# Contract (P0) — F2-conf-03
**Question.** In the fixed-design model y_i = 1 + 0.5 x_i + sigma_i e_i (n=30, e_i iid N(0,1), x and sigma fixed from data/design.csv), do nominal 95% t(28) intervals for the OLS slope reach 95% coverage, using (a) conventional OLS SE and (b) HC1 robust SE?
**Estimands.** (a) P(beta in b̂ ± t.975(28) se_conv); (b) same with se_HC1 = sqrt(n/(n-2) * HC0); (c) exact SD of b̂ = sqrt(sum w_i^2 sigma_i^2), w_i=(x_i-x̄)/Sxx (analytic, valid because design is fixed and errors independent); (d) E[se_conv]. (a),(b),(d) by Monte Carlo, R=2000, fixed seed.
**Outputs.** out/results.json keys: task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc (ddof=1), mean_se_conventional, conventional_ci_undercovers (cov_conv < 0.95 - 3*MCSE), n_replications=2000, n_obs_per_replication=30, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed. Also out/report.md (6 sections incl. MCSE per coverage), out/analysis.py, out/claims.json (incl. claim on nominal coverage).
**Information rules.** Use only design.csv; never redraw x or sigma; only eps redrawn.
**Invalidity.** Design not 30 rows / missing or nonpositive sigma / constant x; R != 2000; unseeded simulation.
**Decision on MCSE.** "Binomial standard error at R=2000" is evaluated at the nominal p=0.95 (the null being tested): sqrt(0.95*0.05/2000). The SE at the estimated p is also reported; conclusion checked under both.