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Name: __________________________ Date: _____________
1. 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.
Use the following to answer question 2:
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.
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2. What percent of the schools have an acceptance rate of less than 20%?
A) 3%.
B) 4%.
C) 12%.
D) 16%.
E) 20%.
3. 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.
4. Which of the following is likely to have a mean that is smaller than the median?
A) the number of candy bars sold in a movie theater on a randomly selected day.
B) the scores of students (out of 100 points) on a very easy exam in which most score
perfectly, but a few do very poorly.
C) the prices of homes in a large city.
D) the scores of students (out of 100 points) on a very difficult exam on which most
score poorly, but a few do very well.
E) the salaries of all National Football League players.
5. The number of new projects started each month at an advertising agency for the last six
months is
2
5 3
3
6
3
The interquartile range for the above data is
A) 1.0.
B) 2.0.
C) 3.0.
D) 4.0.
E) 5.0.
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6. The Insurance Institute for Highway Safety publishes data on the total damage suffered
by compact automobiles in a series of controlled, low-speed collisions. A sample of the
data in dollars, with brand names removed, is
1000 600
800
1000
The variance of the above data is
A) 191.5.
B) 36,667.
C) 165.8.
D) 27,500.
E) 90,000.
7. The time it takes for students to complete a standardized exam is approximately normal
with a mean of 70 minutes and a standard deviation of 10 minutes. Using the 68–95–
99.7 rule, what percentage of students will complete the exam in under an hour?
A) 68%.
B) 47.5%.
C) 32%.
D) 16%.
E) 5%.
Use the following to answer questions 8-10:
For a physics course containing 10 students, the maximum point total for the quarter was 200.
The point totals for the 10 students are given in the stemplot below.
8. This stemplot is most similar to
A) a histogram with class intervals 110  score < 120, 120  score < 130, etc.
B) a symmetric distribution with an outlier.
C) a boxplot of the data.
D) reporting the five-point summary for the data, with the mean.
E) a timeplot of the data with the observations taken in increasing order.
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9. To which of the following data sets does the stemplot correspond?
A) all integers between 116 and 179.
B) 1, 2, 3, 4, 6, 6, 7, 8, 8, 9.
C) 16, 18, 21, 24, 28, 33, 37, 42, 46, 79.
D) 116, 118, 121, 124, 128, 133, 137, 142, 146, 179.
E) 116, 118, 121, 124, 128, 133, 137, 142, 146. The value 179 is an outlier.
10. The median point total for this class is
A) 130.
B) 130.5.
C) 133.
D) 137.
E) 142.
11. A phone-in poll conducted by a newspaper reported that 73% of those who called in
liked business tycoon Donald Trump. The number 73% is a(n)
A) unbiased estimate.
B) sample.
C) parameter.
D) population.
E) statistic.
12. A phone-in poll conducted by a newspaper reported that 73% of those who called in
liked business tycoon Donald Trump. The unknown true percentage of American
citizens who like Donald Trump is a
A) statistic.
B) variable.
C) parameter.
D) population.
E) sample.
13. The sampling distribution of a statistic is
A) the probability that we obtain the statistic in repeated random samples.
B) the mechanism that determines whether randomization was effective.
C) the distribution of values taken by a statistic in all possible samples of the same
size from the same population.
D) the extent to which the sample results differ systematically from the truth.
E) the distribution of a particular sample of a certain size.
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14. I flip a coin 10 times and record the proportion of heads I obtain. I then repeat this
process of flipping the coin 10 times and recording the proportion of heads obtained
many, many times. When done, I make a histogram of my results. This histogram
represents
A) the bias, if any, that is present.
B) a binomial distribution.
C) simple random sampling.
D) the sampling distribution of the proportion of heads in 10 flips of the coin.
E) the true population parameter.
15. If a statistic used to estimate a parameter is such that the mean of its sampling
distribution is equal to the true value of the parameter being estimated, the statistic is
said to be
A) random.
B) biased.
C) variable.
D) unbiased.
E) a proportion.
16. The variability of a statistic is described by
A) the spread of its sampling distribution.
B) the amount of bias present.
C) the different values the statistic will take from each of the samples.
D) the stability of the population it describes.
