AP STATISTICS EXAM REVIEW by DAVID CUSTER (click on topic of choice)

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AP STATISTICSEXAM REVIEWby DAVID CUSTER(click
on topic of choice)
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• TOPIC I
• Describing Data
• (15 questions)

TOPIC II Experimental Design (15 questions)
TOPIC III Probability (18 questions)
TOPIC IV Inference (15 questions)
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TOPIC I Describing Data
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• Univariate Data
• Normal Distributions
• Bivariate Data

START TOPIC
Topic I Topic I Topic I Topic I
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Which observation has the higher z-score?I.
x25.4 µ 12.9 s3.7II. x25.4 µ15.3 s2.7
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I.1.

1. I
2. II
3. z-scores are equal
4. cannot be determined since we dont know the
   standard deviations of the populations
5. cannot be determined since we dont know if the
   populations are normal

Topic I Menu
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Which observation has the higher z-score? I.
x25.4 µ 12.9 s3.7II. x25.4 µ15.3 s2.7
SOLUTION
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I.1.
The z-score for I is 3.38 the z-score for II is
3.74

1. I
2. II
3. z-scores are equal
4. cannot be determined since we dont know the
   standard deviations of the populations
5. cannot be determined since we dont know if the
   populations are normal

Topic I Menu
5
The Quartile and Percentile positions of the
value 10 in the set 10, 6, 8, 9, 12, 17, 32,
16are
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I.2.

1. Q3 38
2. Q2 38
3. Q2 26
4. Q3 26
5. none of these

Topic I Menu
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The Quartile and Percentile positions of the
value 10 in the set 10, 6, 8, 9, 12, 17, 32,
16are
SOLUTION
0
I.2.
When the values are in order, there are 3 values
below 10. This puts 10 in the 37.5 percentile
and the 2nd quartile.

1. Q3 38
2. Q2 38
3. Q2 26
4. Q3 26
5. none of these

Topic I Menu
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The Standard Deviation of the set 5, 7, 7, 8,
10, 11 is 2. Which of the following sets also
has a Standard Deviation of 2?
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I.3.

1. 4, 5, 8, 12, 14
2. 2, 4, 6, 8, 10, 12
3. 3, 5, 5, 6, 8, 9
4. 10, 14, 14, 16, 20, 22
5. none of the above

Topic I Menu
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The Standard Deviation of the set 5, 7, 7, 8,
10, 11 is 2. Which of the following sets also
has a Standard Deviation of 2?
SOLUTION
0
I.3.
There is a uniform decrease of 2 units in this
set. The st. deviation must be the same.

1. 4, 5, 8, 12, 14
2. 2, 4, 6, 8, 10, 12
3. 3, 5, 5, 6, 8, 9
4. 10, 14, 14, 16, 20, 22
5. none of the above

Topic I Menu
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If 12 of the values of a data set lie between a
and b and d is added to each value, then which of
the following is true?
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I.4.

1. 12 still lies between a and b
2. 12 lies between a d and b d
3. (12d) lies between a and b
4. (12d) lies between a d and b d
5. there is no way to tell how much data is between
   a and b

Topic I Menu
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If 12 of the values of a data set lie between a
and b and d is added to each value, then which of
the following is true?
SOLUTION
0
I.4.
A uniform shift of all the data maintains the
percentages of data in shifted intervals.

1. 12 still lies between a and b
2. 12 lies between a d and b d
3. (12d) lies between a and b
4. (12d) lies between a d and b d
5. there is no way to tell how much data is between
   a and b

Topic I Menu
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If a distribution is relatively symmetric and
mount-shaped, order the following (from least to
greatest) 1. a z-score of 1 2. the value
of Q3 3. a value in the 70th percentile
I.5.

1. 1, 2, 3
2. 1, 3, 2
3. 3, 2, 1
4. 3, 1, 2
5. 2, 3, 1

Topic I Menu
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If a distribution is relatively symmetric and
mount-shaped, order the following (from least to
greatest) 1. a z-score of 1 2. the value
of Q3 3. a value in the 70th percentile
SOLUTION
0
I.5.

1. 1, 2, 3
2. 1, 3, 2
3. 3, 2, 1
4. 3, 1, 2
5. 2, 3, 1

The percentile of a z-score of 1 is about 84,
and the percentile of Q3 is 75
Topic I Menu
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Which of the following would NOT be a correct
interpretation of a correlation coefficient of r
-.30
0
I.6.

1. The variables are inversely related
2. The coefficient of determination is 0.09
3. 30 of the variation between the variables is
   linear
4. There exists a weak relationship between the
   variables
5. All are correct

Topic I Menu
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Which of the following would NOT be a correct
interpretation of a correlation coefficient of r
-.30
SOLUTION
0
I.6.
The value of r2 explains the variation between
the variables. Not r.

1. The variables are inversely related
2. The coefficient of determination is 0.09
3. 30 of the variation between the variables is
   linear
4. There exists a weak relationship between the
   variables
5. All are correct

Topic I Menu
15
Which of the following displays is best suited
for categorical data?
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I.7.

1. Box Plot
2. Bar Graph
3. Stem and Leaf Plot
4. Dot Plot
5. Scatterplot

Topic I Menu
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Which of the following displays is best suited
for categorical data?
SOLUTION
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I.7.
In a bar graph, each column is separate, allowing
for categorical separation.

1. Box Plot
2. Bar Graph
3. Stem and Leaf Plot
4. Dot Plot
5. Scatterplot

Topic I Menu
17
Linear regression usually employs the method of
least squares. Which of the following is the
quantity that is minimized by the least squares
process?
0
I.8.

Topic I Menu
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Linear regression usually employs the method of
least squares. Which of the following is the
quantity that is minimized by the least squares
process?
SOLUTION
0
I.8.
Least Squares Regression minimizes the residuals
in the y-direction.

