Selecting an Experimental Design - AP Statistics

1. An engineer wants to test whether two different machine settings (Setting X vs. Setting Y) affect the strength of a plastic part. Parts are produced on four different machines, and the engineer believes machines may differ slightly in calibration, affecting overall strength. Each machine can produce parts under both settings during the day, and the response is part strength. Which experimental design is most appropriate?
   Answer: Randomized block design blocking by machine, then randomly assign Setting X or Y to parts produced on each machine 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.
2. A city wants to test whether two different email subject lines (S1 vs S2) increase the percentage of residents who click a link to complete an online survey. Clicking behavior differs substantially by age group (18–34, 35–54, 55+). The city can randomly assign subject lines to residents' emails. Which experimental design is most appropriate?
   Answer: Randomized block design: block by age group, then randomly assign S1 or S2 within each age group This question tests recognizing when to block on a demographic variable that affects the response. Since clicking behavior varies substantially by age group, we need to control for age to accurately measure the effect of subject lines. A randomized block design (choice A) blocks by age group (18-34, 35-54, 55+), then randomly assigns subject lines within each block, ensuring both subject lines are tested across all age groups while controlling for age-related differences. Choice B ignores age variation, potentially masking treatment effects. Choice C violates the single-email constraint. Choice D is a sampling technique, not a comparative experiment. Choice E blocks by geography rather than the stated source of variation (age).
3. A school cafeteria manager wants to compare three different menu layouts (A, B, C) to see which leads to the highest average number of fruit servings selected per student at lunch. Fruit selection differs a lot by grade level (9th, 10th, 11th, 12th), and the manager can implement only one layout per lunch period. Which experimental design is most appropriate to estimate the effect of layout while accounting for grade level?
   Answer: Randomized block design: block by grade level, then randomly assign lunch periods within each grade to layouts A, B, or C This question tests understanding of randomized block design when experimental units naturally group by a confounding variable. Since fruit selection varies significantly by grade level, we need to control for this variation to isolate the effect of menu layout. A randomized block design (choice C) blocks by grade level, then randomly assigns lunch periods within each grade to layouts A, B, or C, ensuring each layout is tested across all grades while controlling for grade-level differences. Choice A (completely randomized) ignores the grade effect, potentially confounding results. Choice B incorrectly limits comparison to only two layouts. Choice D is a sampling method, not an experimental design. Choice E blocks by day rather than grade, failing to address the stated source of variation.
4. A dermatologist wants to compare two acne creams (Cream A vs. Cream B). Each patient has acne on both the left and right side of their face, and the dermatologist believes acne severity varies a lot from person to person. Each patient can safely use both creams at the same time, one on each side, for 6 weeks, and the response is reduction in acne lesions per side. Which experimental design is most appropriate?
   Answer: Randomized block design blocking by patient, randomly assign Cream A to one side and Cream B to the other side 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.
5. A researcher wants to compare four study strategies (flashcards, practice tests, rereading, and summarizing) on a vocabulary test. Students' prior vocabulary level (low vs high, based on a pretest) is expected to strongly affect outcomes. The researcher has 80 students total and can assign each student to only one strategy. Which experimental design is most appropriate?
   Answer: Randomized block design: block by prior vocabulary level (low/high), then randomly assign strategies within each block 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.
6. A psychologist wants to test whether background music (music vs. silence) and lighting (bright vs. dim) affect memory recall on a standardized test. Each participant can be tested once, and the lab can randomly assign participants to conditions. The psychologist is interested in both main effects and whether the effect of music depends on lighting. Which experimental design is most appropriate?
   Answer: Completely randomized $2\times 2$ factorial design with four groups (music/bright, music/dim, silence/bright, silence/dim) This AP Statistics question assesses selecting a design to examine main effects and interactions between factors like music and lighting on memory recall. The completely randomized 2x2 factorial design in D is ideal, randomly assigning participants to one of four combinations to evaluate both individual effects and whether music's impact varies by lighting, fitting the single-test constraint. Choice A omits lighting, missing interactions; B blocks unnecessarily by gender without mention of its relevance; C uses matched pairs but tests each participant only once per condition, not aligning with the one-test limit; and E is observational, lacking randomization. A common distractor is B, assuming gender matters, but the question focuses on music and lighting factors. Mini-lesson: Opt for factorial designs when interested in interactions between multiple factors; randomize assignments to conditions to ensure causality, avoiding observational approaches that can't establish cause-effect relationships.
