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.

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.

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.

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.

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.

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.

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.

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.

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.

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.