AP STATISTICS MIDTERM REVIEW!!!
2012-2013
Use the following to answer question 1:
In a statistics class with 136 students, the professor records how much money each student has in
his or her possession during the first class of the semester. The histogram below is of the data
collected.
___ 1. The histogram
A) is skewed right.
B) has an outlier.
C) is asymmetric.
D) has a mean less than 30.
E) all of the above.
___ 2. In a study of 1991 model cars, a researcher found that the fraction of the variation in the
price of cars that was explained by the least-squares regression on horsepower was
about 0.64. For the cars in this study, the correlation between the price of the car and its
horsepower was found to be positive. The actual value of the correlation
A) is 0.80.
B) is 0.64.
C) is 0.41.
D) is –0.80.
E) cannot be determined from the information given.
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___ 3. A researcher studies the relationship between the total SAT score (SAT math score plus
SAT verbal score) and the grade point average (GPA) of college students at the end of
their freshman year. In order to use a relatively homogeneous group of students, the
researcher only examines data from high school valedictorians (students who
graduated at the top of their high school class) who have completed their first year of
college. The researcher finds the correlation between total SAT score and GPA at the
end of the freshman year to be very close to 0. Which of the following would be a valid
conclusion from these facts?
A) Since the group of students studied is a very homogeneous group of students, the
results should give a very accurate estimate of the correlation the researcher would
find if all college students who have completed their freshman year were studied.
B) The correlation we would find if all college students who have completed their
freshman year were studied would be even smaller than that found by the
researcher. By restricting to valedictorians, the researcher is examining a group
that will be more informative than those students who have only completed their
freshman year.
C) The researcher made a mistake. Correlation cannot be calculated (that is, the
formula for correlation is invalid) unless all students who completed their
freshman year are included.
D) Since the SAT score involves three separate measures, it is not possible to
determine a correlation between SAT score and GPA.
E) None of the above.
___ 4. For which of the following counts would a binomial probability model be reasonable?
A) The number of traffic tickets written by each police officer in a large city during
one month.
B) The number of hearts in a hand of five cards dealt from a standard deck of 52 cards
that has been thoroughly shuffled.
C) The number of 7's in a randomly selected set of five random digits from a table of
random digits.
D) The number of phone calls received in a one-hour period.
E) All of the above.
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Use the following to answer question 5:
A system has two components that operate in parallel, as shown in the diagram below. Since the
components operate in parallel, at least one of the components must function properly if the system
is to function properly. The probabilities of failures for the components 1 and 2 during one period
of operation are .20 and .03, respectively. Let F denote the event that component 1 fails during one
period of operation and G denote the event that component 2 fails during one period of operation.
Component failures are independent.
___ 5. The probability that the system functions properly during one period of operation is
A) 0.994.
B) 0.970.
C) 0.940.
D) 0.776.
E) 0.006.
___ 6. In a test of ESP (extrasensory perception), the experimenter looks at cards that are
hidden from the subject. Each card contains a star, a circle, a wavy line, or a square.
The subject tries to read the experimenter's mind and name the shape on each card.
What is the probability that the subject gets the first four correct before giving a wrong
answer if he is just guessing?
A) 0.00293.
B) 0.00391.
C) 0.06328.
D) 0.07910.
E) 0.31641.
___ 7. A college basketball player makes 5/6 of his free throws. Assuming free throw attempts
are independent, the probability that he makes exactly three of his next four free throws
is
A)
D)
( ) ( )
( ) ( )
B)
C)
E)
( ) ( )
( ) ( )
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( ) ( )
___ 8. The number of undergraduates at Johns Hopkins University is approximately 2000,
while the number at Ohio State University is approximately 40,000. At both schools a
simple random sample of about 3% of the undergraduates is taken. We conclude that
A) the sample from Johns Hopkins is more accurate than the sample from Ohio State.
B) the sample from Ohio State University is about 20 times more accurate than the
sample from John Hopkins University.
C) the sample from Johns Hopkins has the same accuracy as the sample from Ohio
State.
D) it is impossible to make any statements about the accuracies of the two samples
since the students surveyed were different.
E) the sample from Johns Hopkins is less accurate than the sample from Ohio State.
___ 9. A fair coin (one for which both the probability of heads and the probability of tails are
0.5) is tossed 60 times. The probability that less than 1/3 of the tosses are heads is
A) 0.33.
