A health department randomly samples 200 adults from the city voter list, randomly assigns each to a walking plan or no plan, and compares resting pulse after 8 weeks. What does this design support?

A superintendent randomly samples 160 students from all district high schools, records whether they already use flashcards or notes, and compares exam scores. What conclusion does this design support?

A coach recruits 40 athletes who stayed after practice, randomly assigns them to a protein shake or water, and measures sprint times. What does this experiment support?

A website poll takes responses from visitors who choose to click, groups them by whether they already use a budget app, and compares monthly savings. What does this design support?

A district randomly samples 12 middle-school classrooms, randomly assigns each selected classroom to a new lunch schedule or the old one, and compares classroom average afternoon tardies. What claim is supported?

A hospital randomly selects 180 patients discharged in June, classifies them by whether they chose a follow-up call, and compares readmission rates. What does this observational design support?

A teacher asks 30 nearby students to join a study, randomly assigns each to read on paper or on a tablet, and compares quiz scores. What conclusion is justified?

A gym survey includes members who stop at the front desk, groups them by membership type they already bought, and compares weekly visits. What does this design support?

Students volunteer after seeing a poster at one school, are randomly assigned to workshop A or B, and test gains are compared. A teacher says workshop A raises gains for all students at the school. Is that supported?

A city randomly samples 500 adults, groups them by whether they already bike to work, and compares average stress scores. The report says biking to work lowers stress for city adults. Is that claim supported?

A school randomly samples 120 juniors, randomly assigns them to online tutoring or no tutoring, and finds the tutoring group averages 6 points higher. The principal says online tutoring raises algebra scores for the school's juniors. Is this supported?

A counselor uses 75 students who came to an optional wellness fair, groups them by whether they already own a pet, and compares stress scores. She says pet ownership is associated with stress for these 75 students. Is that supported?

A factory randomly samples 90 bottles from one day's production, randomly assigns each to cap machine A or B, and finds fewer leaks with A. The manager says machine A reduces leaks for that day's bottles. Is this supported?

A teacher picks 36 students, assigns the 18 in the front rows to music and the 18 in the back rows to silence, and compares quiz scores. He says music caused higher scores for these 36 students. Is that supported?

A company randomly samples 300 employees, groups them by how much coffee they already drink, and finds heavier drinkers are more alert. To claim coffee raises alertness for company employees, what random step is needed?

An after-school program gets volunteers, randomly assigns them to plan A or plan B, and finds plan A has higher homework completion. The director wants to generalize the effect to all ninth graders in the district. What random step must be added?

At a store, shoppers who agree at checkout answer a survey, are grouped by the brand they already bought, and average satisfaction is compared. The owner wants results to describe all shoppers that week. What sampling step is needed?

A clinic randomly samples 140 patients with the same diagnosis, groups them by the medication their doctors already chose, and finds faster recovery with drug A. The clinic wants to claim drug A causes faster recovery. What random step is required?

A city randomly selects 250 apartments from its registry, groups residents by whether they already use air filters, and finds fewer allergy symptoms among filter users. Officials want to claim filters reduce allergy symptoms. What must the design add?

State adults volunteer for an online donation study, are randomly assigned to message wording A or B, and wording B gets more donations. Researchers want to generalize that wording B increases donations for all state adults. What random step is missing?