AP Statistics Quiz: Introduction To Planning A Study

What this quiz covers

This quiz focuses on Introduction To Planning A Study, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Statistics.

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. Increase the number of speed measurements each day so the sample size is very large
2. Address potential confounding from time effects (weather, enforcement, traffic) by using a concurrent control segment or randomization (correct answer)
3. Use a more sensitive radar device to reduce measurement error
4. Plan to compute both the mean and median speed for each week
5. Collect data for more weeks so the analysis includes more observations

Explanation: This question tests understanding of confounding in before-after studies. The plan measures speeds before and after installing signs, but many factors could change between weeks: weather conditions, traffic patterns, police enforcement, holidays, or random variation. These time-related confounders could explain any speed differences, not the signs themselves. Using a concurrent control segment without signs (B) or randomizing sign installation across multiple segments would control for these temporal effects. Simply increasing measurements (A) or collecting more weeks (E) doesn't address the confounding. Without controlling for time effects, the study cannot determine if speed changes are due to the signs or other factors that varied between the two weeks.

Question 2

1. Increase the number of users included so the sample size is extremely large
2. Randomly assign notification status (or use a design that addresses confounding) because users who opt in may already be more motivated (correct answer)
3. Switch from average steps to total steps so the response variable is larger
4. Plan to use a histogram of steps for each group in the final report
5. Collect data for more months so the analysis includes more observations per user

Explanation: This question focuses on self-selection bias and confounding. Users who choose to enable step-goal notifications are likely already more motivated about fitness than those who don't enable them. This self-selection creates confounding - any observed differences in steps could be due to pre-existing motivation levels, not the notifications themselves. Random assignment of notification status (B) would eliminate this confounding by ensuring groups are comparable except for notification status. Simply increasing sample size (A) or data collection time (E) won't address this fundamental design issue. Without randomization or other methods to address confounding, the study cannot determine if notifications actually increase steps or if motivated users both enable notifications and walk more.

Question 3

1. Use a random sample of adult residents (e.g., random digit dialing or address-based sampling) rather than a convenience sample at the arena (correct answer)
2. Increase the sample size by interviewing people for more hours at the event
3. Ask additional demographic questions to make the survey more detailed
4. Plan to compute a $95\%$ confidence interval for the proportion who support the arena
5. Use a Likert scale (strongly oppose to strongly support) instead of a yes/no question

Explanation: This question tests understanding of sampling bias in surveys. Interviewing people outside the arena at an event creates severe bias - attendees at arena events are likely sports fans who support arena construction more than typical residents. This convenience sample cannot represent all adult city residents' opinions. To estimate the true proportion of city residents who support the arena, the study needs a random sample of residents (A) through methods like random digit dialing or address-based sampling. Interviewing more people at the arena (B) just increases the biased sample size. Without proper random sampling from the population, the results will overestimate support by capturing mainly arena event attendees rather than representative city residents.

Question 4

1. Randomly assign classes (or students) to music vs. no music to reduce confounding from teacher and class differences (correct answer)
2. Increase the number of quizzes so there are more scores to analyze
3. Use a larger sample size by including 6th and 8th graders as well
4. Decide whether to report the results using medians instead of means
5. Make sure the quizzes are graded quickly so students get feedback

Explanation: This question addresses confounding in educational research. Letting teachers self-select whether to play music creates multiple confounding issues: teachers who choose music might have different teaching styles, enthusiasm levels, or classroom management approaches. Additionally, different classes may have varying ability levels or dynamics. These teacher and class differences could explain any observed quiz score differences, not the music itself. Random assignment of classes or students to music conditions (A) would control for these confounders and allow causal conclusions. Simply increasing quizzes (B) or sample size (C) doesn't address the fundamental design flaw. Without randomization, the study cannot determine if music actually improves scores or if other factors are responsible.

