AP STATISTICS EXAM REVIEW by DAVID CUSTER (click on topic of
choice) TOPIC I: TOPIC I: Describing Data Describing Data (15
questions) (15 questions) TOPIC II: TOPIC II: Experimental Design
Experimental Design (15 questions) (15 questions) TOPIC III: TOPIC
III: Probability (18 questions) (18 questions) TOPIC IV: TOPIC IV:
Inference (15 questions) (15 questions) Slide 2 TOPIC I: Describing
Data Univariate DataUnivariate Data Normal DistributionsNormal
Distributions Bivariate DataBivariate Data Topic I 1111 2222 3333
4444 5555 6666 7777 8888 9999 10 11 12 13 14 15 back to main back
to main Slide 3 Which observation has the higher z-score? I.
x=25.4; =12.9; =3.7 II. x=25.4; =15.3; =2.7 A.I B.II C.z-scores are
equal D.cannot be determined since we dont know the standard
deviations of the populations E.cannot be determined since we dont
know if the populations are normal I.1. Topic I Menu Slide 4 Which
observation has the higher z-score? I. x=25.4; =12.9; =3.7 II.
x=25.4; =15.3; =2.7 A.I B.II C.z-scores are equal D.cannot be
determined since we dont know the standard deviations of the
populations E.cannot be determined since we dont know if the
populations are normal I.1. SOLUTION The z-score for I is 3.38; the
z-score for II is 3.74 Topic I Menu Slide 5 The Quartile and
Percentile positions of the value 10 in the set {10, 6, 8, 9, 12,
17, 32, 16} are: A.Q3; 38 B.Q2; 38 C.Q2; 26 D.Q3; 26 E.none of
these I.2. Topic I Menu Slide 6 The Quartile and Percentile
positions of the value 10 in the set {10, 6, 8, 9, 12, 17, 32, 16}
are: A.Q3; 38 B.Q2; 38 C.Q2; 26 D.Q3; 26 E.none of these I.2.
SOLUTION When the values are in order, there are 3 values below 10.
This puts 10 in the 37.5 percentile and the 2 nd quartile. Topic I
Menu Slide 7 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? A.{4, 5, 8, 12, 14} B.{2, 4, 6, 8, 10, 12} C.{3, 5, 5, 6, 8, 9}
D.{10, 14, 14, 16, 20, 22} E.none of the above I.3. Topic I Menu
Slide 9 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?
A.12% still lies between a and b B.12% lies between a + d and b + d
C.(12+d)% lies between a and b D.(12+d)% lies between a + d and b +
d E.there is no way to tell how much data is between a and b I.4.
Topic I Menu Slide 10 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? A.12% still lies between a and b B.12% lies
between a + d and b + d C.(12+d)% lies between a and b D.(12+d)%
lies between a + d and b + d E.there is no way to tell how much
data is between a and b I.4. A uniform shift of all the data
maintains the percentages of data in shifted intervals. SOLUTION
Topic I Menu Slide 11 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 70 th percentile
A.1, 2, 3 B.1, 3, 2 C.3, 2, 1 D.3, 1, 2 E.2, 3, 1 I.5. Topic I Menu
Slide 12 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 70 th percentile
A.1, 2, 3 B.1, 3, 2 C.3, 2, 1 D.3, 1, 2 E.2, 3, 1 I.5. SOLUTION The
percentile of a z-score of 1 is about 84%, and the percentile of Q3
is 75% Topic I Menu Slide 13 Which of the following would NOT be a
correct interpretation of a correlation coefficient of r = -.30
A.The variables are inversely related B.The coefficient of
determination is 0.09 C.30% of the variation between the variables
is linear D.There exists a weak relationship between the variables
E.All are correct I.6. Topic I Menu Slide 14 Which of the following
would NOT be a correct interpretation of a correlation coefficient
of r = -.30 A.The variables are inversely related B.The coefficient
of determination is 0.09 C.30% of the variation between the
variables is linear D.There exists a weak relationship between the
variables E.All are correct I.6. SOLUTION The value of r 2 explains
the variation between the variables. Not r. Topic I Menu Slide 15
Which of the following displays is best suited for categorical
data? A.Box Plot B.Bar Graph C.Stem and Leaf Plot D.Dot Plot
E.Scatterplot I.7. Topic I Menu Slide 16 Which of the following
displays is best suited for categorical data? A.Box Plot B.Bar
Graph C.Stem and Leaf Plot D.Dot Plot E.Scatterplot I.7. SOLUTION
In a bar graph, each column is separate, allowing for categorical
separation. Topic I Menu Slide 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? A. A. B. B. C. C.