B) 0.109.
C) 0.09.
D) 0.034.
E) 0.005.
___ 10. The average salary of all female workers is $35,000. The average salary of all male
workers is $41,000. What must be true about the average salary of all workers?
A) It must be $38,000.
B) It must be larger than the median salary.
C) It must be lower than the median salary.
D) It could be any number between $35,000 and $41,000.
E) It must be larger than $38,000.
___ 11. The least-squares regression line is
A) the line that makes the square of the correlation in the data as large as possible.
B) the line that makes the sum of the squares of the vertical distances of the data
points from the line as small as possible.
C) the line that passes through the greatest number of data points.
D) the line that best splits the data in half, with half of the points above the line and
half below the line.
E) all of the above.
___ 12. A set of data has a median that is much larger than the mean. Which of the following
statements is most consistent with this information?
A) A stemplot of the data is assymetrical.
B) A stemplot of the data is skewed left.
C) A stemplot of the data is skewed right.
D) The data set must be so large that it would be better to draw a histogram than a
stemplot.
E) A stemplot of the data is symmetric.
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___ 13. A study of the salaries of full professors at Upper Wabash Tech shows that the median
salary for female professors is considerably less than the median male salary. However,
further investigation shows that the median salaries for male and female full professors
are about the same in every department (English, physics, etc.) of the university. This
apparent contradiction is an example of
A) extrapolation.
D) correlation.
B) Simpson's paradox.
E) causation.
C) confounded responses.
___ 14. If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a
regular distribution of outcomes in a large number of repetitions, we say the
phenomenon is
A) random.
D) probabilistic.
B) predictable.
E) none of the above.
C) deterministic.
___ 15. I toss a fair coin a large number of times. Assuming tosses are independent, which of
the following is true?
A) Once the number of flips is large enough (usually about 10,000), the number of
heads will always be exactly half of the total number of tosses. For example, after
10,000 tosses I should have 5000 heads.
B) The proportion of heads will be about 1 2 , and this proportion will tend to get
closer and closer to 1 2 as the number of tosses increases.
C) As the number of tosses increases, any run of heads will be balanced by a
corresponding run of tails so that the overall proportion of heads is 1 2 .
D) If the number of heads is greater than the number of tails for the first 5000 tosses,
then the number of tails will be greater than the number of heads for the next 5000
tosses.
E) All of the above.
___ 16. A study found a correlation of r = –0.61 between the gender of a worker and his or her
income. We may correctly conclude that
A) women earn more than men on the average.
B) women earn less than men on the average.
C) an arithmetic mistake was made, since correlation must always be positive.
D) this result is incorrect, because computing r makes no sense in this situation.
E) on average, women earn 61% less than men.
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___ 17. A basketball player makes 2/3 of his free throws. To simulate a single free throw,
which of the following assignments of digits to making a free throw are appropriate?
A) 0 and 1 correspond to making the free throw and 2 corresponds to missing the free
throw.
B) 01, 02, 03, 04, 05, 06, 07, and 08 correspond to making the free throw and 09, 10,
11, and 12 correspond to missing the free throw.
C) Use a die and let 1, 2, 3, and 4 correspond to making a free throw while 5 and 6
correspond to missing a free throw.
D) A, B, and C are correct.
E) Neither A, B, nor C is correct.
___ 18. In order to assess the effects of exercise on reducing cholesterol, a researcher sampled
50 people from a local gym who exercised regularly and 50 people from the
surrounding community who did not exercise regularly. They each reported to a clinic
to have their cholesterol measured. The subjects were unaware of the purpose of the
study, and the technician measuring the cholesterol was not aware of whether subjects
exercised regularly or not. This is
A) an observational study.
B) an experiment, but not a double-blind experiment.
C) a controlled study.
D) a matched-pairs experiment.
E) a double-blind experiment.
Use the following to answer question 19:
Let the random variable X be a randomly generated number with the uniform probability density
curve given below.
___ 19. Referring to the information above, P(X = 0.25) is
A) 0.
B) 0.025.
C) 0.25.
D) 0.75.
E) 1.
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___ 20. A call-in poll conducted by USA Today concluded that Americans love Donald Trump.
