SCHOOL OF PUBLIC POLICY
GEORGE MASON UNIVERSITY
FALL 2010
OLMSTEAD
PUBP704
STATISTICAL METHODS IN POLICY ANALYSIS
MIDTERM REVIEW QUESTIONS
1. What are the advantages of using a data array to present data?
2. What is the difference between a frequency distribution and a relative frequency distribution?
3. What is the difference between a histogram and an ogive?
4. For each of the following questions, first indicate whether the statement is True or False. Then, briefly
explain your position in two or three sentences. Answering “True” or “False” without an explanation will
not earn credit.
(a) Scores from two groups of students are shown in the histograms. Group B has a larger standard
deviation.
(b) Studies show that the amount of violent television children watch is positively correlated with violent
behavior at school. This implies that policies reducing the amount of violence on television will reduce
violent behavior at school.
5. People are either environmentalists (E) or non-environmentalists (N). Assume that 30% of people are
environmentalists.
People use one of three methods to get to work: riding a bike (B), driving a hybrid (H) or driving an
SUV (S). Environmentalists ride bikes 20% of the time, drive hybrids 40% of the time and drive SUVs
40% of the time. Non-environmentalists ride bikes 10% of the time, drive hybrids 20% of the time and
drive SUVs 70% of the time.
(a) What is the probability that a randomly selected person rides a bike to work?
(b) What is the probability that someone either rides a bike or is an environmentalist?
(c) You observe someone driving a hybrid. What is the probability that they are an environmentalist?
SCHOOL OF PUBLIC POLICY
GEORGE MASON UNIVERSITY
FALL 2010
OLMSTEAD
(d) Riding a bike consumes no gasoline. Driving a hybrid consumes 2 gallons a day. Driving an SUV
consumes 5 gallons a day. How much more gasoline would you expect a non-environmentalist to
consume each day than an environmentalist?
(e) In a randomly chosen group of ten people, what is the probability that exactly three are
environmentalists?
6. Rainfall and Drought in Sudan
Assume that annual rainfall in Sudan is normally distributed with mean 24 inches and standard deviation of
10 inches. A drought occurs if annual rainfall is less than 15 inches.
(a) Calculate the z-score associated with rainfall equal to 15 inches. Briefly explain how we can interpret the
z-score.
(b) Find the probability a drought occurs (that is, annual rainfall is less than 15 inches).
7. For each of the following questions, first indicate whether the statement is True or False. Then, briefly
explain your position in two or three sentences. Answering “True” or “False” without an explanation will
not earn credit.
(a) For a confidence interval with a given confidence level, we can cut the width of the interval in half if we
double the sample size.
(b) If the p-value of a hypothesis test is 0.034, then we will fail to reject the null hypothesis at the 1%
significance level (ie. 99% confidence level).
(c) To test if fertilizer increases output per acre, your null hypothesis is that the output with the fertilizer is
higher than without it.
8. The manager of General Electric’s lightbulb division must estimate the average number of hours that a
lightbulb made by each lightbulb machine will last. A sample of 40 lightbulbs was selected from
machine A and the average burning time was 1416 hours. The standard deviation of burning time is
known to be 30 hours. Construct a 90% confidence interval for the true population mean.
9. A sample of twelve had a mean of 62 and a standard deviation of 10. Construct a 95% confidence
interval for the population mean.
10. For the following cases, specify which probability distribution to use in a hypothesis test:
(a) 𝐻0 : 𝜇 = 27, 𝐻1 : 𝜇 ≠ 27, 𝑥̅ = 33, 𝑠 = 4, 𝑛 = 25
(b) 𝐻0 : 𝜇 = 98.6, 𝐻1 : 𝜇 > 98.6, 𝑥̅ = 99.1, 𝜎 = 1.5, 𝑛 = 50
(c) 𝐻0 : 𝜇 = 382, 𝐻1 : 𝜇 ≠ 382, 𝑥̅ = 363, 𝜎 = 68, 𝑛 = 12
(d) 𝐻0 : 𝜇 = 57, 𝐻1 : 𝜇 > 57, 𝑥̅ = 65, 𝑠 = 12, 𝑛 = 42
SCHOOL OF PUBLIC POLICY
GEORGE MASON UNIVERSITY
FALL 2010
OLMSTEAD
11. Atlas Sporting Goods has implemented a special trade promotion for its propane stove and feels that the
promotion should result in a price change for the consumer. Atlas knows that before the promotion
began, the average retail price of the stove was $44.95, with a standard deviation of $5.75. Atlas samples
25 of its retailers after the promotion begins and finds the mean price for the stoves is now $42.95. At a
.02 significance level, does Atlas have reason to believe that the average retail price to the consumer has
decreased?
12. If a sample of 25 observations reveals a sample mean of 52 and a sample variance of 4.2, test the
hypothesis that the population mean is 65, against the alternative that it is some other value. Use the .01
significance level.
13. To celebrate their first anniversary, Randy decided to buy a pair of diamond earrings for his wife Debbie.
He was shown nine pairs with marquise gems weighing approximately 2 carats per pair. Because of
differences in the colors and qualities of the stones, the prices varied from set to set. The average price
was $2,990, with a sample standard deviation of $370. He also looked at six pairs with pear-shaped
stones of the same two–carat approximate weight. These earrings had an average price of $3,065, with a
standard deviation of $805. On the basis of this evidence, can Randy conclude (at a significance level of
.05) that pear-shaped diamonds cost more, on average, than marquise diamonds?
14. Donna is a production supervisor on the disk-drive assembly line at Winchester Technologies.
Winchester recently subscribed to an easy-listening music service at its factory, hoping that this would
relax the workers and lead to greater productivity. Donna is skeptical about this hypothesis and fears the
music will be distracting, leading to lower productivity. She sampled weekly production for the same six
workers before the music was installed and after it was installed. Her data are given below. At α = .02,
has average production changed at all?
EMPLOYEE
Week without music
Week with music
1
219
235
2
205
186
3
226
240
4
198
203
5
209
221
6
216
205