Test 4A AP Statistics Name:

Part 1: Multiple Choice. Circle the letter corresponding to the best answer.

1. A new headache remedy was given to a group of 25 subjects who had headaches. Four hours after
taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this
information you conclude
(a) that the remedy is effective for the treatment of headaches.
(b) nothing, because the sample size is too small.
(c) nothing, because there is no control group for comparison.
(d) that the new treatment is better than aspirin.
(e) that the remedy is not effective for the treatment of headaches.

2. We wish to draw a sample of 5 without replacement from a population of 50 households. Suppose

the households are numbered 01, 02, . . . , 50, and suppose that the relevant line of the random
number table is 11362 35692 96237 90842 46843 62719 64049 17823.
Then the households selected are
(a) households 11 13 36 62 73
(b) households 11 36 23 08 42
(c) households 11 36 23 23 08
(d) households 11 36 23 56 92
(e) households 11 35 96 90 46

3. A maple sugar manufacturer wants to estimate the average trunk diameter of Sugar Maples trees in
a large forest. There are too many trees to list them all and take a SRS, so he divides the forest
into several hundred 10 meter by 10 meter plots, selects 25 plots at random, and measures the
diameter of every Sugar Maple in each one. This is an example of a
(a) multistage sample.
(b) stratified sample.
(c) simple random sample.
(d) cluster sample.
(e) convenience sample.

4. A researcher for a consumer products company is field testing a new formula for laundry detergent.
He has contracted with 60 families, each with two children, who have agreed to test the product.
He randomly assigns 30 families to the group that will use the new formula and 30 to the group
that will use the company’s current detergent formula. The most important reason for this random
assignment is that
(a) randomization makes the analysis easier since the data can be collected and entered into the
computer in any order.
(b) randomization eliminates the impact of any confounding variables.
(c) randomization is a good way to create two groups of 30 families that are as similar as possible,
so that comparisons can be made between the two groups.
(d) randomization ensures that the study is double-blind.
(e) randomization reduces the impact of outliers.

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5. To test the effect of music on productivity, a group of assembly line workers are given portable
mp3 players to play whatever music they choose while working for one month. For another month,
they work without music. The order of the two treatments for each worker is determined
randomly. This is
(a) an observational study.
(b) a matched pairs experiment.
(c) a completely randomized experiment.
(d) a block design, but not a matched pairs experiment.
(e) impossible to classify unless more details of the study are provided.

6. A survey was done in the town of Mechanicsville to estimate the proportion of cars that are red and
made by companies based in Japan. A simple random sample of 25 cars from a parking lot at Lee-
Davis High School was taken. Which of the following statements is correct?
(a) Since this is a simple random sample, it should be representative of all the cars in
Mechanicsville.
(b) If a simple random sample of 15 cars were taken, we would expect the same amount of
variability in the proportion of red cars as we would with a sample of 25 cars.
(c) An alternative method for getting a representative sample would be to select the 25 cars closest
to a specified location, such as the entrance to the gymnasium.
(d) A different team doing the sampling independently would probably obtain a slightly different
answer for their sample proportion.
(e) The results would be the same regardless of the time of day that the sample is taken.

7. A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of
vitamin C present in freeze dried fruit when stored for these lengths of time. Six fruit packs were
randomly assigned to each of the three storage times. The treatment, experimental unit, and
response are respectively:
(a) A specific storage time, amount of vitamin C, a fruit pack
(b) A fruit pack, amount of vitamin C, a specific storage time
(c) Random assignment, a fruit pack, amount of vitamin C
(d) A specific storage time, a fruit pack, amount of vitamin C
(e) A specific storage time, six fruit packs, amount of vitamin C

8. 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. Which of the
following is the most plausible explanation for this observed association?
(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 Major League Baseball teams
(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 confounding (Major League teams tend to be in large cities with more
people, hence a greater number of divorces).
(d) The association makes no sense, since many married couples go to the ballpark together.
(e) The association is purely coincidental. It is implausible to believe the observed association
could be anything other than accidental.

