# Contract (P0)

Question. In the fixed-design model y_i = 1 + 0.5 x_i + sigma_i eps_i (n=30, x and sigma from data/design.csv, eps iid N(0,1)), do nominal 95% t(28) intervals for the OLS slope achieve 95% coverage?

Estimands. (a) P(beta in beta_hat ± t_.975(28) se_conv), se_conv = conventional OLS SE with s^2 = RSS/(n-2). (b) Same with se_HC1 = sqrt(n/(n-2) * HC0 sandwich). (c) Exact SD of beta_hat: sqrt(sum w_i^2 sigma_i^2), w_i = (x_i - xbar)/Sxx (analytic, valid since design fixed, errors independent). (d) E[se_conv], estimated by MC. (a),(b),(d) by Monte Carlo, R = 2000, fixed seed. Conclusion: undercovers iff coverage_conv < 0.95 - 3MCSE, MCSE = binomial SE at R=2000 (decision: evaluated at nominal p=0.95, sqrt(.95.05/2000); estimate-based SE also reported).

Outputs. out/results.json keys: task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc, mean_se_conventional, conventional_ci_undercovers, n_replications, n_obs_per_replication, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed. Also out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json, out/exclusions.csv.

Information rules. Only data/design.csv; constants from TASK.md; x and sigma never redrawn.

Invalidating conditions. Design file not 30 rows / missing or nonpositive sigma / constant x; R != 2000; non-reproducible seed.