Sampling Demo

{
  "seed": 20261016,
  "repetitions": 5000,
  "sample_size": 20,
  "known_process_mean": 24.0,
  "known_process_sd": 4.0,
  "average_sample_mean": 23.99774600636704,
  "sd_of_sample_means": 0.9161553059435239,
  "theoretical_sd_of_sample_means": 0.8944271909999159,
  "average_sample_sd": 3.947305710821613,
  "nominal_confidence_level": 0.95,
  "intervals_covering_known_mean": 4724,
  "empirical_coverage_fraction": 0.9448,
  "first_five_intervals": [
    {
      "mean": 21.89817142932021,
      "low": 19.573535224890833,
      "high": 24.22280763374959,
      "covers_known_mean": true
    },
    {
      "mean": 23.61355373545937,
      "low": 22.078451331229452,
      "high": 25.148656139689287,
      "covers_known_mean": true
    },
    {
      "mean": 24.394121123267173,
      "low": 22.506993830254974,
      "high": 26.28124841627937,
      "covers_known_mean": true
    },
    {
      "mean": 24.66295772062001,
      "low": 22.579053876108002,
      "high": 26.74686156513202,
      "covers_known_mean": true
    },
    {
      "mean": 24.183896452458693,
      "low": 22.933658998222146,
      "high": 25.43413390669524,
      "covers_known_mean": true
    }
  ],
  "scope": "Independent normal teaching process, not shipment or real-workforce evidence. Each repetition creates a NEW sample.",
  "interpretation": "The method has 95% theoretical coverage under this normal independent model. A finite simulation need not cover in exactly 95% of repetitions. The parameter 24 is fixed throughout."
}