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9. Control groups are used in experiments in order to accomplish which one of the following?
(a) Limit the effects of variables other than the explanatory variable on the outcome.
(b) Control the subjects of a study to ensure that all participate equally.
(c) Guarantee that someone other than the investigators, who have a vested interest in the outcome,
controls how the experiment is conducted.
(d) Achieve a proper and uniform level of randomization.
(e) Reduce variability in results.

10. A survey is to be administered to recent graduates of a certain nursing school in order to compare
the starting salaries of women and men. For a random sample of graduates, three variables are to be
recorded: sex, starting salary, and area of specialization. Which of the following best describes a
conclusion that can be drawn from this study?
(a) Whether being female causes graduates of this nursing school to have lower (or higher) starting
salaries than males.
(b) Whether being female causes graduates in this sample to have lower (or higher) starting salaries
than males.
(c) Whether choosing a certain area of specialization causes females graduates of this nursing
school to have lower (or higher) starting salaries than males.
(d) Whether there is an association between sex and starting salary among graduates of this nursing
school.
(e) Whether there is an association between sex and starting salary at all nursing schools.

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 Part 2: Free Response
Show all your work. Indicate clearly the methods you use, because you will be graded on the
correctness of your methods as well as on the accuracy and completeness of your results and
explanations.

11. Read the following brief article about aspirin and alcohol.
Aspirin may enhance impairment by alcohol
Aspirin, a long time antidote for the side effects of drinking, may actually enhance alcohol’s effect, researchers at
the Bronx Veterans’ Affairs Medical Center say. In a report on a study published in the Journal of the American
Medical Association, the researchers said they found that aspirin significantly lowered the body’s ability to break
down alcohol in the stomach. As a result, five volunteers who had a standard breakfast and two extra-strength
aspirin tablets an hour before drinking had blood alcohol levels 30 percent higher than each had when they drank
alcohol alone. Each volunteer consumed the equivalent of a glass and a half of wine.
That 30 percent could make the difference between sobriety and impairment, said Dr. Charles S. Lieber, medical
director of the Alcohol Research and Treatment Center at the Bronx center, who was co-author of the report with
Dr. Risto Roine.

(a) Explain why this is an experiment and not an observational study.

(b) Identify the explanatory and response variables.

(c) Identify the experimental design used in this study. Justify your answer.

(d) In the second sentence above is the phrase, “…researchers said they found that aspirin
significantly lowered the body’s ability to break down alcohol…” What is the statistical
meaning of the word “significantly” in the context of this study?

(e) This was a controlled experiment. Describe how it was controlled and explain the purpose of
doing so.

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12. High blood pressure adds to the workload of the heart and arteries and may increase the risk of
heart attacks. If not treated, this condition can also lead to heart failure, kidney failure, or stroke.
We wish to test the effectiveness of Angiotensin-converting enzyme (ACE) inhibitors as a
treatment for high blood pressure.

(a) It is well known that men and women may react differently to common cardiovascular drug
treatments. What sort of experimental design would you choose for this study, and why?

(b) Explain why an experiment involving 600 men and 500 women is preferable to one involving
60 men and 50 women.

(c) Assume that 600 men and 500 women suffering from high blood pressure are available for the
study. Describe a design for this experiment. Be sure to include a description of how you
assign individuals to the treatment groups.

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13. Bias is present in each of the following sampling designs. In each case, identify the type of bias
involved and state whether you think the sample result obtained is lower or higher than the actual
value for the population.

(a) A political pollster seeks information about the proportion of American adults who oppose gun
controls. He asks an SRS of 1000 American adults: “Do you agree or disagree with the
following statement: Americans should preserve their constitutional right to keep and bear
arms.” A total of 910, or 91%, said, “Agree” (that is, 910 out of the 1000 oppose gun controls).

(b) A flour company in Minneapolis wants to know what percent of local households bake at least
twice a week. A company representative calls 500 randomly-selected households during the
daytime and finds that 50% of those who responded bake at least twice a week.

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