D. D. E. E. I.8. Topic I Menu Slide 18 Linear regression usually
employs the method of least squares. Which of the following is the
quantity that is minimized by the least squares process? A. A. B.
B. C. C. D. D. E. E. I.8. SOLUTION Least Squares Regression
minimizes the residuals in the y-direction. Topic I Menu Slide 19
Which of the following is NOT true? A.Two sets of data can have the
same means but different variances B.Two sets of data can have the
same variance but different means C.Two different values in a data
set can have the same z-score D.All the absolute values of z-scores
for a data set can be equal E.All of the above are true I.9. Topic
I Menu Slide 20 Which of the following is NOT true? A.Two sets of
data can have the same means but different variances B.Two sets of
data can have the same variance but different means C.Two different
values in a data set can have the same z-score D.All the absolute
values of z-scores for a data set can be equal E.All of the above
are true I.9. SOLUTION Since each value is a distinct distance from
the mean, the z-scores must all be different Topic I Menu Slide 21
In a symmetric, mount-shaped distribution, what percentile has a
z-score of -2? I.10. Topic I Menu Slide 22 Topic I Menu In a
symmetric, mount-shaped distribution, what percentile has a z-score
of -2? I.10. SOLUTION 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 2.5 th percentile Slide 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? A.60
B.62 C.64 D.66 E.68 I.11. Topic I Menu Slide 24 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? A.60 B.62 C.64
D.66 E.68 I.11. SOLUTION We need to solve the following equation
for x: so x=66 Topic I Menu Slide 25 Does the following problem
have a unique solution? If so, find it. If not, show at least two
answers: 5 numbers have Q1=12, Median=15, Q3=18. Find the mean.
I.12. Topic I Menu Slide 26 Does the following problem have a
unique solution? If so, find it. If not, show at least two answers:
5 numbers have Q1=12, Median=15, Q3=18. Find the mean. I.12.
SOLUTION {11, 13, 15, 17, 19} =15 { 9, 15, 15, 17, 19} =15 the data
sets are not unique, but the mean is always 15! YES!!!
surprisingly! Topic I Menu Slide 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? I.13. Topic I Menu Slide 28 Topic I
Menu 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? I.13. SOLUTION 23 students. we arrive at n=23 Slide 29 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. A.51.55 B.52.76 C.56.55 D.56.88 E.59.12
I.14. Topic I Menu Slide 30 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.
A.51.55 B.52.76 C.56.55 D.56.88 E.59.12 I.14. SOLUTION 75(52.6) +
25(48.4) 100 Topic I Menu Slide 31 In skewed-right distributions,
what is most frequently the relationship of the mean, median, and
mode? A.mean > median > mode B.median > mean > mode
C.mode > median > mean D.mode > mean > median E.mean
> mode > median I.15. Topic I Menu Slide 32 Topic I Menu In
skewed-right distributions, what is most frequently the
relationship of the mean, median, and mode? A.mean > median >
mode B.median > mean > mode C.mode > median > mean
D.mode > mean > median E.mean > mode > median I.15.
SOLUTION 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. Slide 33 TOPIC II: Experimental Design
SamplingSampling Designing ExperimentsDesigning Experiments
Observational StudiesObservational Studies Topic II 1111 2222 3333
4444 5555 6666 7777 8888 9999 10 11 12 13 14 15 back to main back
to main Slide 34 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: A.a census B.a survey sample
C.an observational study D.a designed experiment E.none of these
II.1. Topic II Menu Slide 35 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: A.a
census B.a survey sample C.an observational study D.a designed
experiment E.none of these II.1. SOLUTION The director is observing
behavior, not implementing treatments on the group Topic II Menu
Slide 36 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: A.a simple random sample B.a quota sample C.a
convenience sample D.a multi-stage cluster sample E.a census II.2.
