Data Collection Methods - ACT Math

1. A scientist wants to study the natural behaviors of birds in a forest. They observe the birds from a distance without interfering. Is this an experiment or an observational study?
   Answer: Observational, because there's no manipulation This is an observational study because the scientist passively observes bird behaviors without manipulating or interfering with the natural environment. Observational studies involve collecting data without imposing any treatments or interventions on the subjects being studied. The researcher simply records what naturally occurs without changing the birds' environment or behaviors. Choice C incorrectly suggests this is an experiment - experiments require active manipulation of variables, not just controlled observation conditions.
2. To determine the effectiveness of a new advertising campaign, a company surveys every 10th customer who makes a purchase online. Which sampling method is being used?
   Answer: Systematic sampling This is systematic sampling because the company follows a regular pattern, surveying every 10th customer who makes an online purchase. Systematic sampling involves selecting subjects at fixed intervals from an ordered list or sequence, creating a predictable selection method. This approach provides good coverage of the customer base while being more efficient than random sampling. Random sampling (Choice A) would require each online customer to have equal probability of selection regardless of their purchase timing.
3. A university wants to compare average dining hall satisfaction between students living on campus and off campus. They take a list of all students and randomly select 200 on-campus students and 200 off-campus students to survey. This ensures both living situations are included. Which sampling method is being used?
   Answer: Stratified sample by sampling randomly within on-campus and off-campus groups 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.
4. To evaluate a training program, a company assigns some employees to the program while others continue usual work. Their performance is monitored. Is this an experiment or an observational study?
   Answer: Experiment This is an experiment because the company actively assigns employees to different training conditions, manipulating the independent variable to assess the program's effectiveness. Experiments involve researchers imposing treatments on subjects through assignment to establish causal relationships. The comparison between employees in the training program and those continuing usual work allows for causal inference about training effectiveness. An observational study (Choice B) would simply observe employees' natural work patterns without assigning different training conditions.
5. A gym wants to assess member satisfaction with new equipment. They ask every fifth person who enters the facility. Which sampling method is being used?
   Answer: Systematic sampling This is systematic sampling because the gym follows a regular pattern, surveying every fifth person who enters the facility. Systematic sampling involves selecting subjects at fixed intervals from an ordered sequence, creating a predictable selection pattern. This method ensures even coverage across the time period while being more practical than random sampling. Random sampling (Choice A) would require each gym member to have equal probability of selection regardless of their arrival time pattern.
6. To evaluate a new diet program, participants are required to follow it strictly. Researchers monitor weight loss over three months. Is this an experiment or an observational study?
   Answer: Experiment This is an experiment because researchers require participants to follow a strict diet program, actively manipulating their behavior to assess the treatment's effectiveness. Experiments involve imposing treatments or interventions on subjects to establish causal relationships. The requirement that participants strictly follow the diet program represents active manipulation by researchers rather than passive observation. An observational study (Choice B) would track participants' natural eating patterns without requiring adherence to a specific program.
7. A company wants to compare two training videos for new employees. New hires are randomly assigned to watch Video A or Video B, and then all take the same skills test. The company controls which video each person watches. Is this an experiment or an observational study?
   Answer: Experiment because the company assigns a training video and measures the outcome 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.
8. A supermarket wants to know customer satisfaction. They ask shoppers leaving the store for feedback. Which sampling method is being used?
   Answer: Convenience sampling This is convenience sampling because the supermarket selects participants based on their easy accessibility as they exit the store. Convenience sampling chooses subjects who are readily available at a specific location and time, which may not represent the broader customer base. This method introduces location and timing bias since it only captures shoppers present at that particular time. Random sampling (Choice A) would give all customers an equal chance of selection regardless of when they shop.
9. To understand the impact of air pollution, researchers monitor air quality in various neighborhoods and correlate it with health records. Is this an experiment or an observational study?
   Answer: Observational study This is an observational study because researchers monitor existing air quality conditions and correlate them with health records without manipulating any variables. Observational studies examine relationships between variables as they naturally occur without researcher intervention. The researchers observe environmental conditions and health outcomes without imposing treatments or controlling air pollution levels. An experiment (Choice A) would require researchers to manipulate air pollution levels, which would be unethical and impractical.
10. 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?
    Answer: Observational study because the researchers do not assign how people commute 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.
