AP Stats Ch 11-13 Multiple Choice Practice

Two studies are run to compare the experiences of low-income families receiving food stamps to those receiving cash subsidies. The first study interviews 50 families who have been in each government program for at least two years, which the second randomly assigns 50 families to each program and interviews them after 2 years. Which of the following is a true statement?

• Both studies are observational studies because of the time period involved.

• Both studies are observational studies because there is no control group.

• The first study in an observational study; the second is an experiment.

• The first study is an experiment; the second is an observational study.

• Both studies are experiments, because in each, families are receiving treatments (food stamps or cash).

Answer explanation

In the first study, the families were already receiving assistance; in the second study, one of two treatments was applied to each family.

Fifty migraine patients are randomly selected from hospital records. Half the patients are told to drink ice water and sit in the dark when they next experience a migraine; the remaining patients are told to use neither of these possible remedies. Participants then report back as to relief, if any. Serious faults of this experimental design include which of the following?

I. Lack of randomization

II. Probable confounding variables

III. Lack of blinding

• I only

• II only

• III only

• I and II

• II and III

Answer explanation

There is no indication that randomization is being used to decide which patients have the treatment and which patients are in the control group. If the treatment of ice water and darkness helps, there is no way to tell whether ice water or darkness of combination of both is responsible, so the variables will be confounded. Lack of blinding is not a design fault here because blinding is impossible in this experiment.

A sales representative wishes to survey her client base of 47 companies. She has 47 business cards, all of the identical size, from her contacts in the companies, and decides to drop them all in a small box, shake them up, and reach in to pick 5 cards for her sample. This procedure is an example of which type of sampling?

• Cluster

• Convenience

• Simple random

• Stratified

• Systematic

Answer explanation

A simple random sample is one in which every possible sample of the desired size has an equal chance of being selected. In this case, every possible sample of 5 companies has an equal chance of being selected.

A town has one high school, which buses students from urban, suburban, and rural communities. Which of the following sampling techniques is most recommended in studying attitudes of military enlistment after high school graduation for this particular high school?

• Cluster sample

• Simple random sample

• Stratified sample

• Systematic sample

• Voluntary response sample

Answer explanation

In stratified sampling, the population is divided into homogenous groups called strata, and random samples of people from all strata are chosen. In this case, it might well be important to be able to consider separately the responses from each of the three groups (urban, suburban, and rural).

Which of the following is most useful in establishing cause-and-effect relationships?

• A complete census

• A least-squares regression line showing high correlation

• A simple random sample

• A well-designed, well-conducted survey incorporating chance to ensure a representative sample

• A controlled experiment

Answer explanation

Regression lines show association, not causation. Surveys suggest relationships, which controlled experiments can help show to be cause and effect.

Sampling error occurs

• When interviewers make mistakes resulting in bias.

• When interviewers use judgment instead of random choice in picking the sample.

• When samples are too small.

• Because a sample statistic is used to estimate a population parameter.

• In all of the cases.

Answer explanation

Different samples give different sample statistics, all of which are estimates for the same population parameter, and so error, called sampling error, is naturally present.

What is bias in conducting surveys?

• An example of sampling error

• Lack of a control group

• Confounding variables

• Difficulty in concluding cause and effect

• A tendency to favor the selection of certain members of a population or to favor a certain answer.

Answer explanation

Poorly designed sampling techniques result in bias, that is, in a tendency to favor the selection of certain members of a population.

A study is made on whether or not a particular review book helps students achieve high scores on AP exams. In comparing records of 100 students, half of whom purchased the review book, it is noted that the average AP score is higher for those 50 students who purchased the book. Which of the following are true statements?

I. While this study indicates a relationship, it does not prove causation.

II. There could well be a lurking variable responsible for the seeming relationship.

III. Self-selection here makes drawing a conclusion difficult.

• I and II

• I and III

• II and III

• I, II, and III

• None of the answers give the complete set of true responses.

Answer explanation

It may well be that the brightest, most motivated students are the same ones who purchased the review book and do well on the AP exam. If the students could be randomly assigned to purchase or not purchase the book, the results would be more meaningful.

To find out a town's average family size, a researcher interviews a random sample of parents arriving at a pediatrician's office. The average family size in the final 100-family sample is 3.48. Is this estimate probably too low or too high?

• Too low because of undercoverage bias.

• Too low because convenience samples underestimate average results.

• Too high because of undercoverage bias.

• Too high because convenience samples overestimate average results.

• Too high because voluntary response samples overestimate average results.

Answer explanation

The procedure and location described misses all or nearly all childless families.

Which of the following are true statements about blocking?

I. Blocking is to experimental design as stratification is to sampling design.

II. By controlling certain variables, blocking can make conclusions more specific.

III. The paired comparison design is a special case of blocking.

• I and II

• I and III

• II and III

• I, II, and III

• None of the combinations listed gives the complete set of true responses.

Answer explanation

Blocking in experimental design first divides the subjects into representative (homogeneous) groups called blocks, just as stratification in sampling divides subjects into homogenous groups called strata. This procedure can control certain variables by bringing them directly into the picture, and thus conclusions are more specific. The paired comparison (aka matched pairs) design is a special case of blocking in which each pair can be considered a block.