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Grade 11 · unit review

Review: Statistics: Study Design and Careful Inference

Evidence quality depends on how participants and conditions are selected. Random sampling supports population generalization, random assignment supports treatment comparisons, and uncertainty summaries do not repair biased recruitment or uncontrolled causal differences.

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Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. Fictional study 7 randomly assigns volunteers to practice A or B, then uses the same test. What does random assignment primarily help address?
Need a hint?
  • Random assignment distributes participants among treatment groups to reduce systematic preexisting differences.
  • Volunteer recruitment may limit generalization even after treatment assignment is random.
2. In fictional simulation 7, repeated random samples of size 100 have means less spread out than samples of size 10. Which interpretation is warranted?
Need a hint?
  • Repeated samples from one model can give different means.
  • Sample size cannot eliminate a biased selection method or nonresponse problem.
3. A supplied survey report gives estimate 55% with margin ±4 percentage points. What interval is reported?
Need a hint?
  • A reported estimate with an additive margin produces endpoints by subtracting and adding the margin.
  • This exercise interprets a supplied report and does not compute a confidence level or validate the survey.
4. In fictional observational study 7, students choosing a practice app have higher scores. What conclusion fits?
Need a hint?
  • An observational score difference can reflect preexisting differences between groups as well as an intervention.
  • Random sampling alone does not randomize treatment.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. Fictional study 9 randomly assigns volunteers to practice A or B, then uses the same test. What does random assignment primarily help address? Candidate answers: (A) It eliminates every possible study limitation (B) It makes volunteers representative of every school (C) It proves all tests measure the same thing (D) Preexisting differences between treatment groups. 2. In fictional simulation 9, repeated random samples of size 100 have means less spread out than samples of size 10. Which interpretation is warranted? Candidate answers: (A) Larger samples can make the sample mean more stable under this model (B) Larger samples guarantee the population mean exactly (C) Sample size removes nonresponse bias (D) The population changed whenever a sample mean changed. 3. A supplied survey report gives estimate 57% with margin ±4 percentage points. What interval is reported? Candidate answers: (A) 4% to 57% (B) 53% to 61% (C) 53% to 65% (D) 54.72% to 59.28%. 4. In fictional observational study 9, students choosing a practice app have higher scores. What conclusion fits? Candidate answers: (A) Every app user must score above every nonuser (B) Random sampling alone proves the app effect (C) The app caused the whole score difference (D) The groups differ in scores; motivation or other differences may explain part of it.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. Preexisting differences between treatment groups. Random assignment tends to balance preexisting differences across treatment groups. Random sampling addresses population representativeness; the two randomization steps answer different questions. 2. Larger samples can make the sample mean more stable under this model. Repeated-sample variability is sampling variation. With independent sampling from the same finite-variance model, larger samples generally reduce the spread of sample means; they do not guarantee exactness or repair a biased design. 3. 53% to 61%. Subtract and add four percentage points: 57−4=53, 57+4=61. A margin in percentage points is not a 4% multiplicative change. 4. The groups differ in scores; motivation or other differences may explain part of it. App choice was not randomly assigned. Existing motivation, prior preparation or other differences may affect both app use and scores. The observed association is evidence to investigate, not a clean estimate of a treatment effect.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.