for_Medium06_3

forMedium_06_3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bootstrap Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistic: Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([435, 205, 348, 264,  91, 319, 270, 484, 445, 102, 319, 330, 385,\n",
       "        58, 419, 475, 343,   1,  34, 102, 443, 372, 445, 445,  80, 366,\n",
       "       419, 149, 264, 330])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# draw a sample from population\n",
    "sample = np.random.choice(pickups, size=30)\n",
    "sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# bootstrap for mean\n",
    "boot_means = []\n",
    "for _ in range(10000):\n",
    "    bootsample = np.random.choice(sample,size=30, replace=True)\n",
    "    boot_means.append(bootsample.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# simulated mean of mean\n",
    "bootmean = np.mean(boot_means)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# simulated standard deviation of mean\n",
    "bootmean_std = np.std(boot_means)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(252.7, 291.44874000000004)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# simulated mean VS true mean\n",
    "(pickups.mean(), bootmean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(26.336951228264823, 26.85003412725247)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the theorical standard error and simulated standard error\n",
    "(pickups.std()/(30 ** 0.5), bootmean_std)"
   ]
  }
 ],
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