Topic I Menu
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Which of the following is NOT true?
0
I.9.

1. Two sets of data can have the same means but
   different variances
2. Two sets of data can have the same variance but
   different means
3. Two different values in a data set can have the
   same z-score
4. All the absolute values of z-scores for a data
   set can be equal
5. All of the above are true

Topic I Menu
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Which of the following is NOT true?
SOLUTION
0
I.9.
Since each value is a distinct distance from the
mean, the z-scores must all be different

1. Two sets of data can have the same means but
   different variances
2. Two sets of data can have the same variance but
   different means
3. Two different values in a data set can have the
   same z-score
4. All the absolute values of z-scores for a data
   set can be equal
5. All of the above are true

Topic I Menu
21
In a symmetric, mount-shaped distribution, what
percentile has a z-score of -2?
0
I.10.
Topic I Menu
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In a symmetric, mount-shaped distribution, what
percentile has a z-score of -2?
SOLUTION
0
I.10.
2.5th percentile
We should be able to approximate this with the
normal distribution. Area to the left of -2? On
the TI-83 Normalcdf(-1E99, -2) .02275
Topic I Menu
23
Lees z-score on his math test was 1.5. The
class average was a 62.1 and the variance was
6.76. What was Lees actual grade on the test?
0
I.11.

1. 60
2. 62
3. 64
4. 66
5. 68

Topic I Menu
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Lees z-score on his math test was 1.5. The
class average was a 62.1 and the variance was
6.76. What was Lees actual grade on the test?
SOLUTION
0
I.11.
We need to solve the following equation for
x so x66

1. 60
2. 62
3. 64
4. 66
5. 68

Topic I Menu
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Does the following problem have a unique
solution? If so, find it. If not, show at least
two answers5 numbers have Q112, Median15,
Q318. Find the mean.
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I.12.
Topic I Menu
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Does the following problem have a unique
solution? If so, find it. If not, show at least
two answers5 numbers have Q112, Median15,
Q318. Find the mean.
SOLUTION
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I.12.
11, 13, 15, 17, 19 µ15 9, 15, 15, 17, 19
µ15 the data sets are not unique, but the
mean is always 15!
YES!!! surprisingly!
Topic I Menu
27
The average grade on a math test given to two
sections is 60.98. Section I has 27 students
with a mean grade of 57.30. If the mean grade of
Section 2 is 65.30, how many students are in
section 2?
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I.13.
Topic I Menu
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The average grade on a math test given to two
sections is 60.98. Section I has 27 students
with a mean grade of 57.30. If the mean grade of
Section 2 is 65.30, how many students are in
section 2?
SOLUTION
0
I.13.
23 students. we arrive at n23
Topic I Menu
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If the mean of 75 values is 52.6 and the mean of
25 values is 48.4 find the mean of all 100
values.
0
I.14.

1. 51.55
2. 52.76
3. 56.55
4. 56.88
5. 59.12

Topic I Menu
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If the mean of 75 values is 52.6 and the mean of
25 values is 48.4 find the mean of all 100
values.
SOLUTION
0
I.14.

1. 51.55
2. 52.76
3. 56.55
4. 56.88
5. 59.12

75(52.6) 25(48.4) 100
Topic I Menu
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In skewed-right distributions, what is most
frequently the relationship of the mean, median,
and mode?
0
I.15.

1. mean gt median gt mode
2. median gt mean gt mode
3. mode gt median gt mean
4. mode gt mean gt median
5. mean gt mode gt median

Topic I Menu
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In skewed-right distributions, what is most
frequently the relationship of the mean, median,
and mode?
SOLUTION
0
I.15.
The median is resistant, the mean, not at all.
So a right skewed distribution will have a mean
much higher than median, much higher than mode.

1. mean gt median gt mode
2. median gt mean gt mode
3. mode gt median gt mean
4. mode gt mean gt median
5. mean gt mode gt median

Topic I Menu
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TOPIC II Experimental Design
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• Sampling
• Designing Experiments
• Observational Studies

START TOPIC
Topic II Topic II Topic II Topic II
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A personnel director studied the eating habits of
employees by watching a group of employees at
lunch. He wishes to see who buys in the
cafeteria, who brings a home lunch, and who goes
out.The study is categorized as
II.1.

1. a census
2. a survey sample
3. an observational study
4. a designed experiment
5. none of these

Topic II Menu
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A personnel director studied the eating habits of
employees by watching a group of employees at
lunch. He wishes to see who buys in the
cafeteria, who brings a home lunch, and who goes
out.The study is categorized as
SOLUTION
II.1.
The director is observing behavior, not
implementing treatments on the group

1. a census
2. a survey sample
3. an observational study
4. a designed experiment
5. none of these

Topic II Menu
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A personnel director studied the eating habits of
employees by watching a group of employees at
lunch. He wishes to see who buys in the
cafeteria, who brings a home lunch, and who goes
out.If the director only looks at those in one
department, she is performing
II.2.

1. a simple random sample
2. a quota sample
3. a convenience sample
4. a multi-stage cluster sample
5. a census

Topic II Menu
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A personnel director studied the eating habits of
employees by watching a group of employees at
lunch. He wishes to see who buys in the
cafeteria, who brings a home lunch, and who goes
out.If the director only looks at those in one
department, she is performing
SOLUTION
II.2.
Without a properly randomized selection, she is
introducing bias to the study.

1. a simple random sample
2. a quota sample
3. a convenience sample
4. a multi-stage cluster sample
5. a census

Topic II Menu
38
A personnel director studied the eating habits of
employees by watching a group of employees at
lunch. He wishes to see who buys in the
cafeteria, who brings a home lunch, and who goes
out.If the director selects 50 employees at
random and categorizes by gender, she is
II.3.

