Seeded Bootstrap Confidence Interval on a Real Sample

bootstrap-mean-small (ch06) shows the bootstrap mechanism on a 5-value pinned sample — too small for the resampling distribution to mean much. Here the same idea runs on line A's real 40-batch defect-rate sample via lmda bootstrap, with a fixed seed so the resampled confidence interval is byte-for-byte reproducible, not just conceptually repeatable.

The real dataset

data/defect_rate_line_a.csv is line A's 40 batches from the same manufacturing dataset as anova-defect-rate-by-line, filtered down to line == "A" (a plain row subset — every value is copied unchanged from the committed source file, nothing recomputed). | line | batch | defect_rate | |---|---|---| | A | 1 | 0.09 | | A | 2 | 0.025 | | A | 3 | 0.055 | | A | 4 | 0.06 | | A | 5 | 0.035 | The sample mean is exactly the mean value ANOVA reported for group A: 0.046875 over 40 batches. The question here is different from ANOVA's: not "do groups differ" but "how much would this mean itself wobble if we'd drawn a different 40 batches from the same process?"

Percentile bootstrap

lmda bootstrap resamples the 40 defect-rate values with replacement 5000 times, recomputes the mean each time, and reports the 2.5th/97.5th percentiles of that resampled distribution as a 95% confidence interval. --seed fixes the resampling draws so the result is exactly reproducible, not merely "close every time":

lmda bootstrap data/defect_rate_line_a.csv --column defect_rate --stat mean --reps 5000 --confidence 0.95 --seed 20260726 --format json

{
  "ci_lower": 0.04025,
  "ci_upper": 0.054125,
  "column": "defect_rate",
  "confidence": 0.95,
  "estimate": 0.046875,
  "n": 40,
  "reps": 5000,
  "seed": 20260726,
  "stat": "mean"
}

estimate matches the plain sample mean (0.046875); ci_lower/ci_upper bound the plausible range for the population mean this sample was drawn from, at 95% confidence — noticeably wider than the point estimate alone suggests, which is the whole reason to report an interval instead of a bare mean.

Honesty

The resampling and percentile computation are exact and the seed makes the interval exactly reproducible — this is a genuine confidence interval for line A's mean defect rate, not a demonstration, since n=40 is an adequate bootstrap sample size (unlike bootstrap-mean-small's n=5). Two scope limits still apply: (1) the bootstrap only resamples these 40 batches, so it captures batch-to-batch sampling variability but not any bias in how these particular 40 batches were selected or measured; (2) as with the other lessons in this chapter, the dataset is a realistic simulated manufacturing process (lmda's case-study-1 worked example), so this interval describes the simulated data-generating process, not an actual production line.

Implementation notes

data/defect_rate_line_a.csv is a plain row filter of anova-defect-rate-by-line/data/defect_rate.csv (line == "A", all 40 rows, no other column touched) — a reviewer can diff the two files by eye.
The bootstrap command above is re-run against the committed CSV on every validate_source.py pass and must byte-for-byte match the checked-in outputs/bootstrap-line-a-mean.json, including the reported estimate and interval bounds — the fixed --seed is what makes that byte-for-byte match possible for a randomized method.
Cross-reference: bootstrap-mean-small (ch06) for the tiny-sample mechanism trace; standard-error (ch06) for the closed-form analytic alternative to a resampled interval.