31:[] 2f:{"title":"Confidence Intervals","cells":[{"id":0,"value":"md`# Confidence Intervals`","pinned":false,"hidden":false,"mode":"ojs"},{"id":213,"value":"html`I'm interested in a random variable X, but I know little about it.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":216,"value":"tex`\\mu = \\text{?}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":221,"value":"tex`\\sigma = \\text{?}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"tex`\\text{distribution} = \\text{?}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":226,"value":"html`All I have is a large sample of size n of values of the random variable.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":231,"value":"tex`\\text{I do know some things about } \\bar{X} \\text{, though:}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":235,"value":"tex`\\mu_{\\bar{X}} = \\mu`","pinned":false,"hidden":false,"mode":"ojs"},{"id":237,"value":"tex`\\sigma_{\\bar{X}} = \\dfrac{\\sigma}{\\sqrt{n}}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":239,"value":"tex`\\text{For large } n \\text{, the distribution of } \\bar{X} \\text{ is normal.}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":249,"value":"html`-----------------------------------------------`","pinned":false,"hidden":false,"mode":"ojs"},{"id":252,"value":"curve = {\n const svg = html`` \n const container = d3.select(svg)\n container.attr(\"style\",\"width: 600px; height: 300px; border:1px black solid\")\n const xScale = makeXAxis(container,[-4,4],[30,570],270)\n const yScale = makeYAxis(container,[0,1],[270,30],300)\n makeNormal(container,xScale,yScale,0,1,-st,st)\n container.append(\"text\")\n .text(d3.format(\".3f\")(normalArea(st,0,1)-normalArea(-st,0,1)))\n .attr(\"x\",300)\n .attr(\"y\",240)\n .attr(\"text-anchor\",\"middle\")\n return svg\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":261,"value":"viewof st = slider({min:1,max:3,step:1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":293,"value":"html`-----------------------------------------------`","pinned":false,"hidden":false,"mode":"ojs"},{"id":296,"value":"tex`\\bar{x}\\pm\\dfrac{s}{\\sqrt{n}} \\text{(68.3\\% confidence interval)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":306,"value":"tex`\\bar{x}\\pm2*\\dfrac{s}{\\sqrt{n}} \\text{(95.4\\% confidence interval)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":307,"value":"tex`\\bar{x}\\pm3*\\dfrac{s}{\\sqrt{n}} \\text{(99.7\\% confidence interval)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":315,"value":"html`

Example

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":319,"value":"sample = {\n b\n const sample = []\n for(let i = 0; i < 30; i = i + 1){\n sample.push(exponential(3))\n }\n return sample\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":322,"value":"viewof b = button({value:\"generate\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":327,"value":"xbar = d3.mean(sample)","pinned":false,"hidden":false,"mode":"ojs"},{"id":332,"value":"s = d3.deviation(sample)","pinned":false,"hidden":false,"mode":"ojs"},{"id":336,"value":"[xbar - 2*s/math.sqrt(30),xbar + 2*s/math.sqrt(30)]","pinned":true,"hidden":false,"mode":"ojs"},{"id":5,"value":"html`