1. blocking for gender
2. testing for a lurking variable
3. promoting sexual harassment
4. testing for bias
5. none of these

Topic II Menu
39
A personnel director studied the eating habits of
employees by watching a group of employees at
lunch. He wishes to see who buys in the
cafeteria, who brings a home lunch, and who goes
out.If the director selects 50 employees at
random and categorizes by gender, she is
SOLUTION
II.3.

1. blocking for gender
2. testing for a lurking variable
3. promoting sexual harassment
4. testing for bias
5. none of these

She is investigating whether gender affects
lunchtime behavior
Topic II Menu
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Which of the following is NOT a concern in data
collection?
II.4.

1. lurking variables
2. blocking
3. bias
4. non-response
5. all of the above are concerns

Topic II Menu
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Which of the following is NOT a concern in data
collection?
SOLUTION
II.4.
Even blocking methods need to be analyzed

1. lurking variables
2. blocking
3. bias
4. non-response
5. all of the above are concerns

Topic II Menu
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Which of the following is NOT a valid sample
design?
II. 5.

1. Code every member of a population and select 100
   randomly chosen members
2. Divide a population by gender and select 50
   individuals randomly from each group
3. Select individuals randomly and place into gender
   groups until you have the same proportion as in
   the population
4. Select five homerooms at random from all the
   homerooms in a large high school.
5. All of these are valid

Topic II Menu
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Which of the following is NOT a valid sample
design?
SOLUTION
II. 5.
But you may be able to question the validity of
answer (C)

1. Code every member of a population and select 100
   randomly chosen members
2. Divide a population by gender and select 50
   individuals randomly from each group
3. Select individuals randomly and place into gender
   groups until you have the same proportion as in
   the population
4. Select five homerooms at random from all the
   homerooms in a large high school.
5. All of these are valid

Topic II Menu
44
An insurance company conducted a study to
determine the percent of cardiologists who had
been sued over the last 5 yrs.The variable of
interest is
II.6.

1. the doctors specialty, e.g. cardiology,
   obstetrics, etc.
2. the number of doctors who are cardiologists
3. all cardiologists in the American Medical
   Association directory
4. a random sample of 100 cardiologists
5. none of these

Topic II Menu
45
An insurance company conducted a study to
determine the percent of cardiologists who had
been sued over the last 5 yrs.The variable of
interest is
SOLUTION
II.6.

1. the doctors specialty, e.g. cardiology,
   obstetrics, etc.
2. the number of doctors who are cardiologists
3. all cardiologists in the American Medical
   Association directory
4. a random sample of 100 cardiologists
5. none of these

we are interested in the percentage of doctors
who have been sued
Topic II Menu
46
An insurance company conducted a study to
determine the percent of cardiologists who had
been sued over the last 5 yrs.The population of
interest is
II.7.

1. the set of all doctors who were sued for
   malpractice
2. the set of cardiologists who were sued for
   malpractice
3. all doctors
4. all cardiologists
5. all doctors who have malpractice insurance

Topic II Menu
47
An insurance company conducted a study to
determine the percent of cardiologists who had
been sued over the last 5 yrs.The population of
interest is
SOLUTION
II.7.

1. the set of all doctors who were sued for
   malpractice
2. the set of cardiologists who were sued for
   malpractice
3. all doctors
4. all cardiologists
5. all doctors who have malpractice insurance

Just cardiologists, not all doctors.
Topic II Menu
48
An insurance company conducted a study to
determine the percent of cardiologists who had
been sued over the last 5 yrs.Which could be
used to gather the data?
II.8.

1. a designed experiment
2. a census of all cardiologists
3. an observational study of randomly selected
   cardiologists
4. a survey sent to randomly selected cardiologists
5. any answer except (A)

Topic II Menu
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An insurance company conducted a study to
determine the percent of cardiologists who had
been sued over the last 5 yrs.Which could be
used to gather the data?
SOLUTION
II.8.
This population of this observational study is
too large to track everyone down.

1. a designed experiment
2. a census of all cardiologists
3. an observational study of randomly selected
   cardiologists
4. a survey sent to randomly selected cardiologists
5. any answer except (A)

Topic II Menu
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Which of the following is NOT a source of bias in
sample surveys?
II.9.

1. non-response
2. wording of questions
3. voluntary response
4. use of a telephone survey
5. all are sources of bias

Topic II Menu
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Which of the following is NOT a source of bias in
sample surveys?
SOLUTION
0
II.9.
and dont forget even a huge sample size cant
correct a poorly selected sample. Remember the
Literary Digest Poll!

1. non-response
2. wording of questions
3. voluntary response
4. use of a telephone survey
5. all are sources of bias

Topic II Menu
52
Which of the following is NOT a requirement of a
controlled experiment?
0
II.10.

1. control
2. comparison
3. replication
4. randomization
5. all of these are required

Topic II Menu
53
Which of the following is NOT a requirement of a
controlled experiment?
SOLUTION
0
II.10.

1. control
2. comparison
3. replication
4. randomization
5. all of these are required

Topic II Menu
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A randomized block design is NOT
0
II.11.

1. similar to a stratified random sample for surveys
2. a strategy to control for an influence that would
   affect the outcome of the experiment
3. a strategy that depends on randomization
4. only used for gender comparisons
5. all of these describe a randomized block design.

Topic II Menu
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A randomized block design is NOT
SOLUTION
0
II.11.
You can block with any categorical variables!

1. similar to a stratified random sample for surveys
2. a strategy to control for an influence that would
   affect the outcome of the experiment
3. a strategy that depends on randomization
4. only used for gender comparisons
5. all of these describe a randomized block design.

Topic II Menu
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A research team is comparing performance in AP
Statistics based on whether traditional or
activity-based instruction methods were used.
The final grades of 500 students will be
collected.The population of interest is
0
II.12.