Topic II Menu Slide 37 Topic II Menu SOLUTION Without a properly
randomized selection, she is introducing bias to the study. 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:
A.a simple random sample B.a quota sample C.a convenience sample
D.a multi-stage cluster sample E.a census II.2. Slide 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: A.blocking for gender B.testing for a lurking variable
C.promoting sexual harassment D.testing for bias E.none of these
II.3. Topic II Menu Slide 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: A.blocking for gender
B.testing for a lurking variable C.promoting sexual harassment
D.testing for bias E.none of these II.3. SOLUTION She is
investigating whether gender affects lunchtime behavior Topic II
Menu Slide 40 Which of the following is NOT a concern in data
collection? A.lurking variables B.blocking C.bias D.non-response
E.all of the above are concerns II.4. Topic II Menu Slide 41 Which
of the following is NOT a concern in data collection? A.lurking
variables B.blocking C.bias D.non-response E.all of the above are
concerns II.4. SOLUTION Even blocking methods need to be analyzed
Topic II Menu Slide 42 Which of the following is NOT a valid sample
design? A.Code every member of a population and select 100 randomly
chosen members B.Divide a population by gender and select 50
individuals randomly from each group C.Select individuals randomly
and place into gender groups until you have the same proportion as
in the population D.Select five homerooms at random from all the
homerooms in a large high school. E.All of these are valid II. 5.
Topic II Menu Slide 43 Which of the following is NOT a valid sample
design? A.Code every member of a population and select 100 randomly
chosen members B.Divide a population by gender and select 50
individuals randomly from each group C.Select individuals randomly
and place into gender groups until you have the same proportion as
in the population D.Select five homerooms at random from all the
homerooms in a large high school. E.All of these are valid II. 5.
SOLUTION But you may be able to question the validity of answer (C)
Topic II Menu Slide 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: A.the doctors specialty,
e.g. cardiology, obstetrics, etc. B.the number of doctors who are
cardiologists C.all cardiologists in the American Medical
Association directory D.a random sample of 100 cardiologists E.none
of these II.6. Topic II Menu Slide 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: A.the
doctors specialty, e.g. cardiology, obstetrics, etc. B.the number
of doctors who are cardiologists C.all cardiologists in the
American Medical Association directory D.a random sample of 100
cardiologists E.none of these II.6. SOLUTION we are interested in
the percentage of doctors who have been sued Topic II Menu Slide 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: A.the set of all doctors who were sued for
malpractice B.the set of cardiologists who were sued for
malpractice C.all doctors D.all cardiologists E.all doctors who
have malpractice insurance II.7. Topic II Menu Slide 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: A.the set of all doctors who were sued for
malpractice B.the set of cardiologists who were sued for
malpractice C.all doctors D.all cardiologists E.all doctors who
have malpractice insurance II.7. SOLUTION Just cardiologists, not
all doctors. Topic II Menu Slide 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? A.a
designed experiment B.a census of all cardiologists C.an
observational study of randomly selected cardiologists D.a survey
sent to randomly selected cardiologists E.any answer except (A)
II.8. Topic II Menu Slide 49 Topic II Menu 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? A.a designed experiment B.a census of all cardiologists C.an
observational study of randomly selected cardiologists D.a survey
sent to randomly selected cardiologists E.any answer except (A)
II.8. SOLUTION This population of this observation al study is too
large to track everyone down. Slide 50 Which of the following is
NOT a source of bias in sample surveys? A.non-response B.wording of
questions C.voluntary response D.use of a telephone survey E.all
are sources of bias II.9. Topic II Menu Slide 51 Which of the
following is NOT a source of bias in sample surveys? A.non-response
B.wording of questions C.voluntary response D.use of a telephone
survey E.all are sources of bias II.9. SOLUTION and dont forget
even a huge sample size cant correct a poorly selected sample.
Remember the Literary Digest Poll! Topic II Menu Slide 52 Which of
the following is NOT a requirement of a controlled experiment?
