Audit an unfamiliar distribution-fit investigation
Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 75 minutes, as an unvalidated planning estimate. This collection contains 3 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.
Record the observation model, discrepancy, reference procedure and conclusion separately.
Show intermediate calculations and diagnose invalid inference; public solutions are practice, not independent certification.
Loading saved assessment responses…
0 of 3 tasks have recorded responses. No overall mastery score is assigned.
An independent exactly recorded sample is .1,.2,.7,.9. A Uniform[0,1] null was specified before collection. Compute both gap lists and D. A predeclared run of B=199 has 9 reference statistics at least D. Report its rank value and resolution. A colleague reports that the null is 95% likely and chooses to rerun until p<.05. Audit both claims.
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.
Observed positive waiting times are 1,2,3,6. Fit an exponential rate. Rescale the sample to minutes by dividing all times by 60. Specify a reference algorithm, including how every parameter is treated, and prove the discrepancy distribution is rate-free. For B=499 and 24 qualifying refitted references calculate the rank p-value. Explain what changes if times were rounded to the nearest original unit.
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 development sample has counts (40,40,20) for 0,1,2 flags per item. Fit a Binomial(2,theta) model and freeze the estimated theta before opening an independent validation sample of 100 items with counts (30,50,20). Compute the validation Pearson statistic against the frozen model. Which asymptotic degrees of freedom apply conditional on the development record? Contrast refitting on validation and explain the different question. State a condition under which a chi-square tail should not be reported.
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 exactly recorded sample is .1,.2,.7,.9. A Uniform[0,1] null was specified before collection. Compute both gap lists and D. A predeclared run of B=199 has 9 reference statistics at least D. Report its rank value and resolution. A colleague reports that the null is 95% likely and chooses to rerun until p<.05. Audit both claims.
Observed positive waiting times are 1,2,3,6. Fit an exponential rate. Rescale the sample to minutes by dividing all times by 60. Specify a reference algorithm, including how every parameter is treated, and prove the discrepancy distribution is rate-free. For B=499 and 24 qualifying refitted references calculate the rank p-value. Explain what changes if times were rounded to the nearest original unit.
A development sample has counts (40,40,20) for 0,1,2 flags per item. Fit a Binomial(2,theta) model and freeze the estimated theta before opening an independent validation sample of 100 items with counts (30,50,20). Compute the validation Pearson statistic against the frozen model. Which asymptotic degrees of freedom apply conditional on the development record? Contrast refitting on validation and explain the different question. State a condition under which a chi-square tail should not be reported.
