1# Contract (P0) — T2-simulation23**Question.** With few clusters, how reliable are cluster-robust 95% CIs for a population mean μ (point estimate ȳ)?45**Estimands (per cell × procedure).** Design: G ∈ {5,10,30} × ICC ∈ {0,0.2,0.5}; procedures CR0 (z), CR1 (t_{G−1}), WCB (wild cluster bootstrap-t, Rademacher, unrestricted, B=399).6(a) actual coverage P(μ ∈ CI); (b) for CR0/CR1, E[V̂]/Var(ȳ) with exact Var(ȳ) = [ICC Σn_g² + (1−ICC)N]/N²;7(c) MC SE √(p̂(1−p̂)/R); (d) failure regimes: coverage < 0.90; nominal-consistent: |p̂−0.95| ≤ 2 MC SE.8Meaningful under the stated Gaussian random-intercept DGP with the fixed unbalanced cluster sizes (8,16,32,64 repeated); conclusions are conditional on this design.910**Outputs.** out/results.json (task_id, R, B, n_cells, coverage{27}, mc_se_coverage{27}, rel_bias_var{18}, failure_cells, n_failure_cells, nominal_cells, best_procedure_small_G, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/table1.csv (27 rows: estimator, cell_id, G, icc, coverage, mc_se_coverage, rel_bias_var (blank for wcb), mean_ci_halfwidth, R); out/figure1.png; out/report.md (6 sections); out/analysis.py; out/claims.json. Key format `<est>_G<G>_icc<icc>` with icc as 0.0/0.2/0.5.1112**Information rules.** Use exactly the DGP, procedures, R=2000, B=399, per-cell seeds from design.csv; no grid change. Only data/design.csv as input.1314**Invalidity.** Changing R/B/grid/seeds, different procedure definitions, non-deterministic output, or runtime >10 min. Design inconsistencies (e.g. N ≠ Σ n_g) would need to be reported.15