AP Statistics Quiz: Selecting An Experimental Design

What this quiz covers

This quiz focuses on Selecting An Experimental Design, 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. Completely randomized design assigning all 80 students to the four strategies without considering pretest level
2. Matched-pairs design: pair students by teacher, then assign each pair to all four strategies
3. Randomized block design: block by prior vocabulary level (low/high), then randomly assign strategies within each block (correct answer)
4. Latin square design using prior vocabulary level and study strategy as the two blocking variables
5. Systematic assignment: alternate strategies in a fixed repeating order as students enroll

Explanation: This educational research scenario presents a textbook case for randomized block design when a pre-existing characteristic strongly affects outcomes. Prior vocabulary level (low vs high) is expected to influence how well students respond to different study strategies, making it an ideal blocking variable. Option C correctly blocks the 80 students by their pretest vocabulary level, creating homogeneous groups, then randomly assigns the four strategies within each block. This ensures each strategy is tested on both low and high vocabulary students while controlling for initial ability differences. Option A ignores this crucial factor, while B misunderstands matched pairs by trying to assign multiple treatments to pairs. Options D and E either misapply Latin squares or abandon randomization. Blocking by ability level before randomizing treatments is standard practice in educational experiments to reduce variance.

Question 2

1. Completely randomized design assigning individual students within each section to different formats during the same lab period
2. Randomized block design blocking by student GPA, then assign formats to students across sections
3. Cluster randomized design: randomly assign each entire lab section (day) to one of the three formats (correct answer)
4. Matched-pairs design: match students across sections by prior chemistry grade, then assign formats within pairs
5. Latin square design using day of week and instruction format as blocking variables, then assign students

Explanation: This scenario requires cluster randomized design due to the practical constraint that each lab section must use only one instruction format to avoid confusion. The teacher cannot mix formats within a section, making each section (day) an indivisible cluster. Option C correctly identifies this by randomly assigning each entire lab section to one of the three formats. While the teacher suspects day-of-week effects, this becomes a secondary consideration to the primary constraint of needing uniform instruction within each section. Options A and D impossibly suggest mixing formats within sections, while B blocks by an irrelevant variable (GPA) and ignores the section constraint. Option E misapplies Latin squares. When practical constraints require treating groups as units, cluster randomization is necessary even if it means accepting some potential confounding with group characteristics.

Question 3

1. Matched-pairs design: for each time slot, test one sample of X and one of Y back-to-back in random order, then compare paired results (correct answer)
2. Completely randomized design: test all X samples first, then all Y samples
3. Randomized block design: block by material, then randomly assign time slots to blocks
4. Cluster randomized design: randomly select 10 time slots for X and the remaining 10 for Y without pairing nearby slots
5. Observational study: record strengths for whatever material arrives from the supplier first

Explanation: This engineering scenario calls for a matched-pairs design to control for the systematic effect of machine warm-up over time. Since the testing machine's temperature affects measurements and changes throughout the day, testing materials in paired time slots controls for this temporal effect. Option A correctly pairs time slots, testing one sample of each material back-to-back in random order within each pair, then comparing the paired differences. This removes the time/temperature effect from the comparison since both materials in a pair experience similar machine conditions. Option B would confound material with time, C misunderstands blocking, D doesn't control for the warm-up effect, and E abandons experimentation. When a nuisance factor changes systematically over time and you're comparing two treatments, matched pairs with randomized order within pairs provides excellent control.

Question 4

1. Completely randomized design assigning doses to the 9 sessions, ignoring time of day
2. Randomized block design blocking by time of day, but assign the same dose to all sessions within a block
3. Matched-pairs design where each participant receives all three doses in one session
4. Latin square design so that each dose occurs once in each time-of-day category across the 9 sessions (correct answer)
5. Stratified sampling by time of day, then observe reaction times without assigning doses

Explanation: This medical research scenario is perfectly suited for a Latin square design, which efficiently controls for two blocking factors simultaneously. The researcher wants to test three doses at three times of day with only 9 sessions total (3×3), and needs each dose tested once at each time to control for time-of-day effects. Option D correctly identifies the Latin square design, which creates a 3×3 grid where each dose appears exactly once in each row (time of day) and column, using different participants. This elegant design controls for time-of-day effects without increasing the number of sessions needed. Options A and B don't ensure balanced testing across times, C impossibly gives all doses to one participant, and E abandons the experimental nature. Latin squares are ideal when you have two blocking factors and the number of treatments equals the number of levels in each blocking factor.