1. the 500 students chosen
2. the students taught by activity-based statistics
3. the students taught by traditional methods
4. all students in high school.
5. none of these

Topic II Menu
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A research team is comparing performance in AP
Statistics based on whether traditional or
activity-based instruction methods were used.
The final grades of 500 students will be
collected.The population of interest is
SOLUTION
0
II.12.
We are interested in knowing about ALL AP
STATISTICS STUDENTS

1. the 500 students chosen
2. the students taught by activity-based statistics
3. the students taught by traditional methods
4. all students in high school.
5. none of these

Topic II Menu
58
A research team is comparing performance in AP
Statistics based on whether traditional or
activity-based instruction methods were used.
The final grades of 500 students will be
collected.An appropriate design for the study is
II.13.

1. a blocked design experiment
2. a stratified random sample
3. a completely randomized design
4. a simple random sample
5. none of these

Topic II Menu
59
A research team is comparing performance in AP
Statistics based on whether traditional or
activity-based instruction methods were used.
The final grades of 500 students will be
collected.An appropriate design for the study is
SOLUTION
II.13.
B or C. Either one is fine.

1. a blocked design experiment
2. a stratified random sample
3. a completely randomized design
4. a simple random sample
5. none of these

Topic II Menu
60
A survey is to be conducted in your school.
There is to be a total of 40 students in the
sample. Describe how you would choose the
participants ifthere are to be the same number
of freshmen, sophomores, juniors, and seniors in
the sample.
0
II.14.
Topic II Menu
61
A survey is to be conducted in your school.
There is to be a total of 40 students in the
sample. Describe how you would choose the
participants ifthere are to be the same number
of freshmen, sophomores, juniors, and seniors in
the sample.
SOLUTION
0
II.14.
Select a simple random sample of 10 from each
class.
Topic II Menu
62
II.15.
A survey is to be conducted in your school.
There is to be a total of 40 students in the
sample. Describe how you would choose the
participants ifthere are to be the same number
of males and females in the sample
Topic II Menu
63
SOLUTION
II.15.
A survey is to be conducted in your school.
There is to be a total of 40 students in the
sample. Describe how you would choose the
participants ifthere are to be the same number
of males and females in the sample
Select a simple random sample of 20 males and 20
females.
Topic II Menu
64
TOPIC III Probability
START TOPIC

• Random Variables
• Binomial Distributions
• Geometric Distributions
• Sampling Distributions

Topic III Topic III Topic III Topic III
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17 18
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65
If 3 people, Joe, Betsy, and Sue, play a game in
which Joe has a 25 chance of winning and Betsy
has a 40 chance of winning, what is the
probability that Sue will win?
III.1.

1. 25
2. 35
3. 40
4. 65
5. cannot be determined

Topic III Menu
66
If 3 people, Joe, Betsy, and Sue, play a game in
which Joe has a 25 chance of winning and Betsy
has a 40 chance of winning, what is the
probability that Sue will win?
SOLUTION
III.1.

1. 25
2. 35
3. 40
4. 65
5. cannot be determined

Assuming one winner, the probabilities must add
up to 100
Topic III Menu
67
A local law enforcement agency published the
following chart.The percentage of altercations
involving at least one teenager is
III.2.
Altercations Between Percent
Two teens 45
A teen and an adult 37
Two adults 18

1. 8
2. 37
3. 45
4. 55
5. 82

Topic III Menu
68
A local law enforcement agency published the
following chart.The percentage of altercations
involving at least one teenager is
SOLUTION
III.2.
p(two teens) p(teen and adult)
Altercations Between Percent
Two teens 45
A teen and an adult 37
Two adults 18

1. 8
2. 37
3. 45
4. 55
5. 82

Topic III Menu
69
What proportion of Republicans are over 50?
Democrat Republican Independ
18 30 25 18 12
31 40 32 21 10
41 50 17 25 17
over 50 14 32 15
III.3.

1. 61/238
2. 32/96
3. 96/238
4. 32/61
5. cannot be determined

Topic III Menu
70
What proportion of Republicans are over 50?
SOLUTION
Democrat Republican Independ
18 30 25 18 12
31 40 32 21 10
41 50 17 25 17
over 50 14 32 15
III.3.

1. 61/238
2. 32/96
3. 96/238
4. 32/61
5. cannot be determined

There are 96 Republicans of whom 32 are over age
50
Topic III Menu
71
If one person is chosen at random, what is the
probability he is a Democrat between 41 and 50
years old?
Democrat Republican Independ
18 30 25 18 12
31 40 32 21 10
41 50 17 25 17
over 50 14 32 15
III.4.

1. 17/238
2. 17/88
3. 61/238
4. 17/61
5. 88/238

Topic III Menu
72
If one person is chosen at random, what is the
probability he is a Democrat between 41 and 50
years old?
SOLUTION
Democrat Republican Independ
18 30 25 18 12
31 40 32 21 10
41 50 17 25 17
over 50 14 32 15
III.4.
Total of adults is 238. 17 are democrats
between 41 and 50

1. 17/238
2. 17/88
3. 61/238
4. 17/61
5. 88/238

Topic III Menu
73
Given that a person chosen is between 31 and 40,
what is the probability the person is an
Independent?
Democrat Republican Independ
18 30 25 18 12
31 40 32 21 10
41 50 17 25 17
over 50 14 32 15
III.5.

1. 10/238
2. 10/63
3. 10/54
4. 54/238
5. 63/238

Topic III Menu
74
Given that a person chosen is between 31 and 40,
what is the probability the person is an
Independent?
SOLUTION
Democrat Republican Independ
18 30 25 18 12
31 40 32 21 10
41 50 17 25 17
over 50 14 32 15
III.5.

1. 10/238
2. 10/63
3. 10/54
4. 54/238
5. 63/238

There are 63 people between 31 and 40 of whom 10
are Independent.
Topic III Menu
75
What proportion of the citizens sampled are over
50 OR Independent?
Democrat Republican Independ
18 30 25 18 12
31 40 32 21 10
41 50 17 25 17
over 50 14 32 15
III.6.