A.control B.comparison C.replication D.randomization E.all of these
are required II.10. Topic II Menu Slide 53 Which of the following
is NOT a requirement of a controlled experiment? A.control
B.comparison C.replication D.randomization E.all of these are
required II.10. SOLUTION Topic II Menu Slide 54 A randomized block
design is NOT: A.similar to a stratified random sample for surveys
B.a strategy to control for an influence that would affect the
outcome of the experiment C.a strategy that depends on
randomization D.only used for gender comparisons E.all of these
describe a randomized block design. II.11. Topic II Menu Slide 55 A
randomized block design is NOT: A.similar to a stratified random
sample for surveys B.a strategy to control for an influence that
would affect the outcome of the experiment C.a strategy that
depends on randomization D.only used for gender comparisons E.all
of these describe a randomized block design. II.11. SOLUTION You
can block with any categorical variables! Topic II Menu Slide 56 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: A.the 500 students chosen B.the students
taught by activity-based statistics C.the students taught by
traditional methods D.all students in high school. E.none of these
II.12. Topic II Menu Slide 57 Topic II Menu 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:
A.the 500 students chosen B.the students taught by activity-based
statistics C.the students taught by traditional methods D.all
students in high school. E.none of these II.12. SOLUTION We are
interested in knowing about ALL AP STATISTICS STUDENTS Slide 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: A.a blocked design experiment
B.a stratified random sample C.a completely randomized design D.a
simple random sample E.none of these II.13. Topic II Menu Slide 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: A.a blocked design experiment
B.a stratified random sample C.a completely randomized design D.a
simple random sample E.none of these II.13. SOLUTION B or C. Either
one is fine. Topic II Menu Slide 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 if there are to be
the same number of freshmen, sophomores, juniors, and seniors in
the sample. II.14. Topic II Menu Slide 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 if there
are to be the same number of freshmen, sophomores, juniors, and
seniors in the sample. II.14. SOLUTION Select a simple random
sample of 10 from each class. Topic II Menu Slide 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 if there are to be the same number of males and
females in the sample Topic II Menu Slide 63 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 if
there are to be the same number of males and females in the sample
SOLUTION Select a simple random sample of 20 males and 20 females.
Topic II Menu Slide 64 TOPIC III: Probability Random
VariablesRandom Variables Binomial DistributionsBinomial
Distributions Geometric DistributionsGeometric Distributions
Sampling DistributionsSampling Distributions Topic III 1111 2222
3333 4444 5555 6666 7777 8888 9999 10 11 12 13 14 15 16 17 18 back
to main back to main Slide 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?
A.25% B.35% C.40% D.65% E.cannot be determined III.1. Topic III
Menu Slide 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? A.25% B.35%
C.40% D.65% E.cannot be determined III.1. SOLUTION Assuming one
winner, the probabilities must add up to 100% Topic III Menu Slide
67 A local law enforcement agency published the following chart.
The percentage of altercations involving at least one teenager is:
A.8% B.37% C.45% D.55% E.82% III.2. Altercations Between Percent
Two teens 45% A teen and an adult 37% Two adults 18% Topic III Menu
Slide 68 A local law enforcement agency published the following
chart. The percentage of altercations involving at least one
teenager is: A.8% B.37% C.45% D.55% E.82% III.2. Altercations
Between Percent Two teens 45% A teen and an adult 37% Two adults
18% SOLUTION p(two teens) + p(teen and adult) = Topic III Menu
Slide 69 What proportion of Republicans are over 50? A.61/238
B.32/96 C.96/238 D.32/61 E.cannot be determined III.3.
DemocratRepublicanIndepend 18 30 251812 31 40 322110 41 50 172517
over 50 143215 Topic III Menu Slide 70 What proportion of
Republicans are over 50? A.61/238 B.32/96 C.96/238 D.32/61 E.cannot
be determined III.3.DemocratRepublicanIndepend 18 30 251812 31 40
322110 41 50 172517 over 50 143215 SOLUTION There are 96
Republicans of whom 32 are over age 50 Topic III Menu Slide 71 If
one person is chosen at random, what is the probability he is a
Democrat between 41 and 50 years old? A.17/238 B.17/88 C.61/238
D.17/61 E.88/238 III.4. DemocratRepublicanIndepend 18 30 251812 31
40 322110 41 50 172517 over 50 143215 Topic III Menu Slide 72 If
one person is chosen at random, what is the probability he is a
Democrat between 41 and 50 years old? A.17/238 B.17/88 C.61/238
D.17/61 E.88/238 III.4.DemocratRepublicanIndepend 18 30 251812 31
40 322110 41 50 172517 over 50 143215 SOLUTION Total # of adults is
238. 17 are democrats between 41 and 50 Topic III Menu Slide 73
Given that a person chosen is between 31 and 40, what is the
probability the person is an Independent? A.10/238 B.10/63 C.10/54
D.54/238 E.63/238 III.5. DemocratRepublicanIndepend 18 30 251812 31
40 322110 41 50 172517 over 50 143215 Topic III Menu Slide 74 Given
that a person chosen is between 31 and 40, what is the probability
the person is an Independent? A.10/238 B.10/63 C.10/54 D.54/238
E.63/238 III.5.DemocratRepublicanIndepend 18 30 251812 31 40 322110
41 50 172517 over 50 143215 SOLUTION There are 63 people between 31
and 40 of whom 10 are Independent. Topic III Menu Slide 75 What
proportion of the citizens sampled are over 50 OR Independent?
A.54/238 B.61/238 C.100/238 D.115/238 E.cannot be determined III.6.
DemocratRepublicanIndepend 18 30 251812 31 40 322110 41 50 172517
over 50 143215 Topic III Menu Slide 76 What proportion of the
citizens sampled are over 50 OR Independent? A.54/238 B.61/238
C.100/238 D.115/238 E.cannot be determined
III.6.DemocratRepublicanIndepend 18 30 251812 31 40 322110 41 50
172517 over 50 143215 SOLUTION 61/238 + 54/238 15/238 15 adults are
in both categories Topic III Menu Slide 77 If P(A)=0.4, P(B)=0.2,
and P(A and B)= 0.08 Which is true? A.Events A and B are
independent and mutually exclusive B.Events A and B are independent
but not mutually exclusive C.Events A and B are mutually exclusive
but not independent D.Events A and B are neither independent nor
mutually exclusive E.Events A and B are independent but whether
they are mutually exclusive cannot be determined. III.7. Topic III
Menu Slide 78 If P(A)=0.4, P(B)=0.2, and P(A and B)= 0.08 Which is
true? A.Events A and B are independent and mutually exclusive
B.Events A and B are independent but not mutually exclusive
C.Events A and B are mutually exclusive but not independent
D.Events A and B are neither independent nor mutually exclusive
E.Events A and B are independent but whether they are mutually
exclusive cannot be determined. III.7. SOLUTION --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 Slide 79 What is the probability that a
family with 6 children will have 3 boys and 3 girls? POSSIBLE NAME
OF DISTRIBUTION? 1.Binomial Model 2.Geometric Model 3.Uniform Model
4.Normal Model III.8. Topic III Menu Slide 80 What is the
probability that a family with 6 children will have 3 boys and 3
girls? POSSIBLE NAME OF DISTRIBUTION? 1.Binomial Model 2.Geometric
Model 3.Uniform Model 4.Normal Model III.8. SOLUTION This is a
binomial distribution: n=6 p=0.5 6 C 3 (0.5) 3 (0.5) 3 = 0.3125 x=3
Topic III Menu Slide 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? POSSIBLE NAME OF DISTRIBUTION? 1.Binomial
Model 2.Geometric Model 3.Uniform Model 4.Normal Model III.9. Topic
III Menu Slide 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? POSSIBLE NAME OF DISTRIBUTION? 1.Binomial Model
2.Geometric Model 3.Uniform Model 4.Normal Model III.9. SOLUTION
This is a normal distribution: normalcdf(6, 1E99, 5+6/12, 10/12) =
0.2743 Topic III Menu Slide 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? POSSIBLE NAME OF
DISTRIBUTION? 1.Binomial Model 2.Geometric Model 3.Uniform Model
4.Normal Model III.10. Topic III Menu Slide 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? POSSIBLE NAME OF DISTRIBUTION? 1.Binomial Model 2.Geometric
Model 3.Uniform Model 4.Normal Model III.10. SOLUTION Did you think
to use the normal approximation? = np = 4 =p(1p)/n =.0196
normalcdf(-1E99, 6, 4,.0196) = 1.00 How come that didnt work? This
is a binomial distribution: binomcdf(100, 0.04, 6) = 0.8936 Topic
III Menu Slide 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? POSSIBLE NAME OF
DISTRIBUTION? 1.Binomial Model 2.Geometric Model 3.Uniform Model
4.Normal Model III.11. Topic III Menu Slide 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? POSSIBLE NAME OF DISTRIBUTION? 1.Binomial Model
2.Geometric Model 3.Uniform Model 4.Normal Model III.11. SOLUTION
This is a geometric (waiting time) distribution: n=??? (there isnt
one! Thats why its Geometric!) p=0.27; x=4 geometpdf(0.27, 4) =
(.73)(.73)(.73)(.27) = 0.7160 Topic III Menu Slide 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 Slide 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 III.12. SOLUTION This is a
