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AP Statistics Unit 3: Collecting Data

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Unit 3: Collecting Data

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Question 1

A researcher conducts an experiment on pain relief using a matched pairs design. Each of 25 participants tries both Drug A and Drug B on different days, with order randomly assigned. What is the primary advantage of this design over a completely randomized design?

A.It eliminates the placebo effect entirely.B.It reduces variability by controlling for individual differences in pain sensitivity.C.It doubles the effective sample size by using each person twice.D.It allows the researcher to test more than two treatments simultaneously.

Question 2

An experiment randomly assigns participants to one of three diets. After 8 weeks, mean weight loss is compared across groups. Which principle of experimental design ensures that unmeasured variables (like initial metabolism) are evenly distributed among the groups?

A.ReplicationB.ControlC.Random assignmentD.Blinding

Question 3

Researchers studying the effect of sleep on memory randomly assign 30 college students to either 6 hours or 8 hours of sleep, then test their recall the next morning. What is the explanatory variable?

A.Memory recall scoreB.Hours of sleepC.The college studentsD.Whether the study was blinded

Question 4

An experiment randomly assigns 40 patients to receive a new drug or a placebo. Neither the patients nor the doctors evaluating outcomes know which treatment each patient received. What design feature does this describe?

A.ReplicationB.BlockingC.Double-blind designD.Matched pairs design

Question 5

A survey asks: "Do you agree that the city council wastes taxpayer money on unnecessary projects?" What problem does this question have?

A.The question does not use a random sampling method.B.The question is too short to collect meaningful data.C.The question is leading and will likely produce response bias toward agreement.D.The question is subject to nonresponse bias.

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Question 6

A stratified random sample is taken to estimate average income in a city. The population is divided into three strata by neighborhood. Why might stratification produce a more precise estimate than a simple random sample of the same size?

A.Stratification eliminates all bias in the sample.B.Stratification ensures representation from every neighborhood, reducing variability between strata from contaminating the estimate.C.Stratification allows researchers to use larger sample sizes.D.Stratification is only useful when all strata have equal population sizes.

Question 7

A call center randomly selects 50 of its 500 daily calls to monitor for quality. This is an example of what type of sample, and what is its main advantage over a census?

A.Convenience sample; easier to obtainB.Simple random sample; it reduces cost and time while providing unbiased estimatesC.Cluster sample; entire groups of calls are selectedD.Systematic sample; it eliminates variability

Question 8

In an experiment on plant growth, a researcher uses 24 plants from 6 different species (4 of each). She randomly assigns 2 plants of each species to receive fertilizer and 2 to a control group. What design is this?

A.Completely randomized designB.Randomized block design with species as the blocking variableC.Matched pairs designD.Stratified random sample

Question 9

A researcher observes that students who eat breakfast score higher on standardized tests than those who skip breakfast, using data from a voluntary survey. She concludes that eating breakfast improves test scores. Why is this an invalid causal conclusion?

A.The sample size from a voluntary survey is always too small.B.The data are observational; students were not randomly assigned to eat or skip breakfast, so confounding variables may explain the difference.C.Test score differences between groups cannot be measured accurately.D.Voluntary surveys always overrepresent students who skip breakfast.

Question 10

A study finds that towns with more fast-food restaurants have higher rates of obesity. A researcher concludes that fast food causes obesity. Which of the following is the strongest critique of this conclusion?

A.The sample size is too small to draw conclusions.B.This is an observational study; confounding variables (such as income level or physical activity norms) may explain the association.C.Correlation between these variables is always spurious.D.A randomized experiment should have been used to compute the correlation.

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Question 11

A researcher wants to survey voters about a proposed tax increase. She mails surveys to all registered voters, but only 8% respond. Which bias is most likely present?

A.Undercoverage biasB.Response biasC.Nonresponse biasD.Voluntary response bias

Question 12

A school wants to estimate the proportion of students who bike to school. They survey every 10th student on the enrollment list. What type of sampling method is this?

A.Simple random sample (SRS)B.Systematic random sampleC.Stratified random sampleD.Cluster sample

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