assuming that the choice of exterior color and leather color are independent,
what is the probability that a randomly selected sports car from this
manufacturer will be white with gray upholstery?
B. Assuming that we know the car has tan upholstery, what is the probability that
the car is either silver or white?
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Statistics Assignment
Full-Length Practice Exam
Page 21 of 23
3. You are interested in conducting a survey at your school to determine if gender or
ethnicity is related to perceptions about educational opportunity. The school has 1,800
students but you only have resources to interview 100. The student body is
approximately equally divided between males and females. Twelve percent of the
school's population is Asian American, 8% is African American, 10% is Native American,
and 70% is Caucasian. You are interested in being able to generalize the results of your
survey to the entire student body.
A. Describe a technique for obtaining a sample of size 100 that would have a
reasonable chance of producing results that could be generalized to the entire
school.
B. Suppose you sent the surveys out to classes and asked the students to
complete them and return them to the main office. Would the returns be likely
to be biased in any direction? If so, why? In what direction?
C. Suppose you decide to conduct the survey by personal interview. Members of
the student council, all of whom happen to be Caucasian, will conduct personal
interviews with the selected students. One of the survey questions reads, &quot;Do
you agree or disagree with the following statement: All students, regardless of
ethnicity, have equal opportunity to become part of student government.&quot;
What potential bias is present in this question?
4. The following table gives the inflation rate and the corresponding prime lending rate for
7 different years. The equation of the regression line is:
prime lending rate = 3.175 + .654(inflation rate).
Inflation
Rate (x)
3.3
6.2
11
9.1
5.8
6.5
7.6
Prime Lending
Rate (y)
5.2
8
10.8
7.9
6.8
6.9
9
A. What is the predicted prime lending rate when the inflation rate stands at 6%?
B. What is the value of the residual when the inflation rate is 5.8%?
C. Interpret the slope of the regression line for this situation.
D. An eager economist uses these data to predict that the prime lending rate
would be 16.26 if the inflation rate rose to 20%. Comment on this prediction.
_____________
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Statistics Assignment
Full-Length Practice Exam
Page 22 of 23
5. The Director of Student Activities is concerned that she has not hired enough security for
the Sadie Hawkins Day dance, and wants to know approximately how many students will
be attending. If more than 25% of the student body is planning on going to the dance,
she will need to hire more security. She sends out a survey to 300 students, and out of
the 285 who respond, 82 say they plan to attend.
A. On the basis of this survey, should the Director of Student Activities hire more
security? Use appropriate statistical evidence to support your conclusion.
B. There were 15 people who didn't return their surveys. Suppose they had. Is it
possible that the Student Activities Director's decision would have been
different?
6. Suppose you have a friend on the school basketball team but, unfortunately, he is not a
good free throw shooter. Over the course of his career, he has only made 40% of his
shots. Otherwise, he is a good player and gets fouled a lot so he shoots 10 free throws a
game, on average. In the biggest game of the season, he does very well and makes 6
out of 10 free throw attempts.
A. Assuming that each shot is independent, set up the expression you would use
to determine the exact probability that your friend actually makes 6 or more
free throws in a given game.
B. Using the set of random numbers shown here, explain how you would set up a
simulation to determine the probability of making 6 or more free throws out of
10 attempts if your probability of making any one free throw is .4.
98713
51623
21826
41970
04853
19464
65847
94930
19537
00796
57512
53436
96270
18910
78602
49898
08320
97988
17433
54962
84837
45677
37221
36753
42771
52245
46304
07174
41545
39128
38816
71946
51855
01058
96541
62042
17871
00969
47896
47221
76406
88983
24384
75215
39264
89744
25948
98095
35996
05585
C. Suppose you wanted to do a normal approximation to the binomial for this
situation. What are the mean and standard deviation of the binomial
distribution? Is the normal approximation justified in this situation? Explain
why or why not? Would the normal approximation be justified if n = 100?
D. One of your friend's attempts during a game is a &quot;one-and-one.&quot; That is, if he
makes one free throw, he is given the opportunity to take a second shot.
Assuming each shot is independent, is he most likely to make 0, 1, or 2 points
on a &quot;one-and-one&quot; opportunity.
E. What is the probability that the first free throw he makes is his fourth attempt?
_____________
registered users only. No portion of these materials may be reproduced or redistributed in any form without the
express written permission of Apex Learning Inc.
Statistics Assignment
Full-Length Practice Exam
Page 23 of 23
TI-83 screens are used with the permission of the publisher. Copyright &atilde; 1996, Texas
Instruments, Incorporated.
MINITAB is a trademark of Minitab, Inc., and is used herein with the owner's permission.
Portions of MINITAB Statistical Software input and output contained in this course are
printed with permission of Minitab, Inc.
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