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Systematic sampling's weakness: if the list has a repeating pattern (e.g., every 20th voter is a precinct captain), picking every 20th person will over-sample that group — periodicity bias. Switching to a voter-registered list doesn't disqualify the method but raises this red flag. Systematic sampling is NOT always unbiased — it just has equal spacing, not equal probability.

In proportional stratified sampling, strata with larger populations get larger samples. Example: if 60% of a school is 9th graders and 40% is 10th graders, a proportional sample takes 60% of the total from 9th grade and 40% from 10th. Unequal stratum sizes are not just acceptable — they're often necessary for accurate representation.

Cluster: entire cities are included → all residents surveyed. Stratified: cities become strata, and a random sample of individuals is drawn from each. The key difference is whether you include the whole group or just a random portion from each selected group.

Proportional stratified formula: (stratum size ÷ total population) × sample size. Engineering: (200 ÷ 380) × 38 = 0.526 × 38 ≈ 20 people. This ensures Engineering's proportion in the sample matches its proportion in the company (~52.6%).

This is a classic AP trap. Simple random sampling gives every individual an equal chance — but it does not guarantee a perfect representative sample. By chance, the sample might over-represent one group. What SRS guarantees is the absence of systematic bias, not perfect representation. Larger samples reduce this random variation, but never eliminate it.

The sampling frame (gym members) excludes a huge portion of the population (people who don't go to gyms). Gym members exercise significantly more than average — the sample systematically misrepresents the population's exercise habits. This is undercoverage: a whole group is absent from the pool of potential participants.

A confounding variable is a third variable that influences both the independent and dependent variable, creating a false appearance of causation. Hot weather → more ice cream sales AND more swimming → more drownings. Only a randomized experiment can control for confounders. Observational studies can only show association.

This is the #1 AP Statistics misconception. Larger sample size reduces random sampling error (variability) but does NOT fix bias. If your sampling method systematically excludes a group, surveying more people from that same flawed method just gives you more biased data. The famous example: the 1936 Literary Digest poll surveyed 10 million people but still predicted the wrong winner — because their method excluded poor voters.

The question embeds an unproven assumption: "the park has improved safety." Respondents who accept this premise are primed to say yes. This is response bias via leading question — the question wording influences the answer. Neutral version: "Do you support continued park funding?" No assumptions embedded.

Even a perfectly random sample can suffer from response bias. When people are asked by authority figures (doctors, bosses, teachers), they tend to answer in ways they think are expected — not truthfully. This is social desirability bias. Solution: anonymous surveys administered by neutral parties. Random sampling fixes selection bias; it does NOT fix response bias.

Double-blind: both the subjects AND the researchers/administrators are unaware of group assignments. This prevents: (1) participants changing behavior because they know they got the real drug (placebo effect), and (2) researchers unconsciously influencing results or interpreting data favorably. Single-blind: only participants don't know. Double-blind is the gold standard.

There IS a control group (existing fertilizer). Blinding isn't typically required for plant studies. There IS randomization (plots in the same field share similar conditions). The weak point is replication — 3 plots is very few; a single unusual plot could skew results. More replication = more confidence that observed differences are real, not random chance.

The experimental group (also called treatment group) receives the treatment being tested. The control group receives no treatment or a placebo — it's the baseline for comparison. Without a control group, you can't isolate whether the treatment caused any observed change.

The placebo effect is a real physiological/psychological improvement caused by the mere belief of receiving treatment. This is why experiments need control groups — without one, researchers can't tell if improvements are due to the treatment or just expectation. The drug is still considered effective: 60% vs 30% shows the drug effect beyond placebo.

Technically, no observational study can prove causation — you cannot randomly assign people to smoke for ethical reasons. However, strong, consistent associations across many studies, combined with biological plausibility (we understand the mechanism), create overwhelming evidence. Statistically speaking, the study shows strong correlation. Proof of causation requires either a randomized experiment or strong converging evidence.

The defining feature of an experiment is random assignment of a treatment. Here, students are randomly assigned to different dorm types (the treatment). Treatment doesn't have to be medical — it's any condition being manipulated. Because of random assignment, any GPA difference can be attributed to dorm environment, not pre-existing differences between students.

Students who voluntarily choose classical music may differ in many ways — higher motivation, better study habits, higher baseline achievement. These confounders make it impossible to isolate whether music caused better scores. The fix: randomly assign students to "listen to classical music" or "no music" groups. This distributes confounders equally, isolating the music variable.

Straight from your notes: "A study has bias if it systematically produces results that misrepresent a population." And: "Bias may arise if a sample is more likely to include a certain population than another." Memorize this definition word-for-word.

When a large portion of a sample doesn't respond, those non-respondents may differ systematically from respondents. Here, 57% didn't respond — maybe they're busier, less engaged civically, or more satisfied/dissatisfied. This non-response bias can severely distort results. The cluster sampling design is fine; the problem is who actually returned the survey.

This is a two-stage design: (1) Cluster sampling selects 4 schools from 20 — entire schools are the clusters. (2) Within each school, random assignment of classes to treatment/control makes it a randomized experiment. It's NOT stratified because schools aren't strata from which individuals are sampled — they're clusters that are wholly selected. The random assignment of classes within schools is what makes it an experiment, allowing causal conclusions.