1. 54/238
2. 61/238
3. 100/238
4. 115/238
5. cannot be determined

Topic III Menu
76
What proportion of the citizens sampled are over
50 OR Independent?
SOLUTION
Democrat Republican Independ
18 30 25 18 12
31 40 32 21 10
41 50 17 25 17
over 50 14 32 15
III.6.
61/238 54/238 15/238 15 adults are in both
categories

1. 54/238
2. 61/238
3. 100/238
4. 115/238
5. cannot be determined

Topic III Menu
77
If P(A)0.4, P(B)0.2, and P(A and B) 0.08Which
is true?
III.7.

1. Events A and B are independent and mutually
   exclusive
2. Events A and B are independent but not mutually
   exclusive
3. Events A and B are mutually exclusive but not
   independent
4. Events A and B are neither independent nor
   mutually exclusive
5. Events A and B are independent but whether they
   are mutually exclusive cannot be determined.

Topic III Menu
78
If P(A)0.4, P(B)0.2, and P(A and B) 0.08Which
is true?
SOLUTION
III.7.

1. Events A and B are independent and mutually
   exclusive
2. Events A and B are independent but not mutually
   exclusive
3. Events A and B are mutually exclusive but not
   independent
4. Events A and B are neither independent nor
   mutually exclusive
5. Events A and B are independent but whether they
   are mutually exclusive cannot be determined.

--Since P(A and B) is non-zero, they are not
mutually exclusive. --Since P(A and B) does not
equal P(A)P(B), the events are independentthey
just happen in sequence
Topic III Menu
79
What is the probability that a family with 6
children will have 3 boys and 3 girls?
III.8.

• POSSIBLE NAME OF DISTRIBUTION?
• Binomial Model
• Geometric Model
• Uniform Model
• Normal Model

Topic III Menu
80
What is the probability that a family with 6
children will have 3 boys and 3 girls?
SOLUTION
III.8.
This is a binomial distribution n6 p0.5 6C3
(0.5)3 (0.5)3 0.3125 x3

• POSSIBLE NAME OF DISTRIBUTION?
• Binomial Model
• Geometric Model
• Uniform Model
• Normal Model

Topic III Menu
81
What is the probability that a person is over 6
feet tall if the mean height of her age group is
56 and a standard deviation of 10?
III.9.

• POSSIBLE NAME OF DISTRIBUTION?
• Binomial Model
• Geometric Model
• Uniform Model
• Normal Model

Topic III Menu
82
What is the probability that a person is over 6
feet tall if the mean height of her age group is
56 and a standard deviation of 10?
SOLUTION
III.9.
This is a normal distribution normalcdf(6,
1E99, 56/12, 10/12) 0.2743

• POSSIBLE NAME OF DISTRIBUTION?
• Binomial Model
• Geometric Model
• Uniform Model
• Normal Model

Topic III Menu
83
What is the probability that a shipment of 100
fruit will have no more than 6 rotten fruits if
the probability that any one fruit is rotten is
0.04?
III.10.

• POSSIBLE NAME OF DISTRIBUTION?
• Binomial Model
• Geometric Model
• Uniform Model
• Normal Model

Topic III Menu
84
What is the probability that a shipment of 100
fruit will have no more than 6 rotten fruits if
the probability that any one fruit is rotten is
0.04?
SOLUTION
III.10.
This is a binomial distribution binomcdf(100,
0.04, 6) 0.8936
Did you think to use the normal approximation? µ
np 4 svp(1p)/n .0196 normalcdf(-1E99,
6, 4, .0196) 1.00 How come
that didnt work?

• POSSIBLE NAME OF DISTRIBUTION?
• Binomial Model
• Geometric Model
• Uniform Model
• Normal Model

Topic III Menu
85
What is the probability that the first base hit
will occur during the fourth at-bat if the
probability that the hitter gets a base hit is
0.27 for any at-bat?
III.11.

• POSSIBLE NAME OF DISTRIBUTION?
• Binomial Model
• Geometric Model
• Uniform Model
• Normal Model

Topic III Menu
86
What is the probability that the first base hit
will occur during the fourth at-bat if the
probability that the hitter gets a base hit is
0.27 for any at-bat?
SOLUTION
III.11.
This is a geometric (waiting time)
distribution n??? (there isnt one! Thats
why its Geometric!) p0.27 x4
geometpdf(0.27, 4) (.73)(.73)(.73)(.27)
0.7160

• POSSIBLE NAME OF DISTRIBUTION?
• Binomial Model
• Geometric Model
• Uniform Model
• Normal Model

Topic III Menu
87
Suppose a basketball player scores 70 of her
free throws. Assume each shot is independent and
the probability is the same on each trial.
Find the probability she scores on 3 of her
next 5 attempts
III.12.
Topic III Menu
88
Suppose a basketball player scores 70 of her
free throws. Assume each shot is independent and
the probability is the same on each trial.
Find the probability she scores on 3 of her
next 5 attempts
SOLUTION
III.12.
This is a binomial distribution n5 p0.70 5C3
(0.7)3 (0.3)2 0.3087 x3
Topic III Menu
89
Suppose a basketball player scores 70 of her
free throws. Assume each shot is independent and
the probability is the same on each trial.
Find the probability that the first time she
scores is on her 3rd attempt
III.13.
Topic III Menu
90
Suppose a basketball player scores 70 of her
free throws. Assume each shot is independent and
the probability is the same on each trial.
Find the probability that the first time she
scores is on her 3rd attempt
SOLUTION
III.13.
This is a geometric distribution n??? (we wait
til a successtheres no n!) p0.70
x3 geometpdf(0.7, 3) (.3)(.3)(.7)
0.063
Topic III Menu
91
The Central Limit Theorem for sample means is
critical because
III.14.