Question 5

1. Completely randomized design assigning individual students within each class period to music or no music
2. Randomized block design blocking by class period, then randomly assigning students within each period to conditions
3. Matched-pairs design pairing students across periods by prior grades, then assigning music within each pair
4. Cluster randomized design: randomly assign each entire class period to either music or no music (correct answer)
5. Latin square design using class period and seating row as blocking variables, then assign conditions

Explanation: This scenario requires cluster randomized design due to a practical constraint: the teacher cannot apply different treatments (music vs no music) to individual students within the same classroom simultaneously. Option D correctly identifies that entire class periods must be assigned as clusters to either music or no music condition. This is different from blocking - we're not blocking by period to control variation, but rather treating each period as an indivisible unit due to the nature of the treatment. Options A and B impossibly suggest assigning individual students within a class to different conditions. Option C pairs students across periods unnecessarily, and E overcomplicates with Latin squares. Cluster randomization is necessary when treatments must be applied to groups rather than individuals, often due to practical constraints or to avoid treatment contamination.

Question 6

1. Randomized block design blocking by machine, then randomly assign Setting X or Y to parts produced on each machine (correct answer)
2. Completely randomized design assigning settings to parts without recording which machine produced them
3. Matched-pairs design pairing machines and assigning one machine to X and the other to Y for the whole day
4. Systematic design alternating settings X and Y in a fixed pattern on all machines with no randomization
5. Factorial design adding a third factor for operator mood, requiring repeated measures

Explanation: This AP Statistics task requires designing experiments to handle equipment variability, such as machine differences. The randomized block design blocking by machine, with random assignment of settings to parts produced on each, is best to control for calibration variations while testing setting effects on strength. It fits the ability of machines to use both settings daily and focuses on part-level responses. Distractors: B ignores machines; C pairs machines inefficiently; D lacks randomization; E adds irrelevant factors. Mini-lesson: Block on units like machines when they may introduce variability; randomize treatments within blocks for repeated measures, allowing precise estimation of treatment effects despite block differences.

Question 7

1. Completely randomized design: randomly pick 4 of the 8 days for jazz and use pop on the others
2. Randomized block design: block by day-of-week (Tuesday vs. Saturday) and randomly assign jazz/pop within each block (correct answer)
3. Matched-pairs design: play jazz in the morning and pop in the afternoon each day
4. Observational study: record time spent on days when the manager happens to choose jazz or pop
5. Two-factor factorial design using music type and day-of-week as treatments applied to each customer

Explanation: In AP Statistics, selecting an experimental design involves choosing methods to control for confounding variables, such as day-of-week effects here. The randomized block design blocking by day-of-week (Tuesday vs. Saturday) is best, as it accounts for expected differences in busyness by randomizing music types within each block, ensuring balanced comparison over the 8 days. This fits the constraint of one music type per day and allows causal inference about music's effect on time spent. Distractors include A, which ignores blocking and risks confounding; C alters the treatment by splitting days; D lacks randomization; and E misapplies factorial design to customers instead of days. Mini-lesson: Block on variables strongly related to the response, like day-of-week, to isolate the treatment effect; randomize within blocks to avoid bias, especially when units (days) are limited.

Question 8

1. Completely randomized design: randomly assign all students to A, B, or C with no blocking
2. Randomized block design: block by grade level, then randomly assign students within each grade to A, B, or C (correct answer)
3. Matched-pairs design: have each student try all three breakfasts on the same day and compare within-student scores
4. Randomized block design: block by breakfast option, then randomly assign students to grades
5. Completely randomized factorial design: assign students to all combinations of breakfast option and grade level

Explanation: This question tests the skill of selecting an appropriate experimental design in AP Statistics, focusing on controlling for known sources of variation like grade level while comparing treatments. The randomized block design in choice B fits best because it blocks by grade level to reduce variability from this factor, then randomly assigns students within each grade to one of the three breakfast options, ensuring a fair comparison with one breakfast per student. Choice A ignores blocking, potentially confounding results with grade differences; C is impractical as students can't try all breakfasts on the same day given the constraint; D incorrectly blocks by breakfast instead of grade; and E introduces an unnecessary factorial element treating grade as a factor rather than a blocking variable. A key distractor is C, which might appeal if overlooking the one-breakfast limit, but it violates the setup. In a mini-lesson, match designs to constraints by using blocking when a known categorical variable affects the response, ensuring randomization within blocks to maintain validity while controlling extraneous variation.

