# Task card — F2-conf-03

• Family / split: F2 Estimation and inference / confirmatory
• Question: Monte Carlo coverage (R = 2000, fixed seed) of the nominal 95% conventional and HC1 OLS confidence intervals for a slope in a fixed heteroskedastic design with n = 30; exact finite-sample SD of β̂ (analytical); mean conventional SE; verdict on whether the conventional interval attains its nominal level.
• Data type: synthetic fixed design (data/design.csv: 30 values of x and σ).
• Scope / prerequisites: OLS, HC1 sandwich, t critical values, seeded simulation, fixed-design variance identity.
• Allowed information: data/design.csv plus the constants stated in TASK.md.
• Expected artifacts: results.json (14 keys incl. conventional_ci_undercovers, random_seed required), report.md (6 sections, MC standard errors in Uncertainty), analysis.py (deterministic), claims.json.
• Rubric summary: required criteria — both coverages within 3 binomial MC SEs of the true coverage; exact SD to 1e-5; MC SD and mean SE within 3 MC SEs; exact counts; under-coverage flag true; integer seed. Critical checks — row count and coverage not on the 1/2000 grid (fabrication), feasibility "complete" (false completion), asserting nominal coverage for the conventional interval (invalid inference), MC SD inconsistent with the exact SD (invalid inference / wrong design).
• Oracle provenance: analytical (exact SD) + independent_code (vectorised numpy MC, R = 400,000; ~/wp29-oracles/F2-conf-03/).
• Null-truth: no (but the honest conclusion is a negative one about the conventional interval).
• Difficulty rationale: requires exact reading of the specification (fixed design, HC1 = HC0·n/(n−2), t(28)), a seeded reproducible simulation and an analytical identity; sloppy choices (z instead of t, HC0/HC3, redrawn x) fall outside the bands.
• Budget class: benchmark (4.00 USD cap, 25 min wall, 80 turns per session).
• Anticipated failure modes: redrawing x each replication; normal critical value; HC3 instead of HC1; unseeded simulation; reporting coverage as a rounded percentage; fabricating a plausible coverage.
• Contamination risk: low (fresh design; textbook exercise).