1. It states that for large sample sizes, the
   population distribution is approximately normal
2. It states that for large sample sizes, the sample
   is approximately normal
3. It states that for any population, the sampling
   distribution is normal regardless of sample size
4. It states that for large sample sizes, the
   sampling distribution is approximately normal
   regardless of the population distribution
5. It states that for any sample size, the sampling
   distribution is normal

Topic III Menu
92
The Central Limit Theorem for sample means is
critical because
SOLUTION
III.14.

1. It states that for large sample sizes, the
   population distribution is approximately normal
2. It states that for large sample sizes, the sample
   is approximately normal
3. It states that for any population, the sampling
   distribution is normal regardless of sample size
4. It states that for large sample sizes, the
   sampling distribution is approximately normal
   regardless of the population distribution
5. It states that for any sample size, the sampling
   distribution is normal

Topic III Menu
93
The amount of time it takes a high school class
of 1000 freshmen to swim 10 lengths of the school
pool has a distribution that is skewed left due
to some excellent swimmers. The mean amount of
time needed is 9.2 minutes and the standard
deviation is 5.3 min. If 64 students are chosen
at random, then what is the probability their
mean time will exceed 10 minutes?
III.15.
Topic III Menu
94
The amount of time it takes a high school class
of 1000 freshmen to swim 10 lengths of the school
pool has a distribution that is skewed left due
to some excellent swimmers. The mean amount of
time needed is 9.2 minutes and the standard
deviation is 5.3 min. If 64 students are chosen
at random, then what is the probability their
mean time will exceed 10 minutes?
SOLUTION
III.15.
normalcdf(10, 1E99, 9.2, 5.3/v64) 0.113
Topic III Menu
95
It is assumed that 50 of all people catch one or
more colds each year. What is the probability
that out of 400 randomly selected people, 216 or
more will catch one or more colds this year?
III.16.

1. 0.0055
2. 0.0121
3. 0.055
4. 0.11
5. 0.55

Topic III Menu
96
It is assumed that 50 of all people catch one or
more colds each year. What is the probability
that out of 400 randomly selected people, 216 or
more will catch one or more colds this year?
SOLUTION
III.16.
We want p(p gt 216/400 .054) Since np and n(1-p)
exceed 10, we can apply the normal approximation
with µ.5 and s.025 Normalcdf(.54, 1E99, .5,
.025) .055

1. 0.0055
2. 0.0121
3. 0.055
4. 0.11
5. 0.55

Topic III Menu
97
The decision whether the distribution ofo a
sample mean follows a normal or a t-distribution
depends on
III.17.

1. Sample size
2. Whether you have the actual data or only
   statistics of the data
3. Whether you know the population standard
   deviation
4. Whether npgt10 and n(1-p)gt10
5. None of the above

Topic III Menu
98
The decision whether the distribution ofo a
sample mean follows a normal or a t-distribution
depends on
SOLUTION
III.17.

1. Sample size
2. Whether you have the actual data or only
   statistics of the data
3. Whether you know the population standard
   deviation
4. Whether npgt10 and n(1-p)gt10
5. None of the above

Topic III Menu
99
National studies show that 14 of male teenagers
and 12 of female teenagers will be involved in a
major traffic accident while driving. Whats the
probability that independent samples of 100
female teens and 75 male teens will have results
that differ by more than 3 in either direction?
III.18.

1. .042
2. .085
3. .42
4. .85
5. Cannot be determined

Topic III Menu
100
National studies show that 14 of male teenagers
and 12 of female teenagers will be involved in a
major traffic accident while driving. Whats the
probability that independent samples of 100
female teens and 75 male teens will have results
that differ by more than 3 in either direction?
SOLUTION
III.18.
For both genders, np and n(1-p) exceed 5 so we
can use the CLT. z (.03-.02)
.1938 v(.14.86/75
.12.88/100) Using normalcdf(.1938, 1E99)
.423 But we want both directions so add in the
other tail to get an answer of .846

1. .042
2. .085
3. .42
4. .85
5. Cannot be determined

101
TOPIC IV Inference

• Inference on Means
• Inference on Proportions
• Inference on 2-way Tables
• Inference on Regression

START TOPIC
Topic IV Topic IV Topic IV Topic IV
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15
back to main back to main back to main back to main
102
Given H0 µ30, HA µlt30, if you conclude that
the mean is less than 30 when it is actually 27
IV.1.

1. you have made a type II error
2. you have made a type I error
3. the result of your test was not significant
4. you have drawn a correct conclusion
5. all of the above are true

Topic IV Menu
103
Given H0 µ30, HA µlt30, if you conclude that
the mean is less than 30 when it is actually 27
SOLUTION
IV.1.

1. you have made a type II error
2. you have made a type I error
3. the result of your test was not significant
4. you have drawn a correct conclusion
5. all of the above are true

You are rejecting a false null hypothesis. No
problems. Correct decision.
Topic IV Menu
104
The local news station reports that the 97
confidence interval for a candidates support was
(43, 48). What does the phrase 97
confidence mean?
IV.2.

1. 97 of the voters support the candidate
2. 97 of the time, this candidates level of
   support will be between 43 and 48
3. There is a 97 probability that the true level of
   support is between 43 and 48
4. There is a 97 probability that any other sample
   percentage is in the interval (43, 48)
5. none of these is true

Topic IV Menu
105
The local news station reports that the 97
confidence interval for a candidates support was
(43, 48). What does the phrase 97
confidence mean?
SOLUTION
IV.2.
not (D) because youre predicting the range of
the TRUE proportion youre not interested in
predicting the range of other samples!!!
Correct interpretation If this process were
repeated over and over again, about 97 of our
INTERVALS would capture the true proportion.