7. A coach wants to compare two training programs (P1 vs. P2) on athletes' sprint times. Sprint times differ by position group (sprinters vs. middle-distance), and the coach can assign athletes within each position group to a program. However, the coach wants each athlete to follow only one program for the season. Which experimental design is most appropriate to control for position group while comparing programs?
   Answer: Randomized block design: block by position group, then randomly assign athletes within each block to P1 or P2 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.
8. A physical therapist wants to compare two stretching routines (Routine 1 vs. Routine 2) on flexibility improvement. Flexibility varies widely from person to person, and each patient can complete both routines on separate days one week apart, with the order randomized. The therapist will measure improvement after each routine. Which experimental design is most appropriate to reduce person-to-person variability?
   Answer: Matched-pairs design: each patient does both routines in randomized order and results are compared within patient 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.
9. An engineering team wants to test whether two materials (Material X vs Material Y) produce different average breaking strengths. The testing machine warms up over time, potentially affecting measured strength, so the team plans to test 20 samples total in one day. They can randomize the order of tests, and each sample can be tested only once (it breaks). Which experimental design is most appropriate?
   Answer: 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 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.
10. A marketing team wants to test three website layouts (L1, L2, L3) to see which leads to the highest purchase rate. Purchase behavior differs by device type (mobile vs. desktop), and the team can randomly assign incoming visitors to one layout. They have enough traffic to assign visitors within each device type to all three layouts. Which experimental design is most appropriate?
    Answer: Randomized block design: block by device type, then randomly assign visitors within each block to L1, L2, or L3 In AP Statistics, this question on experimental design selection emphasizes controlling for device type differences in purchase rates across website layouts. Choice A's randomized block design, blocking by device and randomizing layouts within blocks, best accounts for this variation while ensuring balanced comparisons with sufficient traffic. Choice B ignores device without blocking; C can't show all layouts to one visitor feasibly; D clusters incompletely, omitting L3 and lacking randomization; E adds irrelevant factors complicating unnecessarily. Distractors like B might attract those undervaluing blocking, but device is a key confounder. Mini-lesson: Employ blocking for categorical variables like device that influence responses; randomize within blocks to isolate treatment effects, especially when constraints like traffic volume allow balanced allocation without repeated exposures.
11. A psychology teacher wants to test whether background music affects quiz performance. The teacher has two class periods of the same course (Period 2 and Period 5). Because the teacher cannot play music for some students and not others within the same room at the same time, the teacher must choose one condition per class period on quiz day. Which experimental design is most appropriate?
    Answer: Cluster randomized design: randomly assign each entire class period to either music or no music 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.
12. An agriculture researcher wants to study the effects of fertilizer type (Type 1 vs. Type 2) and watering schedule (daily vs. every other day) on tomato yield. The researcher has 40 similar tomato plants and can randomly assign each plant to one fertilizer and one watering schedule for the entire growing season. The researcher is also interested in whether the effect of fertilizer depends on watering schedule. Which experimental design is most appropriate?
    Answer: Completely randomized design with 4 treatment groups (all combinations of fertilizer and watering), randomly assign plants to groups 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.
13. A school wants to compare three review methods for an AP Statistics unit test: online practice, in-class worksheets, and peer tutoring. Because different class periods (1st, 3rd, 6th) tend to have different average performance due to time-of-day effects, the researcher wants to ensure each method is used in each period while still randomly assigning students. Each student can use only one method for the week before the test, and the outcome is the test score. Which experimental design is most appropriate?
    Answer: Randomized block design with class period as the blocking variable, then randomly assign methods within each period 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.
14. A medical researcher wants to compare the effect of three doses of a supplement (0 mg, 50 mg, 100 mg) on reaction time. Reaction time is also affected by time of day (morning, afternoon, evening). The researcher can run 9 sessions total and can recruit one participant per session (different participant each session). The researcher wants each dose tested once at each time of day to control for time-of-day effects without increasing the number of sessions. Which experimental design is most appropriate?
    Answer: Latin square design so that each dose occurs once in each time-of-day category across the 9 sessions 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.
15. A horticulture club wants to test whether three fertilizers (A, B, C) affect tomato yield. The garden has 24 plots, but plots differ in sunlight (full sun vs partial shade). The club can apply only one fertilizer to each plot for the season. Which experimental design is most appropriate?