Question 9

1. Completely randomized design with three groups: compare catalysts only and ignore temperature
2. Randomized block design: block by catalyst type and then assign temperature within each block, but do not allow comparison among catalysts
3. Matched-pairs design: run the same batch at both temperatures with all three catalysts
4. Completely randomized $2\times 3$ factorial design with six conditions (each temperature crossed with each catalyst) (correct answer)
5. Observational study: record reaction times from past runs at various temperatures and catalysts without random assignment

Explanation: This AP Statistics question evaluates choosing a design to assess main effects and interactions of temperature and catalysts on reaction time. The completely randomized 2x3 factorial design in D, with six conditions, is most appropriate for randomizing batches to combinations, allowing evaluation of whether optimal catalyst varies by temperature under the one-run constraint. Choice A ignores temperature; B misblocks limiting comparisons; C can't reuse batches for pairs; E lacks randomization. Distractors like C confuse pairing with factorial needs, but batches are single-use. Mini-lesson: Utilize factorial designs for multiple factors and potential interactions; fully cross levels and randomize to conditions, ensuring causality when constraints like single-use units prevent repetitions.

Question 10

1. Randomized block design: block by position group, then randomly assign athletes within each block to P1 or P2 (correct answer)
2. Completely randomized design: randomly assign all athletes to P1 or P2 with no blocking
3. Matched-pairs design: have each athlete do both programs simultaneously and compare sprint times
4. Cluster randomization: assign all sprinters to P1 and all middle-distance athletes to P2
5. Add unnecessary complexity: use a $2\times 2\times 2$ factorial design including program, position group, and shoe brand, requiring athletes to switch shoes weekly

Explanation: In AP Statistics, this skill entails selecting a design to control for position group differences in sprint times while comparing training programs. Choice A's randomized block design, blocking by position and randomizing programs within blocks, effectively reduces group variability with one program per athlete. Choice B lacks blocking; C can't do simultaneous programs; D clusters without randomization; E complicates with irrelevant factors. A common distractor is B, but blocking is needed for fairness. Mini-lesson: Apply blocking for inherent group differences; randomize within blocks to compare treatments reliably, especially under constraints limiting athletes to one treatment without crossover.

Question 11

1. Completely randomized design assigning patients to use only Cream A or only Cream B on their whole face
2. Randomized block design blocking by patient, randomly assign Cream A to one side and Cream B to the other side (correct answer)
3. Randomized block design blocking by which side of the face (left vs. right), then assign patients to creams
4. Systematic assignment: always put Cream A on the left side and Cream B on the right side
5. Factorial design with two factors (patient and cream) and randomize patients to both creams over time

Explanation: This AP Statistics question assesses selecting an experimental design to handle individual variability in comparative studies. The randomized block design blocking by patient, with random assignment of creams to face sides, is most suitable as it treats each patient as a block, controlling for person-to-person differences while allowing direct comparison via simultaneous use on each side. This design aligns with the ability to apply both creams at once and measures reduction per side effectively. Distractors: A doesn't account for individual differences; C blocks incorrectly on side instead of patient; D lacks randomization; E introduces unnecessary time sequencing. Mini-lesson: Use blocking when units (patients) vary inherently; randomize treatments within blocks (sides) to minimize bias, ideal for paired structures like left/right to enhance precision in detecting differences.

Question 12

1. Completely randomized design with 4 treatment groups (all combinations of fertilizer and watering), randomly assign plants to groups (correct answer)
2. Matched-pairs design comparing Type 1 vs. Type 2 fertilizer on the same plant at different times
3. Randomized block design blocking by fertilizer type, then randomize watering schedule only
4. One-factor design: randomly assign plants to fertilizer type, and keep watering schedule the same for all plants
5. Observational study: let gardeners choose fertilizer and watering, then compare yields

Explanation: Selecting an experimental design in AP Statistics here involves studying multiple factors and their interactions efficiently. The completely randomized design with four treatment groups (combinations of fertilizer and watering) is appropriate, as it randomly assigns plants to all combinations, allowing assessment of main effects and interactions without blocking needs. This fits the 40 similar plants and single-assignment constraint, supporting the goal of exploring if fertilizer effects depend on watering. Distractors: B is mismatched for time-based pairing; C blocks unnecessarily; D ignores one factor; E is not experimental. Mini-lesson: For factorial experiments with independent factors, use completely randomized assignment to treatment combinations; this enables interaction analysis, but ensure units are homogeneous to avoid needing blocks.

