Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 100 minutes, as an unvalidated planning estimate. This collection contains 6 tasks; choose a manageable set and return for further sessions. Completing the whole collection may take substantially longer. This is a unit assessment, not a full course or AP examination.
Use the data and assumptions in each new case, not remembered worked-example values.
Show your display, sampling plan or distribution calculation and explain its limitations.
These public written tasks support review; a self-recorded response does not establish independent mastery.
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0 of 6 tasks have recorded responses. No overall mastery score is assigned.
A town is considering earlier bus departures. Design an investigation of unmet early-morning travel demand among adult residents during a named month. Contrast a completed census with a random sample and with an attempted census having nonresponse. Then classify (i) following enrolled residents’ trips next month and (ii) comparing last year’s archived trip records. State what causal claims the observational designs cannot establish and an ethical data plan.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
A research team has a frame of 224 consenting adult volunteers ordered by alternating novice and experienced status. It proposes a systematic sample of 28, then a 2×2 study of interface layout (compact/spacious) and instructions (text/diagram). Give an executable sampling plan, diagnose the ordering problem, repair it, and allocate seven sampled participants to each treatment. Define an outcome, identify feasible blinding and controls, and distinguish what random sampling from this frame and random assignment can justify.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
A new synthetic study has group C: 18 satisfied,12 not satisfied; group D: 8 satisfied,2 not satisfied. Construct a count bar chart and pie for the marginal satisfaction distribution. Then specify both a segmented-bar comparison and a mosaic, explaining their different widths and what they show about association. Do not make a causal claim.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Construct a keyed ordered stem-and-leaf display for 6,14,14,20,23,23,23,37,41,48. Report the strictly-below and at-or-below percentile ranks of 23. Find the nearest-rank 60th percentile cutpoint and explain how it relates to those ranks. Identify the median separately.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
A planning model uses independent Bernoulli samples with pA=0.75,nA=75 and pB=0.5,nB=100. Find the center and spread of D=p̂A−p̂B and estimate P(D<0.20), using Φ(1/√2)≈0.76025. Check expected counts. Then explain what changes if these are before/after observations on the same people rather than independently chosen groups.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Independent samples from normal populations have μA=31,σA=10,nA=25 and μB=28,σB=12,nB=36. Find the sampling distribution of D=X̄A−X̄B and P(1≤D≤5), using Φ(1/√2)≈0.76025. If both sample sizes are quadrupled, compare the center and spread. Finally explain why two strongly skewed finite-variance populations with these same parameters would require a separate approximation argument.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Review and revisit
Use each rubric to identify a valid argument, a missing condition or a step to revise. For independent evaluation, ask a teacher or reviewer to examine the complete reasoning. Self-review and recorded responses are not verified assessment results.
Coverage and targeted lesson returns
A town is considering earlier bus departures. Design an investigation of unmet early-morning travel demand among adult residents during a named month. Contrast a completed census with a random sample and with an attempted census having nonresponse. Then classify (i) following enrolled residents’ trips next month and (ii) comparing last year’s archived trip records. State what causal claims the observational designs cannot establish and an ethical data plan.
A research team has a frame of 224 consenting adult volunteers ordered by alternating novice and experienced status. It proposes a systematic sample of 28, then a 2×2 study of interface layout (compact/spacious) and instructions (text/diagram). Give an executable sampling plan, diagnose the ordering problem, repair it, and allocate seven sampled participants to each treatment. Define an outcome, identify feasible blinding and controls, and distinguish what random sampling from this frame and random assignment can justify.
A new synthetic study has group C: 18 satisfied,12 not satisfied; group D: 8 satisfied,2 not satisfied. Construct a count bar chart and pie for the marginal satisfaction distribution. Then specify both a segmented-bar comparison and a mosaic, explaining their different widths and what they show about association. Do not make a causal claim.
Construct a keyed ordered stem-and-leaf display for 6,14,14,20,23,23,23,37,41,48. Report the strictly-below and at-or-below percentile ranks of 23. Find the nearest-rank 60th percentile cutpoint and explain how it relates to those ranks. Identify the median separately.
A planning model uses independent Bernoulli samples with pA=0.75,nA=75 and pB=0.5,nB=100. Find the center and spread of D=p̂A−p̂B and estimate P(D<0.20), using Φ(1/√2)≈0.76025. Check expected counts. Then explain what changes if these are before/after observations on the same people rather than independently chosen groups.
Independent samples from normal populations have μA=31,σA=10,nA=25 and μB=28,σB=12,nB=36. Find the sampling distribution of D=X̄A−X̄B and P(1≤D≤5), using Φ(1/√2)≈0.76025. If both sample sizes are quadrupled, compare the center and spread. Finally explain why two strongly skewed finite-variance populations with these same parameters would require a separate approximation argument.