E) the vagueness in the wording of the question used to collect the sample data.
17. Suppose you are going to roll a die 60 times and record p̂ , the proportion of times that
an even number (2, 4, or 6) is showing. The sampling distribution of p̂ should be
centered at about
A) 1/6.
B) 1/3.
C) 1/2.
D) 20.
E) 30.
Use the following to answer questions 18-20:
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state
sales tax from 5% to 6%, with the additional revenue going to education. Let p̂ denote the
proportion in the sample that say they support the increase. Suppose that 40% of all adults in
Ohio support the increase.
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18. The mean  p̂ of p̂ is
A) 5%.
B) 40% ± 5%.
C) 40% ± 2.5%.
D) 0.40.
E) 600.
19. The standard deviation  p̂ of p̂ is
A) 0.40.
B) 0.24.
C) 0.0126.
D) 0.00033.
E) 0.00016.
20. The probability that p̂ is more than 0.50 is
A) less than 0.0001.
B) about 0.1.
C) 0.1586.
D) 0.4602.
E) 0.50.
21. A multiple-choice exam has 100 questions, each with five possible answers. If a student
is just guessing at all the answers, the probability that he or she will get more than 30
correct is
A) 0.2500.
B) 0.1230.
C) 0.1056.
D) 0.0062.
E) 0.0400.
22. A random sample of size 25 is to be taken from a population that is normally distributed
with mean 60 and standard deviation 10. The number X of the observations in our
sample that are larger than 60 is to be computed. The sampling distribution of X is
A) normal with mean 60 and standard deviation 10.
B) normal with mean 60 and standard deviation 2.
C) uniform.
D) skewed to the left.
E) none of the above.
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23. In a large population of adults, the mean IQ is 112 with a standard deviation of 20.
Suppose 200 adults are randomly selected for a market-research campaign. The
distribution of the sample mean IQ is
A) exactly normal with mean 112 and standard deviation 1.414.
B) exactly normal with mean 112 and standard deviation 20.
C) approximately normal with mean 112 and standard deviation 0.1.
D) approximately normal with mean 112 and standard deviation 1.414.
E) approximately normal with mean 112 and standard deviation 20.
24. A random variable X has mean  X and standard deviation X. Suppose n independent
observations of X are taken and the average x of these n observations is computed. We
can assert that if n is very large, the sampling distribution of x is approximately normal.
This assertion follows from:
A) the law of large numbers.
B) the central limit theorem.
C) the definition of a sampling distribution.
D) the bell curve.
E) the standard deviation of the sampling distribution.
25. The weights of extra-large eggs have a normal distribution with a mean of 1 ounce and a
standard deviation of 0.1 ounces. The probability that a dozen extra-large eggs has a
total weight of more than 13 ounces is closest to
A) 0.
B) 0.0020.
C) 0.1814.
D) 0.2033.
E) 0.9982.
Use the following to answer questions 26-27:
You measure the heights of a random sample of 400 high school sophomore males in a
Midwestern state. The sample mean is X = 66.2 inches. Suppose that the heights of all high
school sophomore males follow a normal distribution with unknown mean  and standard
deviation  = 4.1 inches.
26. A 95% confidence interval for  (expressed in interval notation) is
A) (58.16, 74.24).
B) (59.46, 72.94).
C) (65.8, 66.6).
D) (65.86, 66.54).
E) (66.18, 66.22).
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27. I compute a 95% confidence interval for . Suppose I had measured the heights of a
random sample of 100 sophomore males, rather than 400. Which of the following
statements is true?
A) The margin of error for our 95% confidence interval would increase.
B) The margin of error for our 95% confidence interval would decrease.
C) The margin of error for our 95% confidence interval would stay the same, since the
level of confidence has not changed.
D)  would increase.
E)  would decrease.
28. The incomes in a certain large population of college teachers have a normal distribution
with mean $35,000 and standard deviation $5000. Four teachers are selected at random
from this population to serve on a salary review committee. What is the probability that
their average salary exceeds $40,000?
A) Essentially 0.
B) 0.0228.
C) 0.1587.
D) 0.3413.
E) 0.9772.
29. P. 659 #10.38
30. P.681 #10.70
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Answer Key
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