1. 97 of the voters support the candidate
2. 97 of the time, this candidates level of
   support will be between 43 and 48
3. There is a 97 probability that the true level of
   support is between 43 and 48
4. There is a 97 probability that any other sample
   percentage is in the interval (43, 48)
5. none of these is true

Topic IV Menu
106
A study of 20 teachers in a school district
indicated that the 95 confidence interval for
the mean salary of all teachers is (38,945,
41,245). What assumptions must be true for this
interval to be valid?
IV.3.

1. no assumptions are necessary. The CLT applies
2. The sample is randomly selected from a population
   of salaries that is a t-distribution
3. the distribution of the sample means is
   approximately normal
4. the distribution of all teachers salaries is
   approximately normal
5. None of the above.

Topic IV Menu
107
A study of 20 teachers in a school district
indicated that the 95 confidence interval for
the mean salary of all teachers is (38,945,
41,245). What assumptions must be true for this
interval to be valid?
SOLUTION
IV.3.
Because our sample size is only 20, you have to
know the population was normal to begin with.
(D) is the best response. I might accept choice
(C) too since the CLT is all about when x-bar is
normal, which is the goal I suppose.

1. no assumptions are necessary. The CLT applies
2. The sample is randomly selected from a population
   of salaries that is a t-distribution
3. the distribution of the sample means is
   approximately normal
4. the distribution of all teachers salaries is
   approximately normal
5. None of the above.

Topic IV Menu
108
In order to reduce the width of a confidence
interval, we can
IV. 4.

1. increase sample size only
2. increase confidence level only
3. increase sample size and increase confidence
   level
4. increase sample size and decrease confidence
   level
5. none of these would reduce the width of the
   interval

Topic IV Menu
109
In order to reduce the width of a confidence
interval, we can
SOLUTION
IV. 4.
Less confidence affords you to predict a much
tighter range of values.

1. increase sample size only
2. increase confidence level only
3. increase sample size and increase confidence
   level
4. increase sample size and decrease confidence
   level
5. none of these would reduce the width of the
   interval

Topic IV Menu
110
If the 95 confidence interval for µ is (6,9),
what conclusion can we draw if we test Ho µ10
vs. Ha µ?10 at a.05?
IV.5.

1. reject Ho
2. fail to reject Ho
3. accept Ho
4. accept Ha
5. There is insufficient information given to draw a
   conclusion

Topic IV Menu
111
If the 95 confidence interval for µ is (6,9),
what conclusion can we draw if we test Ho µ10
vs. Ha µ?10 at a.05?
SOLUTION
IV.5.
A two tailed test of a.05 is equivalent to a 95
confidence interval. 10 is not within the
interval.

1. reject Ho
2. fail to reject Ho
3. accept Ho
4. accept Ha
5. There is insufficient information given to draw a
   conclusion

Topic IV Menu
112
A bakery determines that it will be profitable if
the time it takes to decorate a cake does not
exceed 45 minutes. The owner documents the time
spent on 20 cakes and performs a test. If the
P-value of the test is 0.032, then he should
conclude
IV.6.

1. at a.05, fail to reject Ho
2. at a.05, reject Ho
3. at a.03, reject Ho
4. at a.025, reject Ho
5. We cannot draw a conclusion from this information

Topic IV Menu
113
A bakery determines that it will be profitable if
the time it takes to decorate a cake does not
exceed 45 minutes. The owner documents the time
spent on 20 cakes and performs a test. If the
P-value of the test is 0.032, then he should
conclude
SOLUTION
IV.6.

1. at a.05, fail to reject Ho
2. at a.05, reject Ho
3. at a.03, reject Ho
4. at a.025, reject Ho
5. We cannot draw a conclusion from this information

a p-value of .032 is significant at the 5 level
Topic IV Menu
114
Do boys perform better in math than girls? A
randomly selected group of each gender were given
the same math assessment.What design seems to be
employed?
IV.7.
boys girls
n 110 135
Mean 71.6 68.3
St.Deviation 10.4 11.2

1. Matched Pairs Design
2. Simple Random Design
3. Multi-State Cluster Design
4. Independent Samples Design
5. Randomized Block Design

Topic IV Menu
115
Do boys perform better in math than girls? A
randomly selected group of each gender were given
the same math assessment.What design seems to be
employed?
SOLUTION
IV.7.
We have 2 independent samples here boys and
girls.
boys girls
n 110 135
Mean 71.6 68.3
St.Deviation 10.4 11.2

1. Matched Pairs Design
2. Simple Random Design
3. Multi-State Cluster Design
4. Independent Samples Design
5. Randomized Block Design

Topic IV Menu
116
Do boys perform better in math than girls? A
randomly selected group of each gender were given
the same math assessment.What are Ho and Ha to
determine if boys scores are higher than girls?
IV.8.
boys girls
n 110 135
Mean 71.6 68.3
St.Dev 10.4 11.2

1. Ho µb µg 0 Ha µb µg lt 0
2. Ho µb µg 0 Ha µb µg ? 0
3. Ho µb µg 0 Ha µb µg gt 0
4. Ho µb µg lt 0 Ha µb µg 0
5. Ho µb µg Ha µb ? µg

Topic IV Menu
117
Do boys perform better in math than girls? A
randomly selected group of each gender were given
the same math assessment.What are Ho and Ha to
determine if boys scores are higher than girls?
SOLUTION
IV.8.
Another way to write this would be Ho µb µg
Ha µb gt µg
boys girls
n 110 135
Mean 71.6 68.3
St.Dev 10.4 11.2

1. Ho µb µg 0 Ha µb µg lt 0
2. Ho µb µg 0 Ha µb µg ? 0
3. Ho µb µg 0 Ha µb µg gt 0
4. Ho µb µg lt 0 Ha µb µg 0
5. Ho µb µg Ha µb ? µg

Topic IV Menu
118
Do boys perform better in math than girls? A
randomly selected group of each gender were given
the same math assessment.Suppose the p-value is
.0344. We can then conclude
IV.9.