Question 13

1. Randomized block design blocking by gender, then randomly assign diets within each gender block (correct answer)
2. Completely randomized design assigning all participants to diets with no attention to gender
3. Matched-pairs design pairing participants by first name and assigning diets within pairs
4. Crossover design where each participant tries all three diets in random order over 30 weeks
5. Observational study where participants choose their preferred diet and then compare outcomes

Explanation: Selecting an experimental design in AP Statistics here involves incorporating potential moderators like gender into comparisons of multiple treatments. The randomized block design blocking by gender, with random assignment of diets within each block, is suitable to account for expected gender differences in weight loss while comparing the three diets. This matches the one-diet-per-participant constraint and the goal of fair assessment. Distractors: B disregards gender; C pairs poorly; D requires sequential diets, possibly confounding; E lacks control. Mini-lesson: Use blocking for suspected influential factors like gender; ensure randomization within blocks for multiple treatments, reducing unexplained variability and strengthening causal claims.

Question 14

1. Randomized block design blocking by shelf (top vs. bottom), then randomly assign light color within each shelf (correct answer)
2. Completely randomized design assigning each seedling to a light color and placing them wherever there is space
3. Matched-pairs design where each seedling is moved between shelves weekly to average out temperature
4. Use only the top shelf to eliminate blocking, then randomly assign light colors
5. Observational study: let students choose which light to use for each seedling and record growth

Explanation: In AP Statistics, selecting an experimental design means addressing spatial variability, like shelf temperature differences. The randomized block design blocking by shelf (top vs. bottom), with random assignment of light colors within each, is appropriate to control for temperature effects while comparing growth under red, blue, and white lights. This accommodates the 30 seedlings and single-light assignment, enhancing comparison accuracy. Distractors: B ignores shelves; C disrupts with movement; D eliminates a shelf, wasting resources; E is not experimental. Mini-lesson: Block on environmental factors like shelf position when they affect outcomes; randomize treatments within blocks to balance designs, particularly with multiple treatments and limited units per block.

Question 15

1. Completely randomized design assigning half of participants to silent and half to moderate noise for a single session
2. Matched-pairs design where each participant experiences both conditions in random order (counterbalanced), comparing within person (correct answer)
3. Randomized block design blocking by the day of the week participants choose to attend
4. Observational study where participants choose whether to study in silence or noise
5. Factorial design adding a second factor for participant gender, requiring four treatments per person

Explanation: In AP Statistics, selecting an experimental design often means addressing individual differences through within-subject comparisons. The matched-pairs design where each participant experiences both noise conditions in random order is ideal, controlling for individual memory variability by comparing within persons and using counterbalancing to avoid order effects. This suits the two-session availability and focuses on noise's impact on recall. Distractors: A uses between-subjects, increasing variability; C blocks irrelevantly; D is observational; E adds unnecessary factors. Mini-lesson: Opt for matched-pairs or repeated measures when subjects can receive multiple treatments and individual differences are large; randomize order to counter carryover, enhancing sensitivity to treatment effects.

Question 16

1. Randomized block design: block by greenhouse side (north vs south), then randomly assign F1 or F2 within each block (correct answer)
2. Completely randomized design: randomly assign 20 plants to F1 and 20 to F2 across the whole greenhouse
3. Matched-pairs design: apply both fertilizers to the same plant on different weeks and compare yields
4. Systematic assignment: alternate fertilizers down each row to ensure equal counts
5. Latin square design: use rows, columns, and time as three blocking variables

Explanation: This question assesses selecting an appropriate design when location creates systematic variation in experimental units. The greenhouse has different light conditions between north and south sides, which could affect plant growth regardless of fertilizer. A randomized block design (choice A) blocks by greenhouse side, then randomly assigns fertilizers within each block, controlling for light differences while testing fertilizer effects. Choice B (completely randomized) ignores the light variation, potentially biasing results. Choice C is impossible since you can't apply different fertilizers to the same plant simultaneously. Choice D lacks randomization. Choice E is unnecessarily complex for this two-factor situation. The key principle is blocking on known sources of variation before randomizing treatments.