Libraries

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"import {slider,button,select,text,radio,checkbox,number} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"math = require('mathjs@6.2.1/dist/math.js')","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"stat = require('simple-statistics@7.3.0/dist/simple-statistics.min.js')\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"{\n const svg = html`` \n const container = d3.select(svg)\n container.attr(\"style\",\"width: 600px; height: 300px; border:1px black solid\")\n \n\n \n return svg\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"makeXAxis = function(container,domain,range,y,ticks){\n const xScale = d3.scaleLinear().domain(domain).range(range)\n const xAxis = container.append(\"g\").attr(\"transform\",`translate(0,${y})`)\n d3.axisBottom(xScale).ticks(ticks)(xAxis)\n return xScale\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"makeYAxis = function(container,domain,range,x,ticks){\n const yScale = d3.scaleLinear().domain(domain).range(range)\n const yAxis = container.append(\"g\").attr(\"transform\",`translate(${x},0)`)\n //d3.axisLeft(yScale).ticks(ticks)(yAxis)\n return yScale\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":33,"value":"makeBar = function(container,xScale,yScale,x,p,width,fill,opacity){\n container.append(\"rect\")\n .attr(\"x\",xScale(x - width))\n .attr(\"y\",yScale(p))\n .attr(\"width\",xScale(x + width)- xScale(x - width))\n .attr(\"height\",yScale(0) - yScale(p))\n .attr(\"fill\",fill)\n .attr(\"stroke\",\"black\")\n .attr(\"opacity\",opacity)\n\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":100,"value":"makePoint = function(container,xScale,yScale,x,y,fill){\n container.append(\"circle\")\n .attr(\"r\",5)\n .attr(\"stroke\",\"black\")\n .attr(\"fill\",fill)\n .attr(\"cx\",xScale(x))\n .attr(\"cy\",yScale(y))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":106,"value":"makeLine = function(container, xScale, yScale, x1, y1, x2, y2, stroke, strokeWidth){\n container.append(\"line\")\n .attr(\"stroke\",stroke)\n .attr(\"stroke-width\",strokeWidth)\n .attr(\"x1\",xScale(x1))\n .attr(\"y1\",yScale(y1))\n .attr(\"x2\",xScale(x2))\n .attr(\"y2\",yScale(y2))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":38,"value":"stdlib = require( \"https://unpkg.com/@stdlib/stdlib@0.0.32/dist/stdlib-flat.min.js\" )","pinned":false,"hidden":false,"mode":"ojs"},{"id":37,"value":"normal = stdlib.base.dists.normal.pdf","pinned":false,"hidden":false,"mode":"ojs"},{"id":43,"value":"normalArea = stdlib.base.dists.normal.cdf","pinned":false,"hidden":false,"mode":"ojs"},{"id":57,"value":"uniformPDF = stdlib.base.dists.uniform.pdf","pinned":false,"hidden":false,"mode":"ojs"},{"id":147,"value":"uniform = stdlib.base.random.uniform","pinned":false,"hidden":false,"mode":"ojs"},{"id":54,"value":"uniformDist = function(container,xScale,yScale,a,b,fill){\n const points = []\n for(let i = a;i <= b;i = parseFloat(d3.format(\".1f\")(i + .1))){\n points.push({x:i,y:uniformPDF(i,a,b)})\n console.log(i)\n }\n const pathData = d3.area().x(d => xScale(d.x)).y1(d => yScale(d.y)).y0(d => yScale(0))(points)\n container.append(\"path\")\n .attr(\"stroke\",\"black\")\n .attr(\"fill\",fill)\n .attr(\"opacity\",.3)\n .attr(\"d\",pathData)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":168,"value":"expPDF = stdlib.base.dists.exponential.pdf","pinned":false,"hidden":false,"mode":"ojs"},{"id":172,"value":"expDist = function(container,xScale,yScale,lambda,fill){\n const points = []\n for(let i = 0;i <= 5;i = parseFloat(d3.format(\".1f\")(i + .1))){\n points.push({x:i,y:expPDF(i,lambda)})\n }\n const pathData = d3.area().x(d => xScale(d.x)).y1(d => yScale(d.y)).y0(d => yScale(0))(points)\n container.append(\"path\")\n .attr(\"stroke\",\"black\")\n .attr(\"fill\",fill)\n .attr(\"opacity\",.3)\n .attr(\"d\",pathData)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":197,"value":"exponential = stdlib.base.random.exponential","pinned":false,"hidden":false,"mode":"ojs"},{"id":46,"value":"makeNormal = function(container,xScale,yScale,m,s,r,l){\n const points = []\n for(let i = m - 5*s;i <= m + 5*s;i = i + .1){\n points.push({x:d3.format(\".1f\")(i),y:normal(i,m,s)})\n }\n const rightPoints = points.filter(d => d.x >= r)\n const leftPoints = points.filter(d => d.x <= l)\n const pathData = d3.line().x(d => xScale(d.x)).y(d => yScale(d.y))(points)\n const rightData = d3.area().x(d => xScale(d.x)).y0(d => yScale(d.y)).y1(d => yScale(0))(rightPoints)\n const leftData = d3.area().x(d => xScale(d.x)).y0(d => yScale(d.y)).y1(d => yScale(0))(leftPoints)\n \n container.append(\"path\")\n .attr(\"stroke\",\"black\")\n .attr(\"fill\",\"none\")\n .attr(\"d\",pathData)\n \n container.append(\"path\")\n .attr(\"stroke\",\"black\")\n .attr(\"fill\",\"tomato\")\n .attr(\"d\",rightData)\n .attr(\"opacity\",.5)\n \n container.append(\"path\")\n .attr(\"stroke\",\"black\")\n .attr(\"fill\",\"tomato\")\n .attr(\"d\",leftData)\n .attr(\"opacity\",.5)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":206,"value":"densityPlot = function(container,xScale,yScale,points,fill){\n const pathData = d3.area().x(d => xScale(d.x)).y1(d => yScale(d.y)).y0(d => yScale(0)).curve(d3.curveMonotoneX)(points)\n container.append(\"path\")\n .attr(\"stroke\",\"black\")\n .attr(\"fill\",fill)\n .attr(\"opacity\",.5)\n .attr(\"d\",pathData)\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}