USA Today later reported that 5640 of the 7800 calls for the poll came from the offices
owned by one man, Cincinnati financier Carl Lindner, who is a friend of Donald
Trump. The results of this poll are probably
A) surprising, but reliable since it was conducted by a nationally recognized
organization.
B) biased, but only slightly since the sample size was quite large.
C) unbiased because the calls were randomly made at varying times.
D) biased, overstating the popularity of Donald Trump.
E) biased, understating the popularity of Donald Trump.
___ 21. The distribution of the heights of students in a large class is roughly Normal.
Moreover, the average height is 68 inches, and approximately 95% of the heights are
between 62 and 74 inches. Thus, the standard deviation of the height distribution is
approximately equal to
A) 2
B) 3
C) 6
D) 9
E) 12
Use the following to answer question 22:
___ 22. For this density curve, what percentage of the observations lies between 0.5 and 1.2?
A) 25%.
B) 35%.
C) 50%.
D) 60%.
E) 70%.
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___ 23. Which of the following is true of the correlation coefficient r?
A) It is a resistant measure of association.
B) It does not change if either all the X-data or all the Y-data are multiplied by a
constant.
C) If r is the correlation between X and Y, then –r is the correlation between Y and X.
D) r can never be 0 if there is a linear relationship between X and Y.
E) All of the above.
___ 24. Suppose we measure a response variable Y at each of several times. A scatterplot of log
Y versus time of measurement looks approximately like a positively sloping straight
line. We may conclude that
A) the correlation between time of measurement and Y is negative, since logarithms of
positive fractions (such as correlations) are negative.
B) the rate of growth of Y is positive, but slowing down over time.
C) a logarithmic growth model would approximately describe the relationship
between Y and the time of measurement.
D) a mistake has been made. It would have been better to plot Y versus the logarithm
of the time of measurement.
E) an exponential growth model would approximately describe the relationship
between Y and time of measurement.
___ 25. Items produced by a manufacturing process are supposed to weigh 90 grams. However,
the manufacturing process is such that there is variability in the items produced and
they do not all weigh exactly 90 grams. The distribution of weights can be
approximated by a normal distribution with a mean of 90 grams and a standard
deviation of 1 gram. Using the 68–95–99.7 rule, what percentage of the items will
either weigh less than 87 grams or more than 93 grams?
A) 0.3%.
B) 3%.
C) 6%.
D) 94%.
E) 99.7%.
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___ 26. A researcher observes that, on average, the number of divorces in cities with major
league baseball teams is larger than in cities without major league baseball teams. The
most plausible explanation for this observed association is that
A) the presence of a major league baseball team causes the number of divorces to rise
(perhaps husbands are spending too much time at the ballpark).
B) the high number of divorces is responsible for the presence of a major league
baseball team (more single men means potentially more fans at the ballpark,
making it attractive for an owner to relocate to such cities).
C) the association is due to common response (major league teams tend to be in large
cities with more people and thus with a greater number of divorces).
D) the observed association is purely coincidental. It is implausible to believe the
observed association could be anything other than accidental.
E) the presence of a major league baseball team in a city will increase the mean
income (some wives would expect that their husbands would have more money to
spend on them).
___ 27. A researcher computed the average SAT math score of all high school seniors who took
the SAT exam for each of the 50 states. The researcher also computed the average
salary of high school teachers in each of these states and plotted these average salaries
against the average SAT math scores. The plot showed a distinct negative association
between average SAT math scores and average teacher salaries. A second researcher
conducted a similar study, but computed the average SAT math score for each school
district in the nation and plotted these against the average salary of high school teachers
in each district. The association between average SAT math score and average teacher
salaries in the plot of the second researcher will most likely be
A) about the same as that seen by the first researcher.
B) much weaker than that seen by the first researcher (close to 0).
C) much stronger than that seen by the first researcher, but with the opposite sign.
D) a little weaker than that seen by the first researcher.
E) much stronger than that seen by the first researcher, but with the same sign.
___ 28. The scores on a university examination are normally distributed with a mean of 62 and
a standard deviation of 11. If the bottom 5% of students will fail the course, what is the
lowest mark (rounded to the nearest whole number) that a student can have and still be
awarded a passing grade?
A) 62.
B) 57.
C) 44.
D) 40.
E) 3.
