Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 150 minutes, as an unvalidated planning estimate. This collection contains 10 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.
Choose and justify a method before opening the solution. Include the assumptions, intermediate work and interpretation that make the answer defensible.
These public mixed tasks sample the unit; they are not a secure exam, independent certification or a guarantee of AP or university readiness.
Written responses require human review. Saving a response records practice, not verified correctness. The suggested time is planning guidance, with no timer.
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0 of 10 tasks have recorded responses. No overall mastery score is assigned.
An independent random sample of 200 has 70 successes. Using multiplier 2, construct a normal proportion interval and check observed counts. Plan a separate study for margin at most 0.04 using the conservative probability 0.5 and the same multiplier. Interpret confidence and state one source of error the calculation cannot fix.
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.
Before data collection a team specifies H0:p=0.4 versus H1:p>0.4. It observes 58 successes in 100 independent randomly sampled trials. Compute the null-based statistic; use the supplied upper-tail probability 0.00012 and alpha=0.01 to decide. Define both error types here. If power at p=0.58 is 0.87, what is beta there?
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.
Two independent random samples have 48/120 successes in A and 30/100 in B. Estimate pA−pB and give its interval with multiplier 2. Compute the pooled-null statistic for equality. A prespecified practical improvement threshold is 0.08. Does the interval establish an improvement exceeding that threshold?
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.
The 2×3 observed table has rows (20,30,10) and (30,20,10). Construct expected counts, statistic and degrees of freedom. Use supplied upper-tail probability 0.1353 at alpha=0.05. Explain how the study question changes if this is one random sample cross-classified by two variables versus independent samples from two populations.
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.
For 16 independent observations from a plausibly normal population without severe outliers, x̄=22 and s=8. Construct a mean interval using t*=2.131. Test H0:μ=18 against μ≠18 using a supplied two-sided p-value 0.064. Compare at alpha=0.05, explain the reference df, and distinguish this interval from a prediction for one new observation.
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.
Study P measures the same 9 people before and after; after-minus-before differences have mean 3 and SD 6. Study W compares independent groups with n1=10,n2=20, means 15 and 12, and variances 20 and 40. For each, compute the appropriate SE and test statistic for zero difference; give df (exact for P, Welch approximation for W). Explain why the same raw difference of means need not mean the same uncertainty or 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.
Four fixed outcomes are 1,3,6,8. Exactly two units were randomly assigned treatment. Under the sharp null of no effect for any unit, enumerate treatment-minus-control mean differences. The observed treated units have outcomes 6 and 8. Find the exact two-sided randomization p-value using absolute differences and including ties. Explain why observationally chosen groups would not justify the same reference.
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 researcher has 30 independent patient records, each containing before and after measurements. Explain a bootstrap for the mean change, including one resample construction and a percentile interval from supplied 2.5th and 97.5th percentiles −0.4 and 2.7. Critique resampling the 60 measurements individually, treating the interval as a null distribution, and using more resamples to cure a volunteer-only sample.
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 team runs 20 independent true-null tests, each with exact Type I error probability 0.05 and reports only the smallest p-value. Find the probability of at least one false rejection, and propose a simple familywise control rule. Separately, does an effect interval [−0.12,0.14] establish equivalence within a prespecified margin ±0.05?
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 web poll of 10,000 volunteers reports 62% support and a very narrow nominal normal interval. A different study randomly assigns 80 volunteers to two teaching methods and measures exam scores. Write a short decision brief: what can each study support, what must be checked, and what additional design would support generalization to all students?
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
An independent random sample of 200 has 70 successes. Using multiplier 2, construct a normal proportion interval and check observed counts. Plan a separate study for margin at most 0.04 using the conservative probability 0.5 and the same multiplier. Interpret confidence and state one source of error the calculation cannot fix.
Before data collection a team specifies H0:p=0.4 versus H1:p>0.4. It observes 58 successes in 100 independent randomly sampled trials. Compute the null-based statistic; use the supplied upper-tail probability 0.00012 and alpha=0.01 to decide. Define both error types here. If power at p=0.58 is 0.87, what is beta there?
Two independent random samples have 48/120 successes in A and 30/100 in B. Estimate pA−pB and give its interval with multiplier 2. Compute the pooled-null statistic for equality. A prespecified practical improvement threshold is 0.08. Does the interval establish an improvement exceeding that threshold?
The 2×3 observed table has rows (20,30,10) and (30,20,10). Construct expected counts, statistic and degrees of freedom. Use supplied upper-tail probability 0.1353 at alpha=0.05. Explain how the study question changes if this is one random sample cross-classified by two variables versus independent samples from two populations.
For 16 independent observations from a plausibly normal population without severe outliers, x̄=22 and s=8. Construct a mean interval using t*=2.131. Test H0:μ=18 against μ≠18 using a supplied two-sided p-value 0.064. Compare at alpha=0.05, explain the reference df, and distinguish this interval from a prediction for one new observation.
Study P measures the same 9 people before and after; after-minus-before differences have mean 3 and SD 6. Study W compares independent groups with n1=10,n2=20, means 15 and 12, and variances 20 and 40. For each, compute the appropriate SE and test statistic for zero difference; give df (exact for P, Welch approximation for W). Explain why the same raw difference of means need not mean the same uncertainty or causal claim.
Four fixed outcomes are 1,3,6,8. Exactly two units were randomly assigned treatment. Under the sharp null of no effect for any unit, enumerate treatment-minus-control mean differences. The observed treated units have outcomes 6 and 8. Find the exact two-sided randomization p-value using absolute differences and including ties. Explain why observationally chosen groups would not justify the same reference.
A researcher has 30 independent patient records, each containing before and after measurements. Explain a bootstrap for the mean change, including one resample construction and a percentile interval from supplied 2.5th and 97.5th percentiles −0.4 and 2.7. Critique resampling the 60 measurements individually, treating the interval as a null distribution, and using more resamples to cure a volunteer-only sample.
A team runs 20 independent true-null tests, each with exact Type I error probability 0.05 and reports only the smallest p-value. Find the probability of at least one false rejection, and propose a simple familywise control rule. Separately, does an effect interval [−0.12,0.14] establish equivalence within a prespecified margin ±0.05?
A web poll of 10,000 volunteers reports 62% support and a very narrow nominal normal interval. A different study randomly assigns 80 volunteers to two teaching methods and measures exam scores. Write a short decision brief: what can each study support, what must be checked, and what additional design would support generalization to all students?
