binomial_inference.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7c8bd949",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "01558b35",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 500\n",
    "p = 0.2\n",
    "z = 1.96"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "7fa5c307",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.198 +- 0.03492937770988771\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 413,
       "width": 558
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.binomial(n, p)\n",
    "phat = x/n\n",
    "ci = z * np.sqrt(phat * (1-phat) / n)\n",
    "print('{} +- {}'.format(phat, ci))\n",
    "\n",
    "x = np.random.binomial(n, p, size=10000)\n",
    "\n",
    "plt.hist(x/n, bins=100, color='k', alpha=0.7)\n",
    "plt.axvline(phat, color='r')\n",
    "plt.axvline(phat-ci, color='r', ls='dashed')\n",
    "plt.axvline(phat+ci, color='r', ls='dashed')\n",
    "plt.axvline(p, color='b');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7908dd69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:scipy]",
   "language": "python",
   "name": "conda-env-scipy-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}