Numpy- Election Result.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prior to the election, a research group conducted a survey to determine how many people would vote for Cynthia Ceballos vs. Justin Kerrigan in the mayoral election.\n",
    "\n",
    "Now that the election has occurred, the group wants to compare the survey responses to the actual results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib. pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "survey_responses = ['Ceballos', 'Kerrigan', 'Ceballos', 'Ceballos', 'Ceballos','Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Ceballos', \n",
    "'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Ceballos', 'Ceballos', 'Ceballos', 'Ceballos',\n",
    "'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Ceballos', 'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Ceballos',\n",
    "'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Ceballos', 'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Kerrigan', 'Kerrigan', 'Ceballos', 'Ceballos', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Kerrigan', 'Ceballos']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a list of the different survey responses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33\n"
     ]
    }
   ],
   "source": [
    "total_ceballos=survey_responses.count('Ceballos')\n",
    "print(total_ceballos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "47.142857142857146\n"
     ]
    }
   ],
   "source": [
    "percentage_ceballos= 100*total_ceballos/len(survey_responses)\n",
    "print(percentage_ceballos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "33 people, equivalent to 47% of the survey respondents voted for Ceballos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the real election, 54% of the 10,000 town population voted for Cynthia Ceballos. This is a very different outcome than what the poll predicted. Is there something wrong with the poll? Or if was it an entirely reasonable result given the sample size?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.5        0.47142857 0.6        ... 0.5        0.5        0.57142857]\n",
      "0.217\n"
     ]
    }
   ],
   "source": [
    "possible_surveys=np.random.binomial(70,0.54,size=10000)/70.\n",
    "print(possible_surveys)\n",
    "\n",
    "ceballos_loss_surveys=np.mean(possible_surveys<0.5)\n",
    "print(ceballos_loss_surveys)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This means 22% of the time a survey output would predict Kerrigan winning, even if Ceballos won the actual election. So our survey result is reasonable given the sample size. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(possible_surveys, bins=20, range=(0,1))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[53.97142857 53.25714286 55.14285714 ... 54.42857143 53.22857143\n",
      " 53.91428571]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "possible_surveys_v2=np.random.binomial(7000,0.54,size=10000)/70.\n",
    "print(possible_surveys_v2)\n",
    "\n",
    "ceballos_loss_surveys_v2=np.mean(possible_surveys_v2<0.5)\n",
    "print(ceballos_loss_surveys_v2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the group had increased sample size and instead surveyed 7000 people, 100% of the time the survey would have shown Ceballos winning the election, which is consistent with the actual result. Therefore, sample size is key to the accuracy of survey result.  "
   ]
  }
 ],
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