ACT Math Quiz: Data Collection Methods

What this quiz covers

This quiz focuses on Data Collection Methods, giving you a quick way to practice the rules, question types, and explanations that matter most for ACT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

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

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

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

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 5

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 6

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 7

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 8

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 9

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.

Question 10

1. The layouts are tested for a full month, so the sample is too large
2. Different stores may have different customers, so layout is mixed with neighborhood effects (correct answer)
3. Sales are measured in dollars, which is a quantitative outcome
4. The study compares two layouts, which makes it an observational study

Explanation: Different customer bases between neighborhoods create confounding bias because layout effects cannot be separated from neighborhood demographic differences. The comparison is biased because Store 1 and Store 2 serve different populations who might have different shopping behaviors regardless of shelf layout. Any sales difference could be due to neighborhood characteristics rather than the layout intervention. Choice A incorrectly suggests sample size is the issue, but the problem is confounding variables, not sample size.

Question 11

1. Experiment (correct answer)
2. Observational study
3. Survey
4. Census

Explanation: This is an experiment because researchers actively manipulate the teaching method by assigning different treatments to different classes. Experiments involve imposing treatments on subjects to establish causal relationships between variables. The comparison of test scores between classes using different teaching methods allows researchers to assess the impact of the intervention. An observational study (Choice B) would simply observe existing teaching practices without actively assigning different methods to different groups.

Question 12

1. Cluster sample by selecting two dorm buildings and surveying everyone in those buildings
2. Stratified sample by sampling randomly within on-campus and off-campus groups (correct answer)
3. Convenience sample by surveying students who are currently eating in the dining hall
4. Systematic sample by choosing every 200th student from the full list

Explanation: This is a stratified sample because the university divides students into two distinct housing categories (on-campus and off-campus) and randomly samples from each stratum. Stratified sampling ensures representation from each important subgroup by sampling within predefined categories. By selecting 200 students from each housing type, the university guarantees equal representation from both living situations for comparison purposes. Choice A incorrectly describes cluster sampling, which would involve selecting entire buildings and surveying all residents within them.

Question 13

1. Observational study because the company only measures test scores without changing anything
2. Experiment because the company assigns a training video and measures the outcome (correct answer)
3. Observational study because both groups are new hires and not randomly sampled
4. Experiment because the company surveys employees about which video they prefer

Explanation: This is an experiment because the company actively assigns treatments (Video A or Video B) to subjects and controls the explanatory variable. Experiments involve researcher manipulation of conditions to observe effects on outcomes. The company randomly assigns which video each new hire watches, making this an experimental design rather than passive observation. Choice A incorrectly calls this observational, but observational studies do not involve researcher assignment of treatments.

Question 14

1. Convenience sampling because students are selected from the teacher's school
2. Stratified sampling because random samples are taken separately from each grade (correct answer)
3. Systematic sampling because the teacher chooses students at regular intervals
4. Simple random sampling because every student answers the survey

Explanation: This is stratified sampling because the teacher divides the population into strata (grade levels) and takes random samples separately from each grade. Stratified sampling involves dividing the population into distinct subgroups (strata) based on a characteristic - here, grade level - then randomly sampling from each stratum. This ensures representation from all grades, which is important since homework hours might vary by grade level. Choice A incorrectly calls it convenience sampling, but the teacher uses random selection within each grade, not just easy-to-reach students.

Question 15

1. Experiment because the doctor is studying the effect of coffee on blood pressure
2. Observational study because the doctor does not assign who drinks coffee (correct answer)
3. Experiment because medical records are collected in a clinic setting
4. Neither, because blood pressure cannot be compared across different people

Explanation: This is an observational study because the doctor does not assign who drinks coffee. In an observational study, researchers observe and measure characteristics without manipulating any variables - here, the doctor simply observes existing coffee-drinking habits and blood pressure from medical records. The patients already chose whether to drink coffee before the study began, and the doctor doesn't intervene or assign treatments. Choice A incorrectly calls it an experiment, but studying an effect doesn't make it an experiment - the key is whether the researcher assigns the treatment.

Question 16

1. Stratified sample by dividing residents into neighborhoods and sampling randomly within each neighborhood
2. Simple random sample by selecting residents from the city registry using a random number generator
3. Convenience sample by surveying people who are easiest to reach at the station (correct answer)
4. Systematic sample by choosing every 10th household from an alphabetized city list

Explanation: This is a convenience sample because the researcher is surveying people who are easily accessible at a specific location and time. Convenience sampling occurs when participants are selected based on their availability rather than through a random process. The volunteer is only reaching transit users at one location during peak hours, making this a convenience-based approach. Choice A incorrectly suggests stratified sampling, which would require dividing the entire city population into neighborhoods and sampling randomly from each.

Question 17

1. It excludes students who do not enter the cafeteria that morning (correct answer)
2. It uses a sample size of 120, which is always too small
3. It asks a yes/no question, which cannot measure breakfast habits
4. It is conducted in the morning, when students are more honest

Explanation: This sample is biased because it excludes students who do not enter the cafeteria that morning. The principal is only surveying students who come to the cafeteria, which likely overrepresents students who eat breakfast (since they may be coming to get breakfast) and completely misses students who eat at home or skip breakfast entirely. This is a classic example of selection bias where the sampling location systematically excludes certain groups. Choice B incorrectly suggests 120 is always too small - sample size adequacy depends on the population size and desired precision.

Question 18

1. Survey a random sample of students from the entire university roster (correct answer)
2. Survey only students in 8 a.m. classes, but increase the sample size a lot
3. Survey only students who say they are interested in sleep research
4. Survey students in the library late at night to balance the morning class group

Explanation: To reduce bias, researchers should survey a random sample of students from the entire university roster. Surveying only 8 a.m. class students creates selection bias because these students might have different sleep patterns than the general population (they may wake up earlier or get less sleep to attend morning classes). Random sampling from the complete roster gives all students an equal chance of selection, providing an unbiased estimate of the university-wide average. Choice B's suggestion to increase sample size doesn't fix the fundamental bias problem - a large biased sample is still biased.

Question 19

1. Experiment
2. Observational study (correct answer)
3. Survey
4. Controlled trial

Explanation: This is an observational study because researchers observe participants' natural eating behaviors without imposing any treatments or interventions. Observational studies track subjects over time while they maintain their usual habits, allowing researchers to identify associations but not establish causation. The key characteristic is that researchers do not manipulate any variables or assign treatments to participants. An experiment (Choice A) would require researchers to actively assign different diets or interventions to study groups.

Question 20

1. Census
2. Observational study
3. Survey
4. Experiment (correct answer)

Explanation: This is an experiment because researchers actively manipulate the independent variable by assigning participants to receive either the drug or placebo. In experiments, researchers impose treatments on subjects to establish causal relationships. The random assignment of participants to treatment groups is a hallmark of experimental design that allows for causal inference. An observational study (Choice B) would simply observe participants' natural behaviors without any intervention or treatment assignment.