Question 5

1. Increase the number of participating stores so the sample size is larger
2. Randomly assign stores (or time periods within stores) to menu types to reduce confounding from store differences and manager selection (correct answer)
3. Decide whether to exclude customers who only buy drinks from the analysis
4. Use a more complex statistical model so the result is more convincing
5. Collect data for a longer time so there are more receipts to analyze

Explanation: This question addresses confounding in business experiments. Allowing managers to volunteer their stores for the new menu creates selection bias - managers who volunteer may be more innovative, have better-performing stores, or different customer bases. These store-level differences could explain any spending differences, not the menu layout itself. Random assignment of stores or time periods to menu types (B) would control for these confounders and allow causal conclusions about the menu's effect. Simply increasing stores (A) or collection time (E) doesn't fix this design flaw. Without randomization, the study cannot determine if spending differences are due to the new menu or to systematic differences between volunteer and non-volunteer stores.

Question 6

1. Increase the number of brochures mailed so the sample size is larger
2. Define the response variable precisely (e.g., gallons used per household) to avoid ambiguity
3. Use a randomized comparison group from the town (and avoid selecting only prior supporters) to reduce bias and confounding (correct answer)
4. Plan to analyze the data with a confidence interval instead of a hypothesis test
5. Collect water-use data for more months to increase the number of observations

Explanation: This question tests recognition of selection bias and confounding. The plan sends brochures only to households that previously emailed the environmental group - these are likely already environmentally conscious households who may have been reducing water use anyway. Comparing them to the town average creates both selection bias and confounding. These motivated households don't represent typical town residents, and their water use patterns may differ for reasons unrelated to the brochure. Using a randomized comparison group from the general town population (C) would eliminate this bias and allow valid conclusions about the brochure's effect. Without proper randomization and avoiding selection of prior supporters, any observed differences cannot be attributed to the brochure itself.

Question 7

1. Ensure the volunteer sample is representative of all adult residents, since lack of representativeness limits generalizing to the city (correct answer)
2. Increase the number of reminder texts to improve the chance of finding a statistically significant effect
3. Choose a larger sample size so the margin of error for the vaccination rate is smaller
4. Decide whether to graph vaccination rates with a bar chart or a pie chart in the report
5. Use a double-blind procedure so neither group knows whether they received texts

Explanation: This question focuses on sampling bias and generalizability. The plan recruits volunteers at a health fair, which creates a severely biased sample - people attending health fairs are likely more health-conscious than the general population. This volunteer sample cannot represent all adult city residents, making it impossible to generalize findings to the entire city (the stated population). While the random assignment within this biased sample is good for internal validity, the external validity is compromised. Increasing reminders (B) or sample size (C) won't fix this fundamental sampling problem. To answer questions about the city's residents, the study needs a representative sample through random sampling methods, not convenience sampling at a health fair.

Question 8

1. Use a sampling frame that covers the full adult population (not just petition signers) to reduce selection bias (correct answer)
2. Increase the number of calls made each day to obtain a larger sample size
3. Use a 5-point scale instead of yes/no to measure strength of support
4. Decide whether the analysis will include a confidence interval or only a point estimate
5. Plan to summarize results separately for urban and rural respondents

Explanation: This AP Statistics question on introduction to planning a study addresses sampling bias in opinion surveys for population proportions. Calling only prior petition signers creates selection bias toward environmentally inclined individuals, overestimating support for the plastic bag ban. A sampling frame covering all adults, as in choice A, reduces this bias for representativeness. Choice B, more calls for larger samples, is a common distractor but doesn't fix the biased frame. Mini-lesson: Use probability sampling to mirror the population and avoid voluntary or convenience bias. A flawed frame leads to unreliable estimates. Planning inclusively ensures the sample reflects diverse views accurately.

