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ACT Math Help: Data Collection Methods

Review real example questions for Data Collection Methods in ACT Math.

Question 1 / 10

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A company wants to understand employee satisfaction. They send a survey to a random sample of 100 employees. Which sampling method is being used?

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Question 1

A company wants to understand employee satisfaction. They send a survey to a random sample of 100 employees. Which sampling method is being used?

  1. Convenience sampling
  2. Systematic sampling
  3. Random sampling (correct answer)
  4. Stratified sampling

Explanation: This question tests sampling vocabulary, so the method is identified by how the members of the sample were selected, not by how large the sample is. The problem says the 100 employees were chosen as a random sample, meaning every employee had an equal, chance-based probability of being picked, which is exactly the definition of random sampling; that is why the answer is random sampling. Convenience sampling would mean grabbing whoever was easiest to reach, such as the employees on one floor, and it fails here because nothing about the selection was based on accessibility. Systematic sampling would require an ordered list and a fixed interval like every 10th employee, and stratified sampling would require first splitting the workforce into groups such as departments and then sampling within each group, and neither of those extra structures is described. To classify a sampling method, look only for the selection rule in the wording, since each method is defined by its rule rather than by the size or quality of the resulting sample.

Question 2

A nutritionist wants to study the eating habits of teenagers. They observe what teenagers purchase at a school cafeteria without any interaction. Is this an experiment or an observational study?

  1. Experiment, because data is collected directly
  2. Observational, because there's no interference (correct answer)
  3. Experiment, because of controlled environment
  4. Observational, because it's in a natural setting

Explanation: This is an observational study because the nutritionist passively observes teenager purchasing behaviors without manipulating or interfering with their food choices. Observational studies involve collecting data on naturally occurring behaviors without imposing any treatments or interventions. The researcher simply records what students choose to buy without influencing their decisions or changing the cafeteria environment. Choice A incorrectly suggests this is an experiment - experiments require active manipulation of variables, not just data collection.

Question 3

A researcher wants to estimate average sleep time for students at a large high school. She divides students by grade level and then randomly selects 40 students from each grade to keep a sleep diary for a week. Some students might forget to record sleep. Which sampling method is being used?

  1. Systematic sample by selecting every 40th student from a single combined roster
  2. Stratified sample by selecting random students within each grade level group (correct answer)
  3. Convenience sample by selecting students who are in the researcher's classes
  4. Cluster sample by selecting one grade and surveying every student in that grade

Explanation: This is a stratified sample because the researcher divides students into grade-level strata and then randomly selects participants from within each stratum. Stratified sampling ensures representation from each important subgroup by sampling within predefined categories. By selecting 40 students from each grade level, the researcher guarantees proportional representation across all grades. Choice A incorrectly describes systematic sampling, which would involve selecting every nth student from a single ordered list.

Question 4

A city council wants to gauge the public's reaction to a new policy. They conduct a phone survey using a random digit dial method. Which sampling method is being used?

  1. Stratified sampling
  2. Convenience sampling
  3. Systematic sampling
  4. Random sampling (correct answer)

Explanation: This is random sampling because the random digit dial method gives every phone number (and thus every household) an equal chance of being selected for the survey. Random sampling is characterized by each member of the population having an equal probability of selection. The random digit dial technique ensures that the selection process is not influenced by convenience, location, or other systematic factors. Convenience sampling (Choice B) would involve selecting easily accessible respondents rather than using a random selection process.

Question 5

A health department wants to know whether people who bike to work report lower stress. They survey commuters about how they travel and their stress level, without asking anyone to change their commute habits. Some people may misreport their stress. Is this an experiment or an observational study?

  1. Experiment because commuters are compared in two groups based on biking or not biking
  2. Observational study because the researchers do not assign how people commute (correct answer)
  3. Experiment because the survey includes a large number of commuters
  4. Observational study because commuters are randomly assigned to bike or drive

Explanation: This is an observational study because researchers collect data on existing behaviors without manipulating or assigning commute methods. Observational studies involve measuring variables as they naturally occur without researcher intervention. The health department simply surveys people about their current commuting habits and stress levels without asking anyone to change their behavior. Choice A incorrectly suggests this is an experiment, but experiments require researchers to assign treatments.

Question 6

A researcher wants to learn whether a new 5-minute stretching routine reduces muscle soreness after running. She randomly assigns 60 runners to either do the stretching routine after each run or to keep their usual cool-down routine, then compares reported soreness after two weeks. Is this an experiment or an observational study?

  1. Observational study because the runners report their own soreness
  2. Experiment because the researcher assigns runners to different routines (correct answer)
  3. Observational study because the researcher does not control how far they run
  4. Neither, because two weeks is not long enough to study soreness

Explanation: This is an experiment because the researcher assigns runners to different routines (treatment groups). In an experiment, the researcher actively manipulates or assigns the treatment - here, randomly assigning runners to either do the new stretching routine or keep their usual routine. The random assignment of treatments is the hallmark of an experiment, allowing causal conclusions about the stretching routine's effect. Choice A incorrectly calls it observational because runners self-report soreness, but self-reporting the outcome doesn't make it observational - what matters is that treatments were assigned.

Question 7

A researcher wants opinions about cafeteria food at a large university. She divides students into groups by year (first-year, sophomore, junior, senior) and randomly selects 50 students from each year to survey. This helps ensure each year is represented. Which sampling method is being used?

  1. Simple random sample by choosing only students from one randomly selected dorm
  2. Convenience sample by surveying students who are already eating in the cafeteria
  3. Systematic sample by selecting every 50th student entering the cafeteria
  4. Stratified sample by sampling randomly within each class year group (correct answer)

Explanation: This is a stratified sample because the researcher divides the population into distinct subgroups (year levels) and then randomly samples from each stratum. Stratified sampling ensures representation from each important subgroup by sampling within predefined categories. By sampling 50 students from each year, the researcher guarantees that all class years are proportionally represented. Choice B incorrectly suggests convenience sampling, which would involve surveying only easily accessible students without systematic stratification.

Question 8

To choose a new school mascot, a student council surveys 300 students by standing at the entrance to the gym during a varsity basketball game. Students who don't attend games are underrepresented. Which sampling method is being used?

  1. Systematic sample because the council surveys a fixed number of students
  2. Simple random sample because any student could attend the game and be surveyed
  3. Convenience sample because the survey targets students who are easy to reach at the game (correct answer)
  4. Stratified sample because students are automatically grouped by grade in the gym

Explanation: This is a convenience sample because the council surveys students who are easily accessible at the basketball game location. Convenience sampling occurs when researchers select participants based on availability rather than through a systematic sampling method. Students who don't attend games are systematically excluded, creating bias toward more school-spirited students. Choice B incorrectly suggests random sampling, but random sampling would give every student an equal chance of selection regardless of game attendance.

Question 9

A student wants to estimate the average price of a textbook at her college bookstore. She records the prices of the first 30 textbooks she sees on the "New Arrivals" shelf. That shelf mostly contains expensive new editions. Which characteristic makes this sample biased?

  1. The bookstore is on campus, so the results will generalize to all bookstores
  2. The sample size is 30, which is always too small to estimate an average
  3. Textbook prices are measured in dollars, which introduces measurement error
  4. The sample comes from a single shelf that may not represent all textbooks sold (correct answer)

Explanation: Sampling from only the 'New Arrivals' shelf creates bias because this shelf likely contains expensive new editions that don't represent the full range of textbook prices. Location-based sampling bias occurs when the sampling location systematically includes items with different characteristics than the overall population. The new arrivals shelf would overrepresent recently published, higher-priced textbooks compared to the complete bookstore inventory. Choice B incorrectly suggests sample size is always the issue, but 30 can be adequate if sampled representatively.

Question 10

A sports scientist tests a new hydration drink. She randomly assigns athletes to drink either the new drink or plain water during practice, then measures their sprint times afterward. Athletes know what they drank, which could affect effort. To reduce bias, the researchers should:

  1. Let athletes choose which drink they want, so the groups feel more comfortable
  2. Use a blinded setup where drinks look the same, so athletes don't know which they got (correct answer)
  3. Survey only the fastest athletes, since they provide the most reliable sprint times
  4. Test only athletes who already like the new drink, to avoid negative opinions

Explanation: Using a blinded setup reduces bias by preventing athletes from knowing which drink they received, eliminating placebo effects and expectation bias. Blinding ensures that participants' knowledge of their treatment doesn't influence their performance or responses. When athletes know they received the 'new' drink, they might unconsciously perform differently due to expectations rather than the drink's actual effects. Choice A would introduce bias by allowing self-selection, which could confound results with personal preferences.