ch04_Statistical_Inference.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 4: Statistical Inference.\n",
    "\n",
    "In this notebook we will see how to infer predictions about a population. To\n",
    "this end we will explore the relationship between sample parameters and population parameters and we will propose some methods to assess the quality\n",
    "of parameter estimates of a sample.\n",
    "\n",
    "## Data description\n",
    "\n",
    "Let's consider a dataset of accidents in Barcelona in 2013. This dataset can\n",
    "be downloaded from OpenDataBCN website (http://opendata.bcn.cat/),\n",
    "Barcelona's City Hall open data service. Each register in the dataset represents an accident by a series of features: weekday, hour, address, number\n",
    "of dead and injured people, etc. This dataset will represent our population:\n",
    "the set of all reported traffic accidents in Barcelona during 2013.\n",
    "\n",
    "In https://dieguico.cartodb.com/viz/50b06d8c-13ab-11e5-8619-0e4fddd5de28/public_map you can visualize a map of accidents in the city of Barcelona by hour of day, and by day of week."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pylab as plt\n",
    "from matplotlib import cm\n",
    "import math\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "%matplotlib inline \n",
    "plt.style.use('seaborn-whitegrid')\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='times')\n",
    "plt.rc('xtick', labelsize=10) \n",
    "plt.rc('ytick', labelsize=10) \n",
    "plt.rc('font', size=12) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index([u'Número d'expedient', u'Codi districte', u'Nom districte', u'NK barri',\n",
      "       u'Nom barri', u'Codi carrer', u'Nom carrer', u'Num postal caption',\n",
      "       u'Descripció dia setmana', u'Dia de setmana', u'Descripció tipus dia',\n",
      "       u'NK Any', u'Mes de any', u'Nom mes', u'Dia de mes', u'Hora de dia',\n",
      "       u'Descripció torn', u'Descripció causa vianant', u'Número de morts',\n",
      "       u'Número de lesionats lleus', u'Número de lesionats greus',\n",
      "       u'Número de víctimes', u'Número de vehicles implicats',\n",
      "       u'Coordenada UTM (Y)', u'Coordenada UTM (X)'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"files/ch04/ACCIDENTS_GU_BCN_2013.csv\", encoding='latin-1')\n",
    "print data.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will create a new data column which is the date and a list with the number of accidents for every day of the year:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 25.9095890411\n"
     ]
    }
   ],
   "source": [
    "#Create a new column which is the date\n",
    "data['Date'] = '2013-'+data['Mes de any'].apply(lambda x : str(x)) + '-' +  data['Dia de mes'].apply(lambda x : str(x))\n",
    "data['Date'] = pd.to_datetime(data['Date'])\n",
    "accidents = data.groupby(['Date']).size()\n",
    "print \"Mean:\", accidents.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's suppose that we are interested in describing the number of daily traffic\n",
    "accidents (**accident rate**) in the streets of Barcelona during 2013.  In order to get a first idea of the data, we can plot the number of accidents for each day of 2013:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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rHdos4zWCHnRlQa8kfspfyhZ1P8jl2fyWRqM1ktN9oNeo39OaKBYL3/WdxlXV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\nKDZ0vrGRD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3kqTc9NT7hj4hvXxAyamspm120QP5qaAkZOjntDPT8DWNDsziPTSJLGp/Kk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wgx+ol4GN61Sq0mPOXn1VQz0s6rvcBi0t9nN+vSCMsCwVj7pYx8wYlVNNvvKK3rOXY62uF3B9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\nXIREHQAAAAAAFyFRBwAAAADARf4fmY+xpNZo3z0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11361e950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 4))\n",
    "plt.ylabel('Number of accidents')\n",
    "plt.xlabel('Day')\n",
    "plt.plot(range(0, 365), np.array(accidents), 'b-+', lw=0.7, alpha=0.7)\n",
    "plt.plot(range(0, 365), [accidents.mean()]*365, 'r-', lw=0.7, alpha=0.9)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, we can plot the distribution of our variable of interest: the daily number of accidents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8dpiZmfHWs9T+uVxu2d/+wgsveOsrlUruwYMH3eHh4TX3FwAAlaIr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\nAAYRzAEAAAAAMOj/A5m/RXIy86dWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115e96310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Number of accidents')\n",
    "plt.hist(np.array(accidents), bins=20)\n",
    "ax.axvline(x=accidents.mean(), ymin=0, ymax=40, color=[1, 0, 0])\n",
    "plt.savefig(\"bootmean.png\",dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have access to the whole *population*, the computation of the **accident rate** in 2013 is a simple operation: the total number of accidents divided by 365. As a measure of quality of this parameter we can also compute the standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 25.9095890411 ; STD: 9.10832496246\n"
     ]
    }
   ],
   "source": [
    "print \"Mean:\", accidents.mean(), \"; STD:\", accidents.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But now, let's suppose that we have only access to a limited part of the data\n",
    "(the *sample*): the number of accidents during *some days* of 2013. Can we still\n",
    "give an approximation (an *estimate*) to this population mean?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variability in estimates.\n",
    "\n",
    "Estimates generally vary from one sample to another, and this sampling variation suggests our estimate may be close, but it will not be exactly equal to the parameter.\n",
    "\n",
    "This can be easily checked by generating 10 different samples (composed of 25% of the population) from our population and compute their accident rate estimates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 0: Mean 27.29\n",
      "Sample 1: Mean 25.33\n",
      "Sample 2: Mean 25.59\n",
      "Sample 3: Mean 25.53\n",
      "Sample 4: Mean 26.77\n",
      "Sample 5: Mean 25.70\n",
      "Sample 6: Mean 26.59\n",
      "Sample 7: Mean 26.47\n",
      "Sample 8: Mean 24.33\n",
      "Sample 9: Mean 26.12\n"
     ]
    }
   ],
   "source": [
    "df = accidents.to_frame()\n",
    "m = []\n",
    "\n",
    "for i in range(10):\n",
    "    df['for_testing'] = False\n",
    "    # get a 25% sample \n",
    "    sampled_ids = np.random.choice(df.index,\n",
    "                                   size=np.int64(np.ceil(df.index.size * 0.25)),\n",
    "                                   replace=False)\n",
    "    df.ix[sampled_ids, 'for_testing'] = True\n",
    "    accidents_sample = df[df['for_testing'] == True]\n",
    "    m.append(accidents_sample[0].mean())\n",
    "    print  'Sample '+str(i)+': Mean', '%.2f' % accidents_sample[0].mean()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10299c790>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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L5VQsFiVJ+Xxek5OTTbcvmJqa0nvvvadwONz0OsYYZTIZua6rcrmsZDIp56Bv\n+AcAAAAA2NcCH3H3PE/FYlFjY2MaGxvT2bNnNTIysu28XC6nTCajSqWy47UmJiY0Njamvr4+JZNJ\nTUxMvMzSAQAAAAB46QIP7oVCQTMzM/7jnp4eGWNULpf9Y57nSZKi0eiO1ymVSgqFQv5jx3FUKBQa\nrgMAAAAAwH4TeHBPJBJaXFz0H+fzeYVCIcViMf/Y0tKSEomEarXajtcpFArq6OhoOBaNRmWMaX3R\nAAAAAAC8IoEHd0nq6ury/55KpXT16lX/cS6XU39//zOvUa1Wtx1zHMcfrQcAAAAAYD+yYