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A.P. Statistics Review for Semester 1 Exam 2010-2011
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1. Name two types of quantitative plots from
which the original data can be recovered.
2. A small used car dealer wanted to get an
idea of how many cars her dealership sells
per day. Listed below is the number of
cars per day sold over a two-week period:
14,9,23,7,11,23,17,11,3,24,21,2,20,20
Compute all of the following:
a. the mean number of cars sold per day
b. the range of cars sold per day
c. the variance of cars sold per day
d. the standard deviation of cars sold per
day
e. the median of cars sold per day
f. the first and third quartiles of the
number of cars sold per day
g. the interquartile range of cars sold per
day.
3. Yandra took a general aptitude test and
scored in the 90th percentile for aptitude
in accounting.
a. What percentage of the scores was at
or below her score?
b. What percentage was above?
4. Given the following frequency
distribution:
x values frequency
20 2
29 4
30 4
39 3
44 2
a. What is the mean?
b. What is the median?
c. What is the standard deviation?
5. Match these statements with the possible
choices in the box below:
a. A distribution that is skewed to the left
b. A distribution that is skewed to the right
c. A symmetric distribution
6. Suppose the average score on a national
test is 500 points with a standard
deviation of 100 points. What would the
new mean and standard deviation be if…
a. Each score increases by 25 points?
b. Each score increases by 25%?
c. Each score increases by 25 points, and
then each score increases by 25%?
d. Each score increases by 25%, and then
increases by 25 points?
7. Classify each of the following as either
quantitative or categorical:
a. The number of years each of your
teachers has taught
b. Classifying a statistic as quantitative or
qualitative
c. The length of time spent by the
typical teenager watching television in
a month
d. The daily amount of money lost by the
airlines in the 15 months after the
9/11 attacks
e. The colors of the rainbow
Choices:
(i) mean = median
(ii) median < mean
(iii) median > mean
A.P. Statistics Review for Semester 1 Exam 2010-2011
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8. Are there any outliers in the following five
number summary? If so, what are they?
1 14 17 22 35
9. Match the five number summaries below
with the best choice in the box below:
a. 0, 5, 10, 15, 20
b. 0, 1, 3, 6, 18
c. 2, 14, 17, 18, 19
10. Which is better: A score of 76 on a test,
with a mean of 72 and standard deviation
of 3, or a score of 400 on a test with a
mean of 375 and a standard deviation of
25? Justify your answer.
11. Suppose you draw a graph with a mean of
500 and standard deviation of 50. Then
you draw a second graph with the same
mean but a standard deviation of 75.
Would the second graph be the same,
taller, or flatter than the first graph?
Suppose you draw a third graph with the
same mean as the first graph, but with a
standard deviation of 10. Would the third
graph be the same, taller, or flatter than
the first? (All graphs are drawn on the
same scales)
12. The distribution of scores of a
standardized test is normally distributed
with a mean of 125 and a standard
deviation of 25.
a. About 68% of scores fall between
what two values?
b. About 95% of scores fall between
what two values?
c. About 99.7% of scores fall between
what two values?
d. What test score is associated with a z-
score of -.4124?
e. What z-score is associated with a test
score of 110?
f. If a random test score was randomly
selected from the group, find the
probability that the test score would
be greater than 150.
g. If a random test score was randomly
selected from the group, find the
probability that the test score would
be less than 70.
h. If a random test score was randomly selected
from the group, find the probability that the
test score would be between 75 and 140.
13. A study is done to see if heavier cars really use
more gasoline. Let x be the weight of cars (in
hundreds of pounds), and let y be the miles per
gallon (mpg). The least-squares regression line for
predicting y from x is
^
43.3263 0.6007y x
a. Predict the mpg for a car that weighs 2,000
pounds.
b. How much does a car actually weigh if it is
predicted to get 25mpg?
c. Interpret the slope in the context of the
question.
Choices:
(i) right skewed
(ii) left skewed
(iii) symmetric
A.P. Statistics Review for Semester 1 Exam 2010-2011
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14. Below are three sets of data where x is the
explanatory variable and y is the response
variable. Make a scatterplot of each set of
data. Then, classify each as having a
positive linear relationship, a negative
linear relationship, or not having a linear
relationship.
x 66 68 66 66 67 67 67 68 69
y 65 70 65 64 68 65 67 69 70
x 45 55 74 85 88 95 106 115 125
y 10 60 5 90 20 70 20 40 70
x 0 10 25 5 14 19 7 22 12
y 30 15 3 25 8 6 17 4 15
15. Maurice takes his Organic Chemistry final
exam. After the final exam, the professor
announces that the scores are normally
distributed with a mean of 60 and
standard deviation of 15. The professor
also announces that students who scored
in the top 10 percent will earn an A in the
class, and the students who scored in the
bottom 10 percent will fail the class. All
scores are recorded as whole numbers.
a. What is the lowest score a student can
obtain and still pass the class?
b. What is the lowest score a student can
obtain on the exam and earn an A in
the class?
16. Data is collected from a high school to see
if there is a relationship between the
GPA’s of students on their IQ scores.
Calculations show that the mean and
standard deviation of the IQ scores are_
108.9 and 13.17xx s . Calculations
also show that the mean and standard
deviation of the GPA’s are _
3.447 and 1.89xy s .
#16 continued…..
The correlation between IQ on GPA is r = 0.6337.
a. What is the slope of the least-squares
regression line of IQ scores on GPA’s?
b. Interpret the slope in the context of the
question
c. What is the equation of the least-squares
regression line of IQ scores on GPA’s?
d. What percent of variation is explained by
the LSRL of IQ scores on GPA’s?
17. The diagram below shows a scatterplot of
data of college graduates and their
incomes in a small city in America. The
diagram also displays the least squares
regression line (LSRL) of the data.
a. Look at the two points above the LSRL
near the letter A. Do those points
have a residual? If so, is the residual
positive or negative?
b. Look at the two points below the LSRL
near the letter B. Do those points have
a residual? If so, is the residual
positive or negative?
c. Look at the point on the LSRL near the
letter C. Does that point have a
residual? If so, is it positive or
negative?
Continued on top of next column….
B
A
C
A.P. Statistics Review for Semester 1 Exam 2010-2011
Page 4
18. A study was done to see if there is an
association between race and convicted
murderers receiving the death sentence.
Initially, data is taken from homicide
convictions from 1976-1980 in Florida. It
was shown that 11.2% of whites and 8.5%
of blacks were sentenced to death. Then
the study is looked into a bit further and a
third variable is thrown in. The third
variable is race of the victim. When the
victim was white, 12.3% of whites and
19.3% of blacks were sent to death. When
the victim was black, 0% of whites and
1.3% of blacks were sentenced to death.
From this, we see that when a third
variable is thrown into the observation,
the association changes. What is this
phenomenon known as?
19. Outliers in the y direction of a scatterplot
often have large residuals. Outliers in the x
direction are often called influential
points.
a. Do influential points necessarily have
large residuals?
b. What happens if you remove
influential points from a data set?
20. Johnny wants to see if there is a
correlation between doing homework and
test grades. He asks his statistics teacher
to anonymously give him everyone’s
homework average and test grade average
respectively. Johnny computes the
correlation and discovers r = 0.70. A week
later, the teacher decides to curve the test
and adds ten points to everyone’s test.
What will the new r be?
21. Four data sets of (x,y) have the following
correlations:
Data set A: r = .30
Data set B: r = -.30
Data set C: r = .07
Data set D: r = -.70
Are the following statements true or
false?
a. Points in A show a stronger linear
association than D.
b. Points in C show a stronger linear
association than D.
c. Points in B show a weaker linear
association than A.
d. Points in B show a weaker linear
association than D.
22. Stratified and blocking are two terms that
some students have a hard time
distinguishing between. When do we use
them and why?
23. What are the three principles of
experimental design?
24. A marketing company offers to pay $25 to
the first 100 people who respond to their
advertisement and complete a
questionnaire regarding displays of their
client’s product. What type of sample is
this?
25. What is the difference between an
observational study and an experiment?
26. What is the difference between stratified
sampling and cluster sampling?
27. What is the difference between single
blinding and double blinding?
A.P. Statistics Review for Semester 1 Exam 2010-2011
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28. The table below shows the people abroad
the Titanic, classified according to class of
ticket and whether the ticket holder died
or survived.
First class
Second class
Third class
Crew
Survived 203 118 178 212
Died 122 167 528 673
Tell the proportion of….
a. First class people that survived
b. Survivors who were first class
c. Can you explain what the difference
between part a and part b is?
d. Only looking at the data from the
table, would you argue that there was
a relationship between the kind of
ticket a passenger held and his/her
chances of surviving the Titanic.
Justify your answer.
e. One student tells me more 2nd class
ticket holders survived than 3rd class
ticket holders. Another student tells
me more 3rd class ticket holders
survived than 2nd class ticket holders.
Both were able to justify their answer
correctly (based on the table). How do
you think these students justified their
answers?
f. Would this be considered a study or
experiment? Explain.
29. A college professor in Vermont tries a new
attendance policy to see if more students
attend class. He deducts a point off
students’ grades for each absence. This
year he had a much higher attendance
rate. However, this past winter was very
mild and lacks the snow and cold
temperatures of the past few winters.
The new attendance policy and mild
weather are what type of variables?
30. We need to survey a random sample of
the 300 passengers on a flight from San
Francisco to Tokyo. Name each sampling
method described below:
a. Randomly choose a number between
1 and 10, pick that passenger and then
every 10th passenger after that one as
they board the plane.
b. From the boarding list, randomly
choose 5 people flying first class and
25 of the other passengers.
c. Randomly generate 30 seat numbers
and survey the passengers who sit
there.
d. Randomly selection a seat position
(right window, right center, right aisle,
etc.) and survey all the passengers
sitting in those seats.
31. You’re trying to find out what freshman
think of the food on campus. Below are
several sampling methods.
For parts a and b, name the sampling
method used and describe how it could
introduce bias into the results.
For parts c d, and e, tell what the bias is
in the sampling method.
a. You set up a “Tell Us What You Think”
website and invite freshmen to visit
the site to complete a questionnaire.
b. You stand outside a school cafeteria at
lunchtime and stop people to ask
them questions.
c. You obtain a list of phone numbers of
freshman who live in the dorms and
call each of them.
d. After handing out free pizza coupons,
you begin your survey by asking “Last
year, 90% of all freshman favored
campus food over off-campus food.”
e. You do a completely randomized
sample and send out 100 surveys. You
only get 50 surveys returned.
A.P. Statistics Review for Semester 1 Exam 2010-2011
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32. Before and after experiments, those that
use the same subjects for pre-testing and
post-testing a treatment, use what type of
design?
33. An agricultural researcher is interested in
determining how much water and
fertilizer are optimum for growing a
certain plant. Twenty-four plots of land
are available to grow the plant. The
researcher will apply three different
amounts of fertilizer (low, medium, and
high) and two different amounts of water
(light and heavy). These will be applied at
random in equal combination to each of
the four plots. After 6 weeks, the plants’
heights in each plot will be recorded.
Identify all of the following:
a. Experimental units
b. Factors and their levels
c. Treatments
d. Response Variable
34. A company has developed a new
treatment for hair loss. The company
believes men and women will react
differently to the treatment, so they are
placed into two separate groups. Then,
the men are assigned to two groups, and
the women are assigned to two groups.
One of the two groups for each gender is
given the medication and the other is
given a placebo.
a. Explain why this is a block design.
What is the blocking variable?
b. Matched-pairs is a type of block
design. Would you consider this a
matched-pairs design? Why or why
not?
35. A study is being done to see if preparation
programs affect SAT performance. 100
students are randomly assigned to two
groups, one of which takes the SAT with
no preparation course and one of which
has a preparation course before taking the
SAT. The results are then compared. What
type of study is this?
36. An experiment is being done to test
whether people prefer Coke or Pepsi. Each
subject tries both colas. The order in
which they try the colas is decided
randomly. They do not know which type
of cola they are trying, but each subject
tries both and reports which taste better.
What type of design is this? (Hint:
Blinding is involved, but that is not the
answer. Blinding is a characteristic of an
experiment, not a design. )
37. There are 80 students in an Introductory
Statistics class. You are to select a sample
of 5 for a study. What is one way you can
choose 5 students that will produce a
simple random sample?
38. A large bakery has many different
products for sale. Suppose that 70% of all
customers of the bakery order donuts,
50% order cinnamon rolls, and 40% order
both. If a customer is randomly selected,
what is the probability that
a. She ordered neither donuts nor
cinnamon rolls?
b. Ordered donuts, but not cinnamon
rolls?
c. Ordered cinnamon rolls, but not
donuts?
A.P. Statistics Review for Semester 1 Exam 2010-2011
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39. Events A and B are independent.
P(A)= 0.75 and P(B) = 0.25
Find:
a. P(A B)
b. P(A B)
c. P(A|B)
d. P(B|A)
40. In a particular town, 80% of the people
are employed. We are going to use a
random number table to pick random
samples and see what percentage of those
random samples is employed. Let the
digits 0-7 represent those people who are
employed, and 8-9 represent those who
are not employed. For each of the
following random numbers selected from
a random number table, tell the sequence
and percentage of those employed. For
example if I picked 19223, the sequence
would be EUEEE, and 80% of those are
employed.
a. 95034
b. 05756
c. 28713
d. 96409
41. A commuter must pass through five traffic
lights on her way to work and will have to
shop at each one that is red. She
estimates the probability model for the
number of red lights she hits, as shown
below:
# of red Lights
0 1 2 3 4 5
Probability 0.05 0.25 0.35 0.15 0.15 0.05
a. What is the expected value of red
lights she should expect to hit each
day?
b. What’s the standard deviation of the
distribution of the number of red
lights she is expected to hit?
42. A cat just had a liter of five kittens.
Assume each kitten has an equal chance
of being male or female and the sex of the
kittens are independent.
a. What is the probability that at least 4
of the kittens are female?
b. What is the probability that at most 2
kittens are male?
c. What is the probability that all of the
kittens are male OR all of the kittens
are female?
43. The American Veterinary Association
claims that the annual cost of medical care
for dogs averages $100, with a standard
deviation of $30, and for cats averages
$120, with a standard deviation of $35.
(Note: Medical expenses for dogs and cats
should be considered independent of one
another)
a. What’s the expected sum in the cost
of medical care for dogs and cats?
b. What’s the standard deviation of that
sum?
c. What’s the expected difference in the
cost of medical care for dogs and cats?
d. What’s the standard deviation of that
difference?
Continued on top of next column….
A.P. Statistics Review for Semester 1 Exam 2010-2011
Page 8
44. A basketball player has made 80% of his
foul shots during the season. Assuming
the shots are independent, find the
probability that in tonight’s game he
a. Misses for the first time on his fifth
attempt.
b. Misses his first basket on his fourth
shot?
c. Makes his first basket on one of his
first 3 shots?
45. What is the difference between binomial
and geometric probability models?
46. Assume that 13% of people are left-
handed. If we select 5 people at random,
find the probability of each outcome
described below:
a. There are exactly 3 lefties in the
group
b. There are at least 3 lefties in the
group
47. Suppose for the above example (#46), we
choose 12 people instead of 5.
a. What is the mean and standard
deviation of the number of right-
handers in the group?
b. What is the probability that
(i) They’re not all right-handed?
(ii) There are no more than 10
righties?
(iii) There are exactly 6 of each?
(iv) The majority is right-handed?
48. An Olympic archer is able to hit the bull’s-
eye 70% of the time. Assume each shot is
independent of the others. If she shoots 6
arrows, what’s the probability of each of
the following results?
a. Her first bull’s-eye comes on the
fourth arrow.
b. She gets exactly 4 bull’s-eyes.
c. She misses exactly 4 bull’s-eyes.
d. She gets at least 4 bull’s-eyes.
e. She misses at least 4 bull’s-eyes.
f. She gets at most 4 bull’s-eyes.
g. She misses at most 4 bull’s-eyes.
h. She misses the first 4-bull’s eyes and
gets her first bull’s-eye on the fifth
trial?
i. She gets the first 4-bull’s eyes and
misses her first bull’s-eye on the fifth
trial?
j. How many bull’s-eyes do you expect
her to get?
k. With what standard deviation?
l. How many bull’s-eyes do you expect
her to miss?
m. With what standard deviation?
49. Suppose for the above example (#48), our
archer shoots 10 arrows.
a. Find the mean and standard deviation
of bull’s eyes she may get.
b. Find the mean and standard deviation
of bull’s eyes she may miss.
c. What’s the probability that?
(i) She never misses.
(ii) She gets no more than 8
bull’s-eyes.
(iii) She gets exactly 8 bull’s-eyes.
(iv) She gets the first 5 bull’s-eyes
and misses her first bull’s-eye
on the sixth trial?
(v) She misses the first 3 bull’s-
eyes and gets her first bull’s-
eye on the fourth trial.
(vi) She hits the bull’s-eye more
often than she misses.
(vii) She missed the bull’s-eye
more often than she gets it. Continued on top of next column….
A.P. Statistics Review for Semester 1 Exam 2010-2011
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