Question 17

1. Completely randomized design assigning all 48 students to the three breakfasts, ignoring grade level
2. Randomized block design: block by grade level, then randomly assign students within each grade to the three breakfasts (correct answer)
3. Matched-pairs design: pair students from different grades with similar GPAs, then assign one in each pair to each breakfast
4. Randomized block design: block by breakfast type, then randomly assign grade levels to blocks
5. Latin square design using grade level and teacher as two blocking factors, then assign breakfasts

Explanation: This question tests understanding of when to use randomized block design. The nutritionist suspects attention scores may differ by grade level, making grade a potential confounding variable that should be controlled through blocking. Option B correctly identifies this by blocking students by grade level (creating homogeneous groups of 9th, 10th, 11th, and 12th graders), then randomly assigning students within each grade to the three breakfast types. This ensures each breakfast is tested equally across all grade levels while controlling for grade-level differences. Option A ignores the grade effect entirely, while C unnecessarily pairs students across grades. Option D misunderstands blocking by trying to block on the treatment itself, and E introduces unnecessary complexity with Latin squares when simple blocking suffices. When you have a known source of variability (grade level) and can randomize within groups, randomized block design is the most appropriate choice.

Question 18

1. Completely randomized design assigning all employees to new vs. current training without considering department
2. Randomized block design blocking by department, then randomly assign training program within each department (correct answer)
3. Matched-pairs design pairing employees by alphabetical order and assigning one in each pair to the new program
4. Crossover design where each employee completes both training programs in random order
5. Cluster sample design selecting one department at random and giving everyone there the new program

Explanation: This AP Statistics skill focuses on designing experiments to compare treatments while controlling for group differences, like departments. The randomized block design blocking by department, with random assignment of training programs within each, is best to reduce variability from baseline typing speed differences and ensure fair comparison. It fits the one-program-per-employee constraint and the goal of reducing overall variability. Distractors: A ignores departments; C pairs arbitrarily; D requires both programs, possibly infeasible; E lacks comparison group. Mini-lesson: Block on categorical variables like department when they likely affect the response; randomize within blocks to balance treatments, improving the experiment's ability to detect true differences amid known heterogeneity.

Question 19

1. Completely randomized design assigning all students to the three methods with no attention to class period
2. Randomized block design with class period as the blocking variable, then randomly assign methods within each period (correct answer)
3. Matched-pairs design where each student uses all three methods in random order
4. Stratified random sample of students from each class period, then observe which method they choose
5. Randomized block design blocking on students' favorite method, then assign them to that method

Explanation: This question tests the skill of selecting an experimental design in AP Statistics, focusing on accounting for known sources of variability. The randomized block design with class period as the blocking variable is most appropriate because it ensures each review method is equally represented in each period, controlling for time-of-day effects while allowing random assignment within blocks to minimize bias. This design fits the constraint that each student uses only one method and enables fair comparison of test scores across methods. Distractors like A ignore blocking, potentially confounding results with period differences; C is impractical as students can't use all methods; D is observational, not experimental; and E blocks on an irrelevant variable. A mini-lesson: When a known factor like class period may influence the response, use blocking to group similar units and randomize treatments within blocks, reducing variability and increasing the power to detect treatment effects.

Question 20

1. Completely randomized design: randomly assign patients to Routine 1 or Routine 2 and have them do only that routine
2. Randomized block design: block by day of the week, then assign routines within each day
3. Matched-pairs design: each patient does both routines in randomized order and results are compared within patient (correct answer)
4. Cluster randomization: assign an entire clinic to Routine 1 and another clinic to Routine 2
5. Factorial design: include routine, age group, and gender as factors and require each patient to try all combinations

Explanation: This AP Statistics skill involves choosing a design to minimize person-to-person variability in comparing stretching routines on flexibility. The matched-pairs design in C is most suitable, having each patient try both routines in randomized order and comparing within individuals, directly controlling individual differences. Choice A doesn't account for variability with complete randomization; B blocks by day irrelevantly; D clusters by clinic, introducing group biases; and E's factorial is impractical requiring all combinations. A distractor is A, seeming straightforward, but it overlooks the ability to use within-subject comparisons. Mini-lesson: Select matched pairs when subjects can receive multiple treatments sequentially; randomize order to avoid carryover effects, making it powerful for reducing variability under constraints allowing repeated measures.