{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "79234e4f",
   "metadata": {},
   "source": [
    "# Central Limit Theorem\n",
    "\n",
    "\n",
    "### Set up Python libraries\n",
    "\n",
    "As usual, run the code cell below to import the relevant Python libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "ba52cbb5",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Set-up Python libraries - you need to run this but you don't need to change it\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "import pandas \n",
    "import seaborn as sns\n",
    "sns.set_theme()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c7807e3",
   "metadata": {},
   "source": [
    "### Load and plot the data\n",
    "\n",
    "We will work with a distinctly non-normal data distribution - the scores for a large number of individuals on a 100-item political questionairre called BrexDex. \n",
    "\n",
    "The questions are designed and scored so that a high score overall score on the questionairre indicates an attitude agains Brexit, and a low score indicates an attitude in favour of Brexit.\n",
    "\n",
    "Because the scores relate to a polarizing topic, the data distribution is bimodal\n",
    "\n",
    "(These are made up data by the way!)\n",
    "\n",
    "First load the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "66216ca9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID_code</th>\n",
       "      <th>score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>186640</td>\n",
       "      <td>53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>588140</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>977390</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>948470</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>564360</td>\n",
       "      <td>84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>851780</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>698340</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>693580</td>\n",
       "      <td>51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>872730</td>\n",
       "      <td>78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>385642</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      ID_code  score\n",
       "0      186640     53\n",
       "1      588140     90\n",
       "2      977390     30\n",
       "3      948470     42\n",
       "4      564360     84\n",
       "...       ...    ...\n",
       "9995   851780     81\n",
       "9996   698340     45\n",
       "9997   693580     51\n",
       "9998   872730     78\n",
       "9999   385642     88\n",
       "\n",
       "[10000 rows x 2 columns]"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UKBrexdex=pandas.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/data/UKBrexdex.csv')\n",
    "UKBrexdex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "805661ec",
   "metadata": {},
   "source": [
    "We can see that the dataset contains 10,000 individuals' scores on the BrexDex questionnaire. \n",
    "\n",
    "Let's plot them to get a sense of the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "c3d3da29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(UKBrexdex['score'], bins=range(101))\n",
    "plt.xlabel('score on BrexDex')\n",
    "plt.ylabel('frequency')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ced488a",
   "metadata": {},
   "source": [
    "Obviously, 10,000 is a very large sample (perhaps a national sample). We might be interested giving the questionnarie to a smaller group (say, 100 first year statistics students in Oxford) to see if their attitudes were similar to the larger national sample.\n",
    "\n",
    "What kind of distribution of responses would we expect to get in a sample of 100?\n",
    "\n",
    "### The sample distribution resembles the parent distribution\n",
    "\n",
    "If the Oxford students have attitudes typical of the national sample, we could simulate what their data might look like by drawing a random sample of 100 from our national dataset.\n",
    "\n",
    "We can do this using the tool <tt>numpy.random.choice</tt> which makes a random selection of datapoints from a larger dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "630da21e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[42 85 13 92 48 27 82 73 82 35 80 21 38 86 18 38 24 38 83 19 73 28 80 14\n",
      " 31 76 80 81 76 82 50 78 81 77 22 27 74 50 77  9 48 25 19 33 71 21 24 18\n",
      " 81 86 75 26 85 39 85 39 35 81 80 40 28 84 82 76 22 21 81 35 30 17 22 12\n",
      " 33 48 47 70  9 83 73 30 50 91 37 30 79 78 85 34 52 69 80 31 82 36 20 15\n",
      " 27 32 47 28]\n"
     ]
    }
   ],
   "source": [
    "sample = np.random.choice(UKBrexdex['score'], 100, replace=False)\n",
    "print(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74546f62",
   "metadata": {},
   "source": [
    "Let's plot the data and compare to our national sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "718d25c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2,1,1)\n",
    "sns.histplot(UKBrexdex['score'], bins=range(101))\n",
    "plt.subplot(2,1,2)\n",
    "sns.histplot(sample, bins=range(0,101,5)) # use wider bins for the sample as there are fewer datapoints\n",
    "plt.xlabel('Score on Brexdex (%)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d87cecd",
   "metadata": {},
   "source": [
    "Hopefully we can see that the distribution within the sample resembles the shape of the distribution in the national sample, with two peaks, although somewhat noisier\n",
    "\n",
    "Let's draw a few more random samples, each time of size 100, to check this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "d5530cd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(1,13):\n",
    "    sample = np.random.choice(UKBrexdex['score'], 100, replace=False)\n",
    "    plt.subplot(3,4,i)\n",
    "    sns.histplot(sample, bins=range(0,101,5)) # use wider bins for the sample as there are fewer datapoints   \n",
    "    plt.tight_layout() # automatically adjust subbplot spacing to accomodate axis labels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aca85f8e",
   "metadata": {},
   "source": [
