# 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).