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 12 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.
Save or transcribe actual data, graph artifacts, technology settings and simulation trace rows where requested. A number alone does not demonstrate the workflow.
All datasets stated here are original synthetic teaching cases unless an explicitly attributed real dataset is selected. Distinguish empirical descriptions, assumed generating laws and population claims.
Written artifacts require review. Simulated repetitions are bounded model investigations, not new real-world observations or automatic mastery evidence.
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0 of 12 tasks have recorded responses. No overall mastery score is assigned.
Synthetic package delays are 0,1,1,2,2,3,4,4,7,12 minutes. Construct a dotplot, histogram with bins [0,3),[3,6),[6,9),[9,12] (last endpoint included), and a modified boxplot using median-of-halves quartiles. Explain an unusual value without automatically deleting it.
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.
Compare synthetic completion times A:5,6,6,7,7,8,8,9 and B:2,3,4,4,5,6,10,22 minutes using common-scale displays. Choose summaries for typical time and spread, then discuss a deadline of 9 minutes and sampling scope.
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.
Enter synthetic readings 62,66,68,70,70,70,72,74,78 into technology. Record n, mean, sample SD and a display. Assess a normal approximation and estimate the model fraction below 70−√21 using Φ(−1)=0.1587. Contrast the observed fraction below that cutoff and critique certainty.
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.
Use paired synthetic inputs x=0,1,2,3,4 and y=1,3,2,6,8. Compute Pearson r with technology and provide a scatterplot and centered-sum check. Interpret association, then explain the effect of converting x to 60x and sorting only one column.
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 synthetic time/response pairs (0,5),(1,6),(2,11),(3,14),(4,23),(5,31), use technology to compare linear, quadratic and exponential fits. Supply original-scale SSEs and residual plots. Interpret a linear slope’s units if time is days and response is millimeters, and discuss the intercept and extrapolation to day 20.
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.
Use SamplingMargin to calibrate a 90% margin at n=20 with 200 training draws, then evaluate it on 200 separate draws. Repeat at n=40. Record seeds, selected ranks/margins, error tables and evaluation coverage. Connect an illustrative observed estimate 0.60 to each interval and distinguish four uncertainty sources.
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.
Use RandomizationExplorer with a prespecified two-sided rule and 200 draws. Retain observed assignment, three simulated assignments/statistics, seed, exact tail probability and empirical tail fraction. Separately find the exact two-sided fraction for fixed outcomes 0,2,5,7,9,12 when treatment receives 7,9,12 and control 0,2,5. Explain which causal statement needs randomized 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.
Seven named applicants include three with certification. Uniformly choose chair and deputy without replacement. Compute the probability both are certified and the probability the selected people are exactly two specified certified applicants in either role order. Compare an unordered two-person committee.
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.
Roll a fair six-sided die and toss an independent fair coin. Let X equal the die value if heads and 0 if tails. Construct all elementary outcome mappings or a complete equivalent table, its mass graph and expectation. Explain why the seven distinct X values are not equally likely.
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.
Synthetic daily demand values 0,2,4 occur on 6,3,3 observed days. Build an empirical distribution and graph. A service incurs fixed cost 3 plus 2 per demand unit; construct its cost law and expected cost. Explain what new data would be needed before treating this as a forecast for all seasons.
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 equipment policy A costs 9 in every state. B costs 3 normally and 18 in disruption; C costs 6 normally and 11 in disruption. Compare at disruption probability 0.25 and identify the expected-cost minimizing policy for all 0 ≤ p ≤ 1. If an alert changes the conditional disruption probability to 0.6, reconsider and discuss risk.
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.
Design an equal-chance choice among five people using a fair six-sided die, with at most two attempts. Include a no-decision outcome, prove each unconditional and conditional selection probability, and explain why mapping the unused face to the first person would break fairness.
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
Synthetic package delays are 0,1,1,2,2,3,4,4,7,12 minutes. Construct a dotplot, histogram with bins [0,3),[3,6),[6,9),[9,12] (last endpoint included), and a modified boxplot using median-of-halves quartiles. Explain an unusual value without automatically deleting it.
Compare synthetic completion times A:5,6,6,7,7,8,8,9 and B:2,3,4,4,5,6,10,22 minutes using common-scale displays. Choose summaries for typical time and spread, then discuss a deadline of 9 minutes and sampling scope.
Enter synthetic readings 62,66,68,70,70,70,72,74,78 into technology. Record n, mean, sample SD and a display. Assess a normal approximation and estimate the model fraction below 70−√21 using Φ(−1)=0.1587. Contrast the observed fraction below that cutoff and critique certainty.
Use paired synthetic inputs x=0,1,2,3,4 and y=1,3,2,6,8. Compute Pearson r with technology and provide a scatterplot and centered-sum check. Interpret association, then explain the effect of converting x to 60x and sorting only one column.
For synthetic time/response pairs (0,5),(1,6),(2,11),(3,14),(4,23),(5,31), use technology to compare linear, quadratic and exponential fits. Supply original-scale SSEs and residual plots. Interpret a linear slope’s units if time is days and response is millimeters, and discuss the intercept and extrapolation to day 20.
Use SamplingMargin to calibrate a 90% margin at n=20 with 200 training draws, then evaluate it on 200 separate draws. Repeat at n=40. Record seeds, selected ranks/margins, error tables and evaluation coverage. Connect an illustrative observed estimate 0.60 to each interval and distinguish four uncertainty sources.
Use RandomizationExplorer with a prespecified two-sided rule and 200 draws. Retain observed assignment, three simulated assignments/statistics, seed, exact tail probability and empirical tail fraction. Separately find the exact two-sided fraction for fixed outcomes 0,2,5,7,9,12 when treatment receives 7,9,12 and control 0,2,5. Explain which causal statement needs randomized assignment.
Seven named applicants include three with certification. Uniformly choose chair and deputy without replacement. Compute the probability both are certified and the probability the selected people are exactly two specified certified applicants in either role order. Compare an unordered two-person committee.
Roll a fair six-sided die and toss an independent fair coin. Let X equal the die value if heads and 0 if tails. Construct all elementary outcome mappings or a complete equivalent table, its mass graph and expectation. Explain why the seven distinct X values are not equally likely.
Synthetic daily demand values 0,2,4 occur on 6,3,3 observed days. Build an empirical distribution and graph. A service incurs fixed cost 3 plus 2 per demand unit; construct its cost law and expected cost. Explain what new data would be needed before treating this as a forecast for all seasons.
A fictional equipment policy A costs 9 in every state. B costs 3 normally and 18 in disruption; C costs 6 normally and 11 in disruption. Compare at disruption probability 0.25 and identify the expected-cost minimizing policy for all 0 ≤ p ≤ 1. If an alert changes the conditional disruption probability to 0.6, reconsider and discuss risk.
Design an equal-chance choice among five people using a fair six-sided die, with at most two attempts. Include a no-decision outcome, prove each unconditional and conditional selection probability, and explain why mapping the unused face to the first person would break fairness.