    Answer: Randomized block design: block by sunlight level, then randomly assign fertilizers within each sunlight block This scenario presents a classic case for randomized block design when dealing with a known environmental factor affecting the response. The horticulture club recognizes that sunlight level (full sun vs partial shade) will likely affect tomato yield regardless of fertilizer type, making it a confounding variable. Option A correctly blocks the 24 plots by sunlight level, creating homogeneous groups, then randomly assigns the three fertilizers within each sunlight block. This ensures each fertilizer is tested under both sunlight conditions while controlling for the sunlight effect. Option B would ignore this important environmental factor, potentially biasing results. Option C suggests matched pairs but you can't apply two fertilizers to the same plot simultaneously. Options D and E misunderstand the experimental structure entirely. Randomized block design is ideal when you have a categorical nuisance variable (sunlight) that you can group by before randomization.
16. A researcher is studying whether background music affects proofreading accuracy. Each participant can complete two comparable proofreading passages in one session, but people vary widely in baseline proofreading skill. The researcher wants to compare Silence vs Instrumental Music and can randomize the order in which each participant experiences the two conditions. Which experimental design is most appropriate?
    Answer: Matched-pairs (crossover) design: each participant does one passage in Silence and one with Instrumental Music, with randomized order This question tests recognizing matched-pairs (crossover) design when subjects can receive multiple treatments. Since participants vary widely in baseline proofreading skill and each can complete two passages, we can use each person as their own control. A matched-pairs crossover design (choice B) has each participant experience both conditions (Silence and Music) with randomized order, controlling for individual skill differences while testing the music effect. Choice A treats participants as separate groups, losing the within-person comparison advantage. Choice C incorrectly blocks by passage rather than person. Choice D lacks randomization and control. Choice E assigns conditions to entire sessions rather than individuals. Crossover designs are powerful when subjects can receive all treatments without carryover effects.
17. A biology teacher wants to test whether light color affects plant growth using red, blue, and white grow lights. The classroom has two shelves: the top shelf is consistently warmer than the bottom shelf, and temperature is expected to affect growth. The teacher has 30 identical seedlings and can place each seedling under one light color on one shelf for 4 weeks. Which experimental design is most appropriate?
    Answer: Randomized block design blocking by shelf (top vs. bottom), then randomly assign light color within each shelf 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.
18. A school nutritionist wants to compare three types of breakfast (high-protein, high-carb, and balanced) on students' attention scores after first period. Attention may differ by grade level (9th–12th), and the nutritionist can recruit 12 students from each grade. Each student will eat only one breakfast on the test day, and students within a grade can be randomly assigned. Which experimental design is most appropriate?
    Answer: Randomized block design: block by grade level, then randomly assign students within each grade to the three breakfasts 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.
19. A school nutritionist wants to compare three breakfast options (A, B, C) on students' morning alertness scores. Alertness is known to differ by grade level (9th–12th), and the nutritionist can only serve one breakfast to each student on the test day. Within each grade, there are enough volunteers to try all three breakfasts, and students will be tested during the same first-period class. Which experimental design is most appropriate to reduce the effect of grade level while fairly comparing the three breakfasts?
    Answer: Randomized block design: block by grade level, then randomly assign students within each grade to A, B, or C 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.
20. A bakery wants to compare two oven temperature settings (T1 vs T2) on average cookie crispness. The bakery has two ovens that tend to bake slightly differently, and each batch must be baked entirely in one oven. The bakery can bake 24 batches total and can choose which oven and temperature each batch uses. Which experimental design is most appropriate?
    Answer: Randomized block design: block by oven (Oven 1 vs Oven 2), then randomly assign T1 or T2 to batches within each oven This question addresses blocking when equipment creates systematic variation. Since the two ovens bake slightly differently, oven type could confound temperature effects if not controlled. A randomized block design (choice B) blocks by oven, then randomly assigns temperatures to batches within each oven, ensuring both temperatures are tested in both ovens while controlling for oven-specific effects. Choice A ignores oven differences, potentially biasing results. Choice C is impractical as you can't bake the same batch twice. Choice D is observational, not experimental. Choice E is unnecessarily complex for a two-factor situation. The principle is to block on known sources of variation (ovens) before randomizing treatments (temperatures).

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