Use the following to answer question 29:
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5, you win $1;
if number of spots showing is 6, you win $4; and if the number of spots showing is 1, 2, or 3, you
win nothing. Let X be the amount that you win on a single play of the game.
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___ 29. Referring to the information above, the variance of X is
A) 1.
B) 1.414.
C) 3/2.
D) 2.
E) 13/6.
___ 30. In a certain game of chance, your chances of winning are 0.2. If you play the game five
times and outcomes are independent, the probability that you win at most once is
A) 0.0819.
B) 0.2.
C) 0.3277.
D) 0.4096.
E) 0.7373.
___ 31. A fourth-grade teacher gives homework every night in both mathematics and language
arts. The time to complete the mathematics homework has a mean of 10 minutes and a
standard deviation of 3 minutes. The time to complete the language arts assignment has
a mean of 12 minutes and a standard deviation of 4 minutes. Assuming the times to
complete homework assignments in math and language arts are independent, the
standard deviation of the time required to complete the entire homework assignment is
A) 16 minutes.
D) 3 minutes.
B) 5 minutes.
E) 16 9 minutes.
C) 4 minutes.
___ 32. Suppose we roll a red die and a green die. Let A be the event that the number of spots
showing on the red die is 3 or less and B be the event that the number of spots showing
on the green die is more than 3. The events A and B are
A) disjoint.
D) reciprocals.
B) complements.
E) dependent.
C) independent.
___ 33. Will a fluoride mouthwash used after brushing reduce cavities? Twenty sets of twins
were used to investigate this question. One member of each set of twins used the
mouthwash after each brushing; the other did not. After six months, the difference in
the number of cavities of those using the mouthwash was compared with the number of
cavities of those who did not use the mouthwash. This experiment uses
A) random placebos.
D) a block design.
B) double-blinding.
E) a matched-pairs design.
C) double replication.
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___ 34. A particularly common question in the study of wildlife behavior involves observing
contests between “residents” of a particular area and “intruders.” In each contest, the
“residents” either win or lose the encounter (assuming there are no ties). Observers
might record several variables. Which of the following variables is categorical?
A) the duration of the contest (in seconds).
B) How long the “intruder” lives in the area before it is accepted as a “resident. ”
C) whether the “residents” win or lose.
D) the total number of contests won by the “residents.”
E) the number of animals involved in the contest.
___ 35. Event A occurs with probability 0.8. The conditional probability that event B occurs
given that A occurs is 0.5. The probability that both A and B occur
A) is 0.3.
B) is 0.4.
C) is 0.5.
D) is 0.8.
E) cannot be determined from the information given.
___ 36. In order to take a sample of 90 members of a local gym, I first divide the members into
men and women, and then take a simple random sample of 45 men and a separate
simple random sample of 45 women. This is an example of a
A) two-step sample.
D) randomized comparative experiment.
B) stratified random sample.
E) block design.
double-blind
simple
random
sample.
C)
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Use the following to answer question 37:
Each of the following two histograms represents the distribution of acceptance rates (percent
accepted) among 25 business schools in 1995. The histograms use different class intervals but are
based on the same data. In each class interval, the left endpoint is included but not the right.
___ 37. Which interval contains fewer than half of all the observations?
A) 20% < acceptance rate < 35%.
D) 30% < acceptance rate < 45%.
B) 22.5% < acceptance rate < 37.5%.
E) 30% < acceptance rate < 52.5%.
C) 25% < acceptance rate < 40%.
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Use the following to answer question 38:
The boxplot below is of the birthweights (in ounces) of a sample of 160 infants born in a local
hospital.
___ 38. The number of children with birthweights between 100 and 120 ounces is
approximately
A) 40.
B) 50.
C) 80.
D) 100.
E) cannot be determined.
___ 39. A study is conducted to determine if one can predict the yield of a crop based on the
amount of yearly rainfall. The response variable in this study is
A) the yield of the crop.
D) either bushels or inches of water.
B) the amount of yearly rainfall.
E) the month the crop is harvested.
C) the experimenter.
___ 40. Suppose that A and B are two independent events with P(A) = 0.2 and P(B) = 0.4.
P(A  BC) is
A) 0.08.
B) 0.12.
C) 0.52.
D) 0.60.
E) 0.92.
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Answer Key
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E
A
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A
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B
B
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B
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