    "Notice that we always manage to reproduce the bimodal shape, albeit with random variability. \n",
    "\n",
    "<b>The distribution within each sample resembles the parent distribution from which it is drawn, ie the UK national sample.</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c71802ed",
   "metadata": {},
   "source": [
    "# The sampling distribution of the mean\n",
    "\n",
    "The mean Brexdex score can be obtained from the UK national sample as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "9ee2c060",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49.8748"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UKBrexdex['score'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bae11f22",
   "metadata": {},
   "source": [
    "The mean score in the national sample is 49.9%.\n",
    "\n",
    "Given that each of our smaller samples (with $n=100$) resemble the parent distribution, we might expect that the mean of each of these samples approximates the mean of the UK national sample.\n",
    "\n",
    "Let's try drawing a large number of random samples with $n=100$, and getting the mean of each one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "6d38684f",
   "metadata": {},
   "outputs": [],
   "source": [
    "nSamples = 10000 # we will draw 10,000 samples\n",
    "n=100 # each sample contains n people\n",
    "\n",
    "m=np.empty(nSamples) # make an array to store the means\n",
    "\n",
    "for i in range(nSamples):\n",
    "    sample = np.random.choice(UKBrexdex['score'], 100, replace=False)\n",
    "    m[i]=sample.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc288d93",
   "metadata": {},
   "source": [
    "Let's plot the resulting means:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "88c7c5b8",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'sample mean')"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(m)\n",
    "plt.xlabel('sample mean')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eef22b6c",
   "metadata": {},
   "source": [
    "The distribution of sample means is approximately normal.\n",
    "\n",
    "## Expected value of the mean\n",
    "\n",
    "The expected value of the sample mean is simply the mean of the parent distribution. In other words, the means obtained from our 10,000 samples cluster around the mean of the UK national sample, which was 49.9."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "id": "92491ca9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49.873296"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.mean() # get the mean of the 10,000 sample means"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "849278ef",
   "metadata": {},
   "source": [
    "## Standard Error of the mean\n",
    "\n",
    "Although the sample means group around the mean of the parent distrbution, there is some random variation, as some samples (by chance) contain higher Brexdex scores than others.\n",
    "\n",
    "The variability of the sample means is quantified by the standard deviation of the sampling distribution of the mean (ie the sd of the data in the histogram above), which is about 2.46."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "c67b5b43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4659929432956615"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef8c2741",
   "metadata": {},
   "source": [
    "As we saw in the lecture, the standard deviation of the sampling distribution of the mean has a special name, the <b><i>standard error of the mean</i></b> or SEM, and is given by the formula:\n",
    "\n",
    "$$ SEM = \\frac{\\sigma}{\\sqrt{n}} $$\n",
    "\n",
    "... where $\\sigma$ is that standard deviation of the parent distribution, which in this case where we (unusually) have access to the UK national sample of 10000 individuals, we can obtain as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "858fe19d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.792720561876358"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UKBrexdex['score'].std()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce457e72",
   "metadata": {},
   "source": [
    "Shall we check if the formula for the SEM gives us a match to the standard deviation of the sampling distribution of the mean?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "fd5930ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sd of sampling distriution (from simulation) = 2.4659929432956615\n",
      "SEM from the formula = 2.479272056187636\n"
     ]
    }
   ],
   "source": [
    "print('sd of sampling distriution (from simulation) = ' + str(m.std()))\n",
    "\n",
    "SEM = UKBrexdex['score'].std()/(n**0.5) # n to the power 0.5 is sqrt of n\n",
    "print('SEM from the formula = ' + str(SEM))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eb83ea4",
   "metadata": {},
   "source": [
    "This is not a bad match!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0137acd3",
   "metadata": {},
   "source": [
    "## $SEM \\propto \\frac{1}{\\sqrt{n}} $"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28ed0c0c",
   "metadata": {},
   "source": [
    "The standard error of the mean is inversely proportional to $\\sqrt{n}$\n",
    "\n",
    "In other words, the random variability in sample means decreases as sample size $n$ increases - but in proportion to $\\sqrt{n}$ not $n$ itself\n",
    "\n",
    "We can see this if we construct the sampling distribution of the mean for samples of different sizes, say $n=50, 100, 1000$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "4ede1ad7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nSamples = 10000 # we will draw 10,000 samples\n",
    "m=np.empty(nSamples) # make an array to store the means\n",
    "\n",
    "nVals = [50,100,1000] # values of n to try\n",
    "\n",
    "# this loop tries different values of n\n",
    "for j in range(len(nVals)): \n",
    "    \n",
    "    # this loop draws 10,000 samples of size n\n",
    "    for i in range(nSamples):\n",
    "        sample = np.random.choice(UKBrexdex['score'], nVals[j], replace=False)\n",
    "        m[i]=sample.mean()\n",
    "        \n",
    "    # plot the distribution for each value of n\n",