11. To understand exercise habits, researchers survey people at a gym. Which characteristic makes this sample biased?
    Answer: Location bias This represents location bias because surveying people at a gym creates a sample that is not representative of the general population's exercise habits. Location bias occurs when the sampling location systematically excludes certain groups or overrepresents others. Gym-goers are likely to exercise more than the general population, making the sample unrepresentative for understanding overall exercise habits. Random sampling error (Choice B) refers to natural variation in samples, not systematic bias from sampling location.
12. A researcher is studying the effect of sleep on memory. Participants are asked to follow their regular sleep patterns and complete memory tests. Is this an experiment or an observational study?
    Answer: Observational study This is an observational study because researchers observe participants following their natural sleep patterns without imposing any interventions or treatments. Observational studies track subjects' existing behaviors and measure outcomes without manipulation by researchers. Participants maintain their regular sleep habits while researchers simply observe and measure memory performance. An experiment (Choice A) would require researchers to assign different sleep schedules or manipulate sleep duration to establish causal relationships.
13. To assess the popularity of a new TV show, a broadcaster surveys viewers who watched the premiere episode. Which characteristic makes this sample biased?
    Answer: Selection bias This represents selection bias because the broadcaster only surveys viewers who watched the premiere episode, systematically excluding those who didn't watch the show. Selection bias occurs when the sampling method favors certain groups, making the sample unrepresentative of the broader viewing population. People who watched the premiere are likely more interested in the show than the general population, leading to inflated popularity ratings. Random sampling error (Choice B) refers to natural variation in samples, not systematic exclusion of non-viewers.
14. To evaluate the popularity of a new app, a company surveys users who have downloaded it within the last week. Which characteristic makes this sample potentially biased?
    Answer: Only recent downloads are considered The characteristic that makes this sample potentially biased is that only recent downloads from the last week are considered. Temporal bias occurs when sampling is limited to a specific recent time period, as early adopters may systematically differ from the general user population in terms of enthusiasm, tech-savviness, or satisfaction levels. New app users might have different experiences than users who download later, creating a skewed representation of overall app popularity. The other characteristics (online surveys, age diversity, or anonymity) do not introduce systematic temporal bias.
15. 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?
    Answer: Observational, because there's no interference 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.
16. A grocery store wants to know which of two shelf layouts leads to higher sales. For one month, Store 1 uses Layout A and Store 2 uses Layout B, then sales are compared. The stores are in different neighborhoods with different customer bases. Which characteristic makes this comparison potentially biased?
    Answer: Different stores may have different customers, so layout is mixed with neighborhood effects 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.
17. A teacher wants to estimate the average number of hours students at her school spend on homework each week. She divides the school into grade levels (9th, 10th, 11th, 12th) and randomly selects 30 students from each grade to survey. Which sampling method is being used?
    Answer: Stratified sampling because random samples are taken separately from each grade 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.
18. A pharmaceutical company conducts a trial to test a new drug. They give the drug to one group of patients and a placebo to another. Which study design is being used?
    Answer: Experiment with control group This is an experiment with a control group because researchers actively manipulate the treatment variable (drug vs. placebo) and include a comparison group that receives no active treatment. Controlled experiments involve deliberately imposing different treatments on randomly assigned groups to establish cause-and-effect relationships. The placebo group serves as the control, allowing researchers to isolate the drug's effects from psychological factors. This design is the gold standard for testing treatment effectiveness in clinical trials.
19. A health clinic wants to determine the average waiting time for patients. They record the waiting time for every patient visiting the clinic over a week. Which study design is being used?
    Answer: Observational study This is an observational study because the health clinic passively collects data on naturally occurring waiting times without manipulating any variables or imposing treatments. Observational studies involve recording existing conditions or behaviors as they naturally occur without researcher intervention. The clinic simply measures and records waiting times for all patients during normal operations without changing procedures or scheduling. No experimental manipulation is involved, just systematic data collection of current clinic performance.
20. A principal wants to estimate the average time students spend on homework each night. She sends an optional online survey link through the school newsletter, and only students who choose to respond are counted. Students with strong feelings may be more likely to answer. Which characteristic makes this sample biased?
    Answer: The survey is voluntary, so respondents may differ from nonrespondents in homework habits Voluntary response bias makes this sample biased because students who choose to respond may systematically differ from those who don't respond. Self-selection creates bias when respondents have stronger opinions or different characteristics than non-respondents. Students with particularly heavy or light homework loads might be more motivated to complete the survey than those with average amounts. Choice B incorrectly focuses on the variable type rather than the sampling bias issue.

Start this quiz