Question 9

1. Randomly assign students (or class periods) to music versus no music to avoid confounding with teacher differences (correct answer)
2. Increase the number of quizzes given so the sample size of scores is larger
3. Use a harder quiz so there is more variation in scores
4. Report both the mean and median quiz score for each group
5. Use a 90% confidence level to make the interval narrower

Explanation: This question in AP Statistics' introduction to planning a study examines experimental design flaws, particularly confounding in non-randomized setups. The plan lets teachers choose music based on preference, confounding the music effect with teacher styles or class compositions. Randomly assigning music conditions, as in choice A, is vital to isolate the music's impact on quiz scores. Choice B, more quizzes for larger samples, tempts as a distractor since it increases data but ignores confounding. Mini-lesson: Randomization in experiments balances groups, reducing bias from extraneous variables like teacher differences. Without it, associations may be spurious. Always design to control for known confounders for reliable causal inferences.

Question 10

1. Use a sampling method that reaches a representative sample of all commuters, not just followers of transit pages (correct answer)
2. Increase the number of questions about commute satisfaction to provide more context
3. Plan to use a matched pairs design by pairing each transit user with a driver in the same neighborhood
4. Decide whether to report commute time in minutes or in hours
5. Increase the sample size by leaving the survey open for an extra month

Explanation: AP Statistics' introduction to planning a study covers sampling techniques to avoid bias in comparative studies. Posting the survey on transit social media pages introduces selection bias, as it overrepresents transit users and may not reach drivers representatively, skewing commute time comparisons. Addressing this by using a method for a representative sample of all commuters, per choice A, is essential for unbiased estimates. Choice E, extending the survey period for a larger sample, distracts because size alone doesn't correct for a non-representative frame. Mini-lesson: Ensure the sampling frame covers the entire population to prevent undercoverage; stratified or cluster sampling can help with subgroups. Biased samples lead to invalid generalizations. Planning for inclusivity strengthens the study's credibility.

Question 11

1. Ensure the productivity metric is measured the same way in every department
2. Randomly assign departments (or employees) to the 4-day policy or the standard schedule to reduce confounding (correct answer)
3. Increase the number of departments in the study to make the sample size larger
4. Use a smaller significance level (like $\alpha=0.01$) to reduce Type I error
5. Collect data for multiple quarters so the dataset has more rows

Explanation: This AP Statistics question on introduction to planning a study highlights the importance of experimental design to establish causality. The plan allows departments to vote on the 4-day workweek, creating self-selection where more productive departments might adopt it, confounding productivity comparisons. The critical fix is random assignment to schedules, as in choice B, to minimize confounding and enable causal claims about the policy's effect. Choice C, increasing the number of departments, is a distractor because while it boosts sample size and power, it doesn't eliminate bias from non-random selection. Mini-lesson: In experiments, randomization distributes confounders evenly, distinguishing treatment effects from other variables. Observational designs risk lurking variables, so plan for control groups and random allocation. This ensures robust evidence for policy decisions like workweek changes.

Question 12

1. Increase the sample size by extending the sign-up period so more students join the tutoring group
2. Decide whether to use a one-sided or two-sided statistical test for the score comparison
3. Create a plan to randomly assign interested students to tutoring or no tutoring to reduce confounding from self-selection (correct answer)
4. Use a more precise grading rubric so math scores have less measurement error
5. Collect additional demographic variables so the final report includes more subgroup summaries

Explanation: This question tests the AP Statistics skill of introduction to planning a study, focusing on designing experiments to minimize bias and confounding. The proposed plan relies on voluntary sign-up for tutoring, which introduces self-selection bias because motivated students may join and naturally perform better, confounding the effect of tutoring on math scores. The most important aspect to address is creating a randomized assignment to tutoring groups, as in choice C, to ensure comparability and allow causal inferences. A common distractor is choice A, which suggests increasing sample size; while larger samples reduce variability, they do not fix bias from non-random assignment. In planning studies, remember that observational studies like this initial plan can show associations but not causation due to confounders, whereas randomized experiments help isolate treatment effects. Always prioritize randomization in experiments to balance unknown factors across groups. This approach strengthens the validity of conclusions about the tutoring program's impact.

