Simulation of Confidence Interval for Population Mean with Known Variance

viewof settings = Inputs.form([
  Inputs.range([-5, 5], {value: 1, label: tex`\text{pop mean, }\mu`, step: 0.01}),
  Inputs.range([0.01, 5], {value: 1, label: tex`\text{pop stdev, }\sigma`, step: 0.01}),
  Inputs.range([0, 99], {value: 90, label: "confidence level", step: 1}),
  Inputs.range([0, 200], {value: 50, label: "sample size, n", step: 1})
  ])

viewof nrep = Scrubber(d3.ticks(1, 1000, 1000), {
  autoplay: false,
  loop: false,
  initial: 1,
  delay: 350,
  format: x => `number of datasets = ${x.toFixed(0)}`
})

textinfo = md`
Out of a total of ${nrep} samples, ${d3.sum(data.map(d => d.rep <= nrep && (mu >= d.lower && mu <= d.upper)))} (**<span style="color:red">${(d3.sum(data.map(d => d.rep <= nrep && (mu >= d.lower && mu <= d.upper)))*100/nrep).toFixed(3)}%</span>**) of the ${confidence}% confidence intervals contained the true population mean ${tex`\mu= `} ${mu}.
`

viewof lockvertical = Inputs.toggle({label: "Lock vertical axis", value: false})

plt = Plot.plot({
  width: 1600, // or a dynamic value based on `width` variable
  height: 600,
  style: {fontSize: "20px"},
  y: {
    label: "mean",
    domain: lockvertical ? [mu- 3, mu + 3] : [mu - 5*sigma/Math.sqrt(nobs),mu + 5*sigma/Math.sqrt(nobs)]
  },
  x: {
    label: "sample number",
    domain:  [0, nrep]
  },
  marks: [
    Plot.ruleX([0]),    
    Plot.ruleX(data, {
      filter: d => (d.rep <= nrep && mu >= d.lower && mu <= d.upper),
      x: "rep",
      y1: "lower",
      y2: "upper",  
      stroke: "steelblue",
      strokeWidth: 2.5
    }),
    Plot.dot(data, {filter: d => (d.rep <= nrep && mu >= d.lower && mu <= d.upper), x: "rep", y: "xbar", fill: "steelblue", r: 3}),

    Plot.ruleX(data, {
      filter: d => d.rep <= nrep && (mu < d.lower || mu > d.upper),
      x: "rep",
      y1: "lower",
      y2: "upper",  
      stroke: "orange",
      strokeWidth: 3.5
    }),
    Plot.dot(data, {filter: d => d.rep <= nrep && (mu < d.lower || mu > d.upper), x: "rep", y: "xbar", fill: "orange", r: 3}),
    Plot.ruleY([mu], {stroke: "#D22B2B", strokeWidth: 2.5})

  ]
})

Figure 1: https://observablehq.com/@mattiasvillani/confidence-interval-for-a-mean

import {Scrubber} from "@mbostock/scrubber"

function simulate_means(mu, sigma, nobs, nrep){
  
  const tvalue = jstat.studentt.inv(1-(1-(confidence/100))/2, nobs-1);
  var data = [];
  for (let j = 1; j <= nrep; j++){
        let sample = d3.range(nobs).map(d => d3.randomNormal(mu,sigma)())
        let xbar = d3.mean(sample)
        let s = jstat.stdev(sample, true) 
        let lower = xbar - tvalue*s/Math.sqrt(nobs)
        let upper = xbar + tvalue*s/Math.sqrt(nobs)
        data.push({rep: j, xbar: xbar, lower: lower, upper: upper})
  }
  return data
}

jstat = require('jstat')

mu = settings[0]
sigma = settings[1]
confidence = settings[2]
nobs = settings[3]

data = {
  nobs;
  mu;
  sigma;
  const d = new Date();
  let time = d.getTime();
  const data = simulate_means(mu, sigma, nobs, 1000)
  return data
}