binomial distribution: n=5 p=0.70 5 C 3 (0.7) 3 (0.3) 2 = 0.3087
x=3 Topic III Menu Slide 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 3 rd attempt III.13. Topic III
Menu Slide 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 3 rd attempt III.13. SOLUTION This is a geometric
distribution: n=??? (we wait til a successtheres no n!) p=0.70; x=3
geometpdf(0.7, 3) = (.3)(.3)(.7) = 0.063 Topic III Menu Slide 91
The Central Limit Theorem for sample means is critical because A.It
states that for large sample sizes, the population distribution is
approximately normal B.It states that for large sample sizes, the
sample is approximately normal C.It states that for any population,
the sampling distribution is normal regardless of sample size D.It
states that for large sample sizes, the sampling distribution is
approximately normal regardless of the population distribution E.It
states that for any sample size, the sampling distribution is
normal III.14. Topic III Menu Slide 92 The Central Limit Theorem
for sample means is critical because A.It states that for large
sample sizes, the population distribution is approximately normal
B.It states that for large sample sizes, the sample is
approximately normal C.It states that for any population, the
sampling distribution is normal regardless of sample size D.It
states that for large sample sizes, the sampling distribution is
approximately normal regardless of the population distribution E.It
states that for any sample size, the sampling distribution is
normal III.14. SOLUTION Topic III Menu Slide 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 Slide 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? III.15. SOLUTION normalcdf(10, 1E99, 9.2, 5.3/64) = 0.113
Topic III Menu Slide 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? A.0.0055 B.0.0121 C.0.055 D.0.11 E.0.55 III.16.
Topic III Menu Slide 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? A.0.0055 B.0.0121 C.0.055 D.0.11 E.0.55 III.16.
SOLUTION We want p(p > 216/400 =.054) Since np and n(1-p) exceed
10, we can apply the normal approximation with =.5 and =.025
Normalcdf(.54, 1E99,.5,.025) =.055 Topic III Menu Slide 97 The
decision whether the distribution ofo a sample mean follows a
normal or a t- distribution depends on: A.Sample size B.Whether you
have the actual data or only statistics of the data C.Whether you
know the population standard deviation D.Whether np>10 and
n(1-p)>10 E.None of the above III.17. Topic III Menu Slide 98
The decision whether the distribution ofo a sample mean follows a
normal or a t- distribution depends on: A.Sample size B.Whether you
have the actual data or only statistics of the data C.Whether you
know the population standard deviation D.Whether np>10 and
n(1-p)>10 E.None of the above III.17. SOLUTION Topic III Menu
Slide 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? A..042 B..085 C..42 D..85
E.Cannot be determined III.18. Topic III Menu Slide 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? A..042 B..085 C..42 D..85 E.Cannot be determined III.18.
SOLUTION For both genders, np and n(1-p) exceed 5 so we can use the
CLT. z = (.03-.02) =.1938 (.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 Slide 101 TOPIC IV:
Inference Inference on MeansInference on Means Inference on
ProportionsInference on Proportions Inference on 2-way
TablesInference on 2-way Tables Inference on RegressionInference on
Regression Topic IV 1111 2222 3333 4444 5555 6666 7777 8888 9999 10
11 12 13 14 15 back to main back to main Slide 102 Given H0: =30,
HA: 0 D.Ho: b g < 0; Ha: b g = 0 E.Ho: b = g ; Ha: b g IV.8.
