1[2 {"id":"C1","text":"The conventional 95% OLS interval does not attain nominal coverage: estimated coverage 0.844, more than three binomial MC standard errors below 0.95.","results_keys":["coverage_conventional","conventional_ci_undercovers","undercover_threshold","mcse_coverage_conventional"],"status":"supported","caveat":"Conditional on this fixed design and normal errors; MC uncertainty ±~0.016."},3 {"id":"C2","text":"The HC1 interval improves coverage to 0.902 but still falls short of 95% at n = 30.","results_keys":["coverage_hc1","mcse_coverage_hc1"],"status":"supported","caveat":"Uses t(28) critical values as specified; other small-sample corrections not evaluated."},4 {"id":"C3","text":"The exact finite-sample SD of the slope estimator is 0.268, confirmed by the Monte Carlo SD of 0.270.","results_keys":["sd_beta_exact","sd_beta_mc"],"status":"supported","caveat":"Analytic value is exact; MC value has sampling error ~0.004."},5 {"id":"C4","text":"The conventional SE is biased downward: its mean (0.190) is about 71% of the true SD, which explains the undercoverage.","results_keys":["mean_se_conventional","sd_beta_exact"],"status":"supported","caveat":"Mean estimated from 2000 replications."}6]7