Question 13

1. Switch to a probability sampling method (such as an SRS of county adults) to improve representativeness (correct answer)
2. Increase the number of surveyors so a larger sample can be collected in the same time period
3. Use a longer survey with more questions to make responses more detailed
4. Plan to compute a 99% confidence interval instead of a 95% confidence interval
5. Decide in advance how to round the reported sample proportion

Explanation: In AP Statistics, introduction to planning a study emphasizes selecting appropriate sampling methods to ensure representativeness and reduce bias. The plan uses a convenience sample at a gym, which likely undercovers non-gym-goers or those unavailable on Saturday mornings, leading to biased estimates of the county's flu shot proportion. Switching to a probability sampling method like a simple random sample (SRS), as in choice A, is crucial to give every adult an equal chance of selection and improve generalizability. Choice B, increasing sample size via more surveyors, might seem appealing for precision, but it doesn't address the underlying bias in who is sampled. A mini-lesson on planning studies: Use random sampling to avoid selection bias and ensure the sample mirrors the population, enabling reliable inferences. Non-probability samples, like convenience ones, often lead to undercoverage or voluntary response bias. Prioritizing representativeness is key before data collection.

Question 14

1. Increase the sample size by adding more weeks of observation
2. Use a plan that allows random assignment of reminders to volunteers to avoid confounding with prior volunteering frequency (correct answer)
3. Decide whether to measure volunteer hours in minutes or in hours
4. Create a more detailed sign-in sheet so volunteers can describe their tasks
5. Plan to compute the correlation between reminders received and hours volunteered

Explanation: This question tests AP Statistics skills in introduction to planning a study, particularly avoiding confounding in experimental designs. Sending reminders only to frequent volunteers confounds the reminder effect with prior volunteering habits, as they may volunteer more regardless. Implementing random assignment of reminders, per choice B, is essential to assess true impact. Choice A, more observation weeks for size, is a distractor; it increases data but not comparability. Mini-lesson: Randomize treatments to balance baseline differences and enable causation claims. Selective assignment risks biased comparisons. Thoughtful planning enhances the study's ability to inform practices like volunteer engagement.

Question 15

1. Increase the number of athletes by including junior varsity teams to get a larger sample
2. Randomly assign teams (or athletes) to stretching routine versus usual routine to reduce confounding by sport and coaching (correct answer)
3. Decide whether to report strains per athlete or total strains per team
4. Use a smaller margin of error goal when planning the analysis
5. Collect more detailed injury descriptions so the final report is more thorough

Explanation: In AP Statistics, introduction to planning a study focuses on experimental randomization to mitigate confounding in treatment comparisons. Letting coaches decide on the stretching routine confounds results with sport types or coaching styles, as teams choosing it might differ inherently. Random assignment to routines, per choice B, is key to establishing causality in strain reduction. Choice A, adding junior varsity for size, distracts because larger samples help precision but not bias correction. Mini-lesson: Experiments require random allocation to treatments to even out confounders across groups. Observational approaches risk misattributing effects. Prioritize design elements that support valid conclusions about interventions.

Question 16

1. Use a random sample of full‑time students (for example, from the registrar's list) to reduce undercoverage (correct answer)
2. Increase the sample size by surveying for several weeks instead of one evening
3. Ask students to provide their major so results can be broken down by department
4. Decide whether to use a dotplot or histogram when displaying the data
5. Use more precise response options (like 0.1-hour increments) to reduce rounding

Explanation: AP Statistics introduces planning a study by stressing representative sampling to minimize bias in estimating population parameters. Surveying only dining hall students at a specific time causes undercoverage of those not eating there, like commuters or evening studiers, biasing average study hours. Using a random sample from the full-time student list, as in choice A, addresses this for better representation. Choice B, surveying longer for more responses, is a distractor; it enlarges the sample but perpetuates the bias. Mini-lesson: A good sampling frame should include all population members; simple random sampling ensures every individual has an equal chance. Avoid convenience samples that exclude subgroups. This foundation allows accurate population inferences.

