Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 120 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 a method and state its assumptions before opening answer guidance. Use sketches, tables and intermediate calculations when they support your argument.
These public tasks sample the published unit. A saved response records practice, not a secure examination result or a guarantee of semester or AP readiness.
Written answers require human review for correctness, completeness and interpretation. Suggested time is planning guidance; the interface has no timer.
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0 of 10 tasks have recorded responses. No overall mastery score is assigned.
A school invites volunteers through its sports newsletter to compare two study reminders. It randomly assigns each volunteer one reminder and measures the number of assignments submitted on time. Define the observational unit, variables and a statistical question. Explain which causal and population claims the design could support, name two selection limitations, and propose a design that improves generalization without losing random assignment.
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.
Among 80 morning commuters, 48 use the bus; among 120 afternoon commuters, 42 use it. Construct the full two-way count table. Find P(bus), P(morning | bus), and P(bus | morning). Are time group and bus use independent in this empirical distribution? Explain why reversing a conditional is not justified.
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 data 2, 4, 4, 6, 9, 11, compute mean, median and sample variance. Use the median-of-halves convention for quartiles and the 1.5 IQR rule for outliers. Describe what changes if 11 is replaced by 41 and why the original boxplot cannot reveal whether the two 4s were repeats from the same person.
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 synthetic length model is normal with mean 50 mm and SD 4 mm. Given P(Z≤1.5)=0.9332 and P(Z≤−1)=0.1587, find P(46≤X≤56). Convert to Y=2X+3: state its mean, SD and the corresponding interval. Explain whether these calculations validate the normal model.
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 paired observations are (0,1),(1,3),(2,2),(3,6). Compute the least-squares slope and intercept from centered sums, and the residuals. Calculate r² using the centered sums. Explain what residual inspection and the observational design can and cannot tell you about a causal claim or prediction at x=30.
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 fictional sorting sensor marks 90% of defective items and 5% of nondefective items. Defects make up 2% of production. Use a natural-frequency table for 10,000 items to find the probability of a defect given a mark. Also find the probability an item is either defective or marked. State the assumptions behind using this model for a new production batch.
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 synthetic game pays 0, 4 or 10 tokens with probabilities 1/2, 1/3 and 1/6. It costs 3 tokens to play. Find the expected net result and its variance. Explain why neither a positive expected value nor its variance establishes that a particular person should play.
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.
Under independent trials with constant success probability 1/4, compute the chance of exactly two successes in four trials and the chance of at least one. Then explain why drawing four objects without replacement from a box containing two successes and six failures uses a different model, and give its probability of exactly two successes.
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 draws from a population have mean 12 and finite SD 6. Give the mean and SD of the sample mean for n=9 and n=36. Explain separately what the law of large numbers and central limit theorem say. Could the same standard-error calculation justify a biased volunteer sample or guarantee normal individual observations?
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 probability sample of 50 from a roster of 300 people has 3 successes. An analyst proposes a normal-approximation confidence interval and says it will have a 95% probability of containing the fixed population proportion after it is computed. Audit the sampling fraction, success counts and interpretation. Describe a next step without pretending an invalid calculation becomes valid by producing endpoints.
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 school invites volunteers through its sports newsletter to compare two study reminders. It randomly assigns each volunteer one reminder and measures the number of assignments submitted on time. Define the observational unit, variables and a statistical question. Explain which causal and population claims the design could support, name two selection limitations, and propose a design that improves generalization without losing random assignment.
Among 80 morning commuters, 48 use the bus; among 120 afternoon commuters, 42 use it. Construct the full two-way count table. Find P(bus), P(morning | bus), and P(bus | morning). Are time group and bus use independent in this empirical distribution? Explain why reversing a conditional is not justified.
For data 2, 4, 4, 6, 9, 11, compute mean, median and sample variance. Use the median-of-halves convention for quartiles and the 1.5 IQR rule for outliers. Describe what changes if 11 is replaced by 41 and why the original boxplot cannot reveal whether the two 4s were repeats from the same person.
A synthetic length model is normal with mean 50 mm and SD 4 mm. Given P(Z≤1.5)=0.9332 and P(Z≤−1)=0.1587, find P(46≤X≤56). Convert to Y=2X+3: state its mean, SD and the corresponding interval. Explain whether these calculations validate the normal model.
Four paired observations are (0,1),(1,3),(2,2),(3,6). Compute the least-squares slope and intercept from centered sums, and the residuals. Calculate r² using the centered sums. Explain what residual inspection and the observational design can and cannot tell you about a causal claim or prediction at x=30.
A fictional sorting sensor marks 90% of defective items and 5% of nondefective items. Defects make up 2% of production. Use a natural-frequency table for 10,000 items to find the probability of a defect given a mark. Also find the probability an item is either defective or marked. State the assumptions behind using this model for a new production batch.
A synthetic game pays 0, 4 or 10 tokens with probabilities 1/2, 1/3 and 1/6. It costs 3 tokens to play. Find the expected net result and its variance. Explain why neither a positive expected value nor its variance establishes that a particular person should play.
Under independent trials with constant success probability 1/4, compute the chance of exactly two successes in four trials and the chance of at least one. Then explain why drawing four objects without replacement from a box containing two successes and six failures uses a different model, and give its probability of exactly two successes.
Independent draws from a population have mean 12 and finite SD 6. Give the mean and SD of the sample mean for n=9 and n=36. Explain separately what the law of large numbers and central limit theorem say. Could the same standard-error calculation justify a biased volunteer sample or guarantee normal individual observations?
A probability sample of 50 from a roster of 300 people has 3 successes. An analyst proposes a normal-approximation confidence interval and says it will have a 95% probability of containing the fixed population proportion after it is computed. Audit the sampling fraction, success counts and interpretation. Describe a next step without pretending an invalid calculation becomes valid by producing endpoints.