boysgirls n110135 Mean71.668.3 St.Dev10.411.2 Topic IV Menu Slide
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? A.Ho:
b g = 0; Ha: b g < 0 B.Ho: b g = 0; Ha: b g 0 C.Ho: b g = 0; Ha:
b g > 0 D.Ho: b g < 0; Ha: b g = 0 E.Ho: b = g ; Ha: b g
IV.8.boysgirlsn110135 Mean71.668.3 St.Dev10.411.2 SOLUTION Another
way to write this would be Ho: b = g ; Ha: b > g Topic IV Menu
Slide 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. boysgirls
n110135 Mean71.668.3 St.Dev10.411.2 A.at =.025, reject Ho B.at
=.02, reject Ho C.at =.01, reject Ho D.at =.025, fail to reject Ho
E.We cannot draw a conclusion from this information Topic IV Menu
Slide 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:
IV.9.boysgirlsn110135 Mean71.668.3 St.Dev10.411.2 A.at =.025,
reject Ho B.at =.02, reject Ho C.at =.01, reject Ho D.at =.025,
fail to reject Ho E.We cannot draw a conclusion from this
information SOLUTION.0344 is not significant at.025,.02, or.01. We
must fail to reject it at these levels. Topic IV Menu Slide 120 The
rejection region for a test Ho: p=.4 vs. Ha: p 1.96 or z 1.96 or z
< -1.96 B.Reject Ho if z > 1.645 or z 1.645 or z < -1.645
C.Reject Ho if z < -1.96 D.Reject Ho if z < -1.645 E.Reject
Ho if t > 2.59 IV.10. Topic IV Menu Slide 121 The rejection
region for a test Ho: p=.4 vs. Ha: p 1.96 or z 1.96 or z < -1.96
B.Reject Ho if z > 1.645 or z 1.645 or z < -1.645 C.Reject Ho
if z < -1.96 D.Reject Ho if z < -1.645 E.Reject Ho if t >
2.59 IV.10. SOLUTION invnorm(.05) because the entire.05 rejection
region is in the left tail. Topic IV Menu Slide 122 The power of a
test is described by all of the following EXCEPT A.Power = p(
rejecting Ho when Ha is true) B.Power = 1 C.Power = + D.The
calculation of power requires knowing the values of 0, a, , and
E.All of these are correct descriptions of the concept of power.
IV.11. Topic IV Menu Slide 123 The power of a test is described by
all of the following EXCEPT A.Power = p( rejecting Ho when Ha is
true) B.Power = 1 C.Power = + D.The calculation of power requires
knowing the values of 0, a, , and E.All of these are correct
descriptions of the concept of power. IV.11. SOLUTION But it IS
true that as one increases, the other has to decrease. just not
always by the same amount Topic IV Menu Slide 124 In a matched
pairs test of 75 pairs, which of the following assumptions is
necessary? A.The distribution of the paired differences should be
approximately normal B.The population variances should be equal
C.The samples are randomly and independently selected D.The sets of
values for each variable are approximately normal E.None of these
assumptions is necessary. IV.12. Topic IV Menu Slide 125 In a
matched pairs test of 75 pairs, which of the following assumptions
is necessary? A.The distribution of the paired differences should
be approximately normal B.The population variances should be equal
C.The samples are randomly and independently selected D.The sets of
values for each variable are approximately normal E.None of these
assumptions is necessary. IV.12. SOLUTION Topic IV Menu And being
good stats students, you will either make sure n>25 or do a
quick little graph to show there arent any outliers. Right? Slide
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 Slide 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% 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% IV.13. SOLUTION Topic IV Menu Slide 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? A.The
confidence interval is not valid B.A significance test will not be
significant at the 10% level C.There is sufficient evidence to
conclude that the slope of the true regression line is 0 D.There is
sufficient evidence to conclude that the slope of the true
regression line is not 0. E.None of these is valid. IV.14. Topic IV
Menu Slide 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? A.The confidence interval is not valid B.A
significance test will not be significant at the 10% level C.There
is sufficient evidence to conclude that the slope of the true
regression line is 0 D.There is sufficient evidence to conclude
that the slope of the true regression line is not 0. E.None of
these is valid. IV.14. SOLUTION 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. Topic IV
Menu Slide 130 Topic IV Menu What is the expected number of males
who prefer chocolate? A.27.8 B.29.2 C.31.3 D.36.3 E.None of these
IV.15.malefemalechocolate3216 vanilla144 strawberry310 Slide 131
What is the expected number of males who prefer chocolate? A.27.8
B.29.2 C.31.3 D.36.3 E.None of these IV.15.malefemalechocolate3216
vanilla144 strawberry310 SOLUTION 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 Topic IV Menu
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