AP Statistics
Chapter 5 PRACTICE
Name
1. The results of an experiment are said to be statistically significant if... ?
(a) they are important to statisticians, regardless of their importance to the investigators.
(b) both investigators and statisticians agree the results are meaningful and important.
(c) they are important to the investigators, regardless of their importance to the statisticians.
(d) the observed effect is too large to attribute plausibly to chance.
(e) they support the findings of previous, similar studies.
2. In addition to control by comparing several treatments, the other two principles that are important in
well designed experiments: (choose two)
(a) randomization by assigning researchers by chance
(b) randomization by assigning subjects by chance
(c) replication by doing a study more than once
(d) replication by doing a study with many subjects
(e) blocking to remove bias
3. A placebo is
(a) an experimental treatment.
(b) a control treatment.
(c) a source of bias.
(d) double-blind.
(e) important for replication.
4. For each of the following, choose TRUE or FALSE.
The people in this statistics class are
(a) a sample of the juniors & seniors at Newton South
(b) a sample of all high school juniors & seniors in the U.S.
(c) a representative sample of all students at Newton South
(d) a random sample of all students at Newton South
(e) not a sample.
5. Which error or bias would be most worrisome in conducting a daytime door-to-door survey
of political opinions?
(a) computational errors
(b) interviewer contamination
(c) lack of double-blind setup
(d) non-response
(e) false information given by the subjects
6. Analyze the following situation for sources of bias, and discuss whether the sample statistic is likely
to be higher or lower than the population parameter.
A political pollster seeks information about the proportion of Americans that oppose gun control.
The organization asks a simple random sample of 1000 American adults: "do you agree or disagree
that Americans should preserve their constitutional right to keep and bear arms?" 91% of the people
agreed.
7. In a study on the effect of reinforcement on learning from texts, one group of students is given candy
after each page they read, while another group gets candy at random with probability 1/3 after each
page. What would be a good control group for this experiment?
8. In a study to determine the effectiveness of various training methods, the cross-country team at
Newton South is randomly divided into three groups. Group 1 does interval training on the track,
group 2 does long slow runs on hills, and group 3 does stadiums.
What is/are factors in this experiment?
What is/are the treatments?
Levels of the treatments?
What would be explanatory variable(s)?
What would be response variable(s)?
9. Design an experiment to determine whether ballet lessons improve professional baseball players'
batting averages. Think especially carefully about what to use as a control group. Is matched pairs
appropriate?
10. In a survey of computer use in schools, surveys were mailed to 10,000 randomly selected high
school teachers in the country. Of the 3,600 who returned the survey, 27% said they had easy access
to computers. How would you respond to someone who claimed "27% of high school teachers have
easy access to computers?" [Of course, it's easy to criticize, it's a lot harder to figure out how to get
better data!]
11. A study of weight training attempts to determine which of two methods gives greater gains in
strength. Describe a design for an experiment whose population is the members of a particular gym.
12. Why do almost all studies use a sample instead of attempting to reach everyone in the population of
interest?
13. Why is randomization always a good idea?
ANSWERS
1. d
2. b and d
3. b
4. All are false.
5. d
6. Response bias (due to question wording). It should be phrased more neutrally. For example, "Do you
support or oppose regulations that limit access to certain types of guns?" Probably it's less than 91%
in the population.
7. a group that got no candy
8. The factors are the explanatory variable: type of training. The treatments are the three training
methods. Levels would be different amounts of each type of training, but here it implies that there's
only one level for each treatment. The response variable might be the time in the next cross-country
race. It would be good to have some controls or matched pairs/triples (people who ran the same
speed in previous races; or have each person rotate through the three types of training in a random
order and see which one gives the biggest improvement).
9. I'd block them by previous year's batting average, then randomly sample from each, make half of
them take ballet lessons during the off season, and then compare the mean change in batting average
in those who took the lessons versus the mean change in those who didn’t.
10. It's junk, because of nonresponse. Who knows what the other 64% of the teachers who didn't return
the survey might be thinking? There’s no obvious bias in one direction or another, but that doesn’t
mean that this is a representative sample.
11. Pretty good method: First, give a pretest to divide them into blocks based on current strength. Then,
within each block, randomly assign half to each method; finally, measure the change in strength.
Better method: Give the pretest, then give a random half of the people method 1 first, the other half
method 2 first. Then, measure the mean gain in strength for each method. Using each person as
his/her own comparison is almost always the best control!
12. Because it's too much work/too expensive to ask everyone.
13. Because there may be lurking variables you're unaware of, and randomization helps to even out their
effects.