    "    plt.subplot(3,1,j+1)\n",
    "    sns.histplot(m)\n",
    "    plt.legend('n = ' + str(nVals[j]))\n",
    "    plt.xlim([40,60])\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.xlabel('sample mean')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4bc3d07",
   "metadata": {},
   "source": [
    "## Normal Distribution\n",
    "\n",
    "The <b>Central Limit Theorem</b> states that when $n$ is sufficiently large, the sampling distribution of the means of samples of size $n$ is a normal distribution, with a mean equivalent to the mean of the parent distribution, and a standard deviation equivalent to the SEM.\n",
    "\n",
    "Let's check how well our sampling distribution for samples of size n=100 matches the predicted normal distribution.\n",
    "\n",
    "First we regenerate our 10,000 samples of size 100:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "fdf776a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nSamples = 10000 # we will draw 10,000 samples\n",
    "n=100 # each sample contains n people\n",
    "\n",
    "m=np.empty(nSamples) # make an array to store the means\n",
    "\n",
    "for i in range(nSamples):\n",
    "    sample = np.random.choice(UKBrexdex['score'], n, replace=False)\n",
    "    m[i]=sample.mean()\n",
    "    \n",
    "sns.histplot(m)\n",
    "plt.xlabel('sample mean')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7434f51",
   "metadata": {},
   "source": [
    "Now we make our predicted normal sampling distribution of the mean.\n",
    "\n",
    "Its mean $\\mu$ should be the mean of the parent distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "2e566c44",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49.8748\n"
     ]
    }
   ],
   "source": [
    "mu = UKBrexdex['score'].mean()\n",
    "print(mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "880d5044",
   "metadata": {},
   "source": [
    "Its standard deviation should be the SEM: \n",
    "\n",
    "$$SEM = \\frac{\\sigma}{\\sqrt{n}} $$\n",
    "\n",
    "where $\\sigma$ is the standard deviaition of the parent distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "b801b477",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.479272056187636\n"
     ]
    }
   ],
   "source": [
    "SEM = UKBrexdex['score'].std()/(n**0.5)\n",
    "print(SEM)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "922431eb",
   "metadata": {},
   "source": [
    "Then we obtain the PDF of the normal distribution $\\mathcal{N}(\\mu, SEM)$ for a suitable range of x-axis values (based on the histogram above):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "e7672f99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(40.5,60.5) # x axis values are from 40.5 to 60.5 (the .5 is to match the middle of the bars in the histogram)\n",
    "p = stats.norm.pdf(x,mu,SEM) \n",
    "freq = p*nSamples # expected frequency of each sample mean is the probability of that sample mean, time total number of samples (10,000 in our example)\n",
    "\n",
    "sns.histplot(m, bins=range(40,60))\n",
    "plt.plot(x,freq,'r')\n",
    "plt.xlabel('sample mean')\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f55976b4",
   "metadata": {},
   "source": [
    "This is not a bad match!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "787c8903",
   "metadata": {},
   "source": [
    "## How unusual is my sample mean?\n",
    "\n",
    "Say we give the Brexdex questionnaire to 100 statistics undergraduates in Oxford, and their mean score is 55.1, as opposed to the mean in the UK national sample, 49.9. Can we infer that the students have different political attitude to the UK population as a whole?\n",
    "\n",
    "The sampling distribution of the mean tells us the distribution of sample means we expect to get if we draw samples from the parent population (the UK national sample)\n",
    "\n",
    "### Using the simulated sampling distribution of the mean\n",
    "\n",
    "What proportion of sample means in our simulated sampling distribution exceeded 55.1?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "ec77c438",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "proportion of sample means greater than 55.1 = 0.0181 or 1.81%\n"
     ]
    }
   ],
   "source": [
    "# regenerate the sampling distribubtion\n",
    "nSamples = 10000 # we will draw 10,000 samples\n",
    "n=100 # each sample contains n people\n",
    "\n",
    "m=np.empty(nSamples) # make an array to store the means\n",
    "\n",
    "for i in range(nSamples):\n",
    "    sample = np.random.choice(UKBrexdex['score'], 100, replace=False)\n",
    "    m[i]=sample.mean()\n",
    "    \n",
    "print('proportion of sample means greater than 55.1 = ' + str((m>55.1).mean()) +  ' or ' + str((m>55.1).mean()*100) + '%')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22df2259",
   "metadata": {},
   "source": [
    "In other words, the mean Brexdex score of the students was high enough that we would expect it to occur less than 2% of the time for samples drawn from the UK national population - we might conclude that the political attitudes of the students differ from those of the population as a whole.\n",
    "\n",
    "### Using the Normal distribution\n",
    "\n",
    "We can ask how likely this mean was to have occurred under the assumption that the Oxford students have similar political attitudes to the population as a whole, using the CDF of the normal distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "id": "ba834c38",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "proportion of sample means greater than 55.1 = 0.01753478848973844 or 1.753478848973844%\n"
     ]
    }
   ],
   "source": [
    "mu = UKBrexdex['score'].mean()\n",
    "SEM = UKBrexdex['score'].std()/(n**0.5)\n",
    "\n",
    "p = 1-stats.norm.cdf(55.1,mu,SEM) \n",
    "print('proportion of sample means greater than 55.1 = ' + str(p) +  ' or ' + str(p*100) + '%')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "848070ad",
   "metadata": {},
   "source": [
    "Hopefully this proportion agrees fairly well with the proportion of actual sample means exceeding 55.1 in the simulation"
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