Question 17

1. Randomly assign seating locations (front vs back) to students to reduce confounding from motivation or prior achievement (correct answer)
2. Increase the number of students by combining results across multiple schools
3. Use a different test with more questions so scores are more precise
4. Decide whether to use a boxplot or a histogram to compare the two groups
5. Collect data on students' favorite subjects to add interest to the report

Explanation: AP Statistics' introduction to planning a study emphasizes randomization in experiments to control for self-selection and confounding. Students choosing seats introduce bias, as front-sitters might be more motivated, confounding seating's effect on scores. Randomly assigning seats, as in choice A, eliminates this for causal insights. Choice B, combining schools for more students, distracts by addressing size over design flaws. Mini-lesson: Randomization prevents systematic differences between groups, isolating the variable of interest. Without it, lurking variables like motivation skew results. Strong designs yield trustworthy evidence on factors like classroom seating.

Question 18

1. Increase the sample size by surveying more students who visit the nurse's office
2. Select students using a method that is likely to represent the whole student body, not just nurse visitors (correct answer)
3. Ask students to report exact bedtimes and wake times instead of a yes/no question
4. Decide whether to analyze results separately by grade level after data are collected
5. Use a larger font on the survey to reduce skipped questions

Explanation: This question tests recognition of selection bias in health-related surveys. The nurse's plan to survey only students visiting the nurse's office creates a biased sample, as these students may be experiencing health issues that could be related to sleep deprivation, making them unrepresentative of the general student body. Option B correctly identifies that selecting students using a method likely to represent the whole student body is most critical. Students who visit the nurse may systematically differ in their sleep patterns from those who don't. While increasing the sample size of nurse visitors (A) might improve precision, it won't fix the bias. The other options about measurement details (C), subgroup analysis (D), or survey formatting (E) are less important than ensuring the sample represents all students. In planning studies about population characteristics, avoiding selection bias through proper sampling is paramount.

Question 19

1. Increase the sample size by surveying for more days so the margin of error will be smaller
2. Use a random sampling method that gives every student a known chance to be selected (correct answer)
3. Rewrite the survey to include more questions so students explain their reasoning
4. Decide in advance which graph (bar chart or pie chart) will be used to display results
5. Plan to compute a confidence interval instead of only reporting the sample proportion

Explanation: This question tests understanding of sampling bias in survey design. The student council's plan to survey only students passing by the cafeteria creates a convenience sample that may not represent all students at the school - some students might not eat in the cafeteria, have different lunch periods, or avoid that area. Option B correctly identifies that using a random sampling method giving every student a known chance of selection is most critical for obtaining valid estimates about the entire student population. While increasing sample size (A) can reduce margin of error, it won't fix the fundamental bias problem if the sampling method is flawed. The other options address less critical issues like survey content (C), visualization planning (D), or analysis methods (E). When planning a study to estimate a population parameter, ensuring representative sampling through proper randomization is the foundation that makes all subsequent statistical inference valid.

Question 20

1. Increase the sample size by keeping the survey open longer so more students respond
2. Ensure the sampling method reduces voluntary response bias so the sample better represents first-year students (correct answer)
3. Plan to use a correlation coefficient rather than a difference in means
4. Add more questions about study habits to make the survey more interesting
5. Use a larger font size and clearer formatting for the online survey

Explanation: This question focuses on voluntary response bias in sampling. Posting a survey link on social media creates severe bias - only students who see the post, are motivated to respond, and willing to share exam scores will participate. This self-selected sample likely overrepresents certain types of students (perhaps more engaged or proud of their scores) and cannot represent all first-year students. The voluntary nature of uploading exam screenshots compounds this bias. To properly study the association in the population, the study needs a sampling method that reduces voluntary response bias (B), such as random sampling with higher response rates. Increasing response time (A) would just get more biased responses. Without addressing this sampling bias, findings cannot generalize to all first-year students.