1. at a.025, reject Ho
2. at a.02, reject Ho
3. at a.01, reject Ho
4. at a.025, fail to reject Ho
5. We cannot draw a conclusion from this information

boys girls
n 110 135
Mean 71.6 68.3
St.Dev 10.4 11.2
Topic IV Menu
119
Do boys perform better in math than girls? A
randomly selected group of each gender were given
the same math assessment.Suppose the p-value is
.0344. We can then conclude
SOLUTION
IV.9.
.0344 is not significant at .025, .02, or .01.
We must fail to reject it at these levels.

1. at a.025, reject Ho
2. at a.02, reject Ho
3. at a.01, reject Ho
4. at a.025, fail to reject Ho
5. We cannot draw a conclusion from this information

boys girls
n 110 135
Mean 71.6 68.3
St.Dev 10.4 11.2
Topic IV Menu
120
The rejection region for a test Ho p.4 vs. Ha
plt.4, with n50 and a.05 is given by
IV.10.

1. Reject Ho if z gt 1.96 or z lt -1.96
2. Reject Ho if z gt 1.645 or z lt -1.645
3. Reject Ho if z lt -1.96
4. Reject Ho if z lt -1.645
5. Reject Ho if t gt 2.59

Topic IV Menu
121
The rejection region for a test Ho p.4 vs. Ha
plt.4, with n50 and a.05 is given by
SOLUTION
IV.10.
invnorm(.05) because the entire .05 rejection
region is in the left tail.

1. Reject Ho if z gt 1.96 or z lt -1.96
2. Reject Ho if z gt 1.645 or z lt -1.645
3. Reject Ho if z lt -1.96
4. Reject Ho if z lt -1.645
5. Reject Ho if t gt 2.59

Topic IV Menu
122
The power of a test is described by all of the
following EXCEPT
IV.11.

1. Power p( rejecting Ho when Ha is true)
2. Power 1 ß
3. Power a ß
4. The calculation of power requires knowing the
   values of µ0, µa, s, and a
5. All of these are correct descriptions of the
   concept of power.

Topic IV Menu
123
The power of a test is described by all of the
following EXCEPT
SOLUTION
IV.11.
But it IS true that as one increases, the other
has to decrease. just not always by the same
amount

1. Power p( rejecting Ho when Ha is true)
2. Power 1 ß
3. Power a ß
4. The calculation of power requires knowing the
   values of µ0, µa, s, and a
5. All of these are correct descriptions of the
   concept of power.

Topic IV Menu
124
In a matched pairs test of 75 pairs, which of the
following assumptions is necessary?
IV.12.

1. The distribution of the paired differences should
   be approximately normal
2. The population variances should be equal
3. The samples are randomly and independently
   selected
4. The sets of values for each variable are
   approximately normal
5. None of these assumptions is necessary.

Topic IV Menu
125
In a matched pairs test of 75 pairs, which of the
following assumptions is necessary?
SOLUTION
IV.12.

1. The distribution of the paired differences should
   be approximately normal
2. The population variances should be equal
3. The samples are randomly and independently
   selected
4. The sets of values for each variable are
   approximately normal
5. None of these assumptions is necessary.

And being good stats students, you will either
make sure ngt25 or do a quick little graph to show
there arent any outliers. Right?
Topic IV Menu
126
A pharmaceutical company claims that 50 of adult
males living in a city in the Midwest get at
least two colds per year. A random sample of 100
adult males living in the city reported that only
42 got two or more colds. Do these data
provide evidence (at the 5 significance level)
that the true proportion of people is less than
50
IV.13.
Topic IV Menu
127
A pharmaceutical company claims that 50 of adult
males living in a city in the Midwest get at
least two colds per year. A random sample of 100
adult males living in the city reported that only
42 got two or more colds. Do these data
provide evidence (at the 5 significance level)
that the true proportion of people is less than
50
SOLUTION
IV.13.
Of course you would want to run through the
entire test properly, but we fail to reject
at the 5 level. there is not enough evidence to
say the proportion is less than 50
Topic IV Menu
128
If a 90 confidence interval for the slope of a
regression line does not contain 0, then which of
the following is a valid conclusion?
IV.14.

1. The confidence interval is not valid
2. A significance test will not be significant at
   the 10 level
3. There is sufficient evidence to conclude that the
   slope of the true regression line is 0
4. There is sufficient evidence to conclude that the
   slope of the true regression line is not 0.
5. None of these is valid.

Topic IV Menu
129
If a 90 confidence interval for the slope of a
regression line does not contain 0, then which of
the following is a valid conclusion?
SOLUTION
IV.14.
If 0 isnt in the interval, we are 90 confident
that the slope is NOT zero. This is exactly
what a regression test would conclude the
slope is NOT zero.

1. The confidence interval is not valid
2. A significance test will not be significant at
   the 10 level
3. There is sufficient evidence to conclude that the
   slope of the true regression line is 0
4. There is sufficient evidence to conclude that the
   slope of the true regression line is not 0.
5. None of these is valid.

Topic IV Menu
130
What is the expected number of males who prefer
chocolate?
IV.15.

1. 27.8
2. 29.2
3. 31.3
4. 36.3
5. None of these

male female
chocolate 32 16
vanilla 14 4
strawberry 3 10
Topic IV Menu
131
What is the expected number of males who prefer
chocolate?
48 of 79 people prefer chocolate (60.76), so we
expect 60.76 of the 49 males to like chocolate.
.6076(49) 29.77 or if you prefer the book
formula (row total x column total) total
number 29.77
SOLUTION
IV.15.

1. 27.8
2. 29.2
3. 31.3
4. 36.3
5. None of these

male female
chocolate 32 16
vanilla 14 4
strawberry 3 10
Topic IV Menu