Sampling and Experiments Worksheet with Answers – AP Statistics (Free PDF)

Problem 1 Statistical or Not ★★★

Decide whether each question is a statistical question (one that expects variability in the answers). Explain briefly.

1. How many players are on the roster of the Lincoln High soccer team?
2. How many text messages do Lincoln High students send on a typical day?
3. What is the height of each player on the soccer team?

Problem 2 Systematic Sampling ★★★

A principal has an alphabetical list of 800 students. She randomly picks a starting number from 1 to 20, gets 4, and surveys the 4th student, then every 20th student after that. Name the sampling method and explain why it is not an SRS.

Problem 3 Identifying Cluster Sampling ★★★

A county has 36 bus routes. The transportation office randomly selects 5 routes and surveys every rider on those 5 routes. Name the sampling method and state one advantage and one risk.

Problem 4 Stratified Sample Design ★★★

A fitness club wants opinions on a new class schedule. The 30 members shown are grouped by membership type (each row is one type). One member is chosen from every row.

Name the sampling method and explain why a club would choose it instead of an SRS.

Problem 5 Voluntary Response Bias ★★★

A radio station asks listeners to call in and vote on whether the city should build a new skate park. 412 listeners call; 361 vote yes. Explain why the 87.6% yes figure should not be generalized to all residents of the city.

Problem 6 Undercoverage ★★★

A pollster selects a random sample of numbers from the landline phone directory to estimate the percent of adults in a town who support a school bond. Identify the type of bias and the direction in which it is likely to affect the estimate if younger adults support the bond more than older adults.

Problem 7 Wording and Response Bias ★★★

A survey asks: “Don’t you agree that the cafeteria should stop selling delicious, affordable pizza?” (a) Identify the problem. (b) Rewrite the question so that it is neutral.

Problem 8 Observational Study or Experiment ★★★

Classify each study as an observational study or an experiment.

1. Researchers examine school records and compare the grades of students who play an instrument with those who do not.
2. A coach randomly assigns 30 swimmers to one of two warm-up routines and compares their 100-meter times.
3. A nurse asks patients how many hours they sleep and records their blood pressure.

Problem 9 Confounding Variables ★★★

A study finds that people who drink at least 3 cups of tea a day have a lower rate of heart disease. The researchers did not assign how much tea anyone drank. Identify the explanatory and response variables and describe a possible confounding variable.

Problem 10 Random Assignment with Random Numbers ★★★

Twenty hikers, labeled 1 to 20, will test two types of boots. A calculator generates these integers from 1 to 20: 3, 13, 1, 17, 3, 20, 4, 11, 5, 13, 4, 1, 16, 3, 18, 1, 6, 19, 6, 7, 5, 17, 5, 10, 14, 9, 18, 2, 9, 11. Use the list, skipping repeats, to choose 10 hikers for the new boots. Which hikers get the new boots?

Problem 11 Parts of an Experiment ★★★

The diagram shows an experiment on a headache drug.

Identify the experimental units, the explanatory variable, its treatments and the response variable.

Problem 12 Why Blinding Matters ★★★

In a study of a new back brace, the patients know whether they received the brace or a sham brace, and the doctor who rates their pain also knows. Explain how a double-blind design would remove bias, and describe who must be blinded.

Problem 13 Randomized Block Design ★★★

A gardener tests two fertilizers on 20 rose plants. Ten are young plants and ten are mature plants, and age strongly affects growth.

Explain why blocking by age is better than a completely randomized design here and describe how to randomize.

Problem 14 Matched Pairs Design ★★★

A researcher compares two brands of running shoes using 15 runners. Describe a matched-pairs design where each runner tests both brands, including how randomization is used and what is compared.

Problem 15 Scope of Inference ★★★

For each study, state whether the results can be generalized to a larger population, whether a cause-and-effect conclusion is justified, or both.

1. A school randomly samples 120 of its 1,500 students and asks about sleep. No treatment is imposed.
2. Twenty-four volunteers from a gym are randomly assigned to one of two diets and weight changes are compared.
3. A random sample of 200 adults in a state is chosen and each is randomly assigned to one of two reminder letters; later the response rates are compared.

Problem 16 Sample Size and Variability ★★★

A pollster takes many random samples of size 50 and many random samples of size 800 from the same large population. The sample proportions from the size-50 samples range from 0.30 to 0.70; those from the size-800 samples range from 0.45 to 0.55. What does this show about sample size? Does a larger sample remove bias from a poorly designed survey?

Problem 17 Design an Experiment ★★★

A school wants to find out whether listening to instrumental music while studying changes vocabulary quiz scores. Eighty volunteers are available. Describe a completely randomized design, including treatments, random assignment, control and the comparison.

Problem 18 Critique a Flawed Experiment ★★★

A teacher wants to know whether flashcards help students learn spelling words. She gives flashcards to her first-period class and none to her fifth-period class, then compares their test scores. First period meets at 8 a.m. and fifth period right after lunch. Explain why she cannot conclude that flashcards cause a difference and suggest an improvement.

Problem 19 Multiple Sources of Bias ★★★

A company mails a questionnaire to 3,000 customers chosen at random and asks, “How satisfied are you with our fantastic, award-winning service?” Only 270 customers return it. Identify two sources of bias and explain how each could affect the result.

Problem 20 Interpreting a Study Result ★★★

Sixty volunteers from a college were randomly assigned to walk 15 minutes (30 students) or sit quietly 15 minutes (30 students) before a memory test. The bar graph shows the mean scores.

The difference (78 − 64 = 14 points) is much larger than expected from random assignment alone. What conclusion about cause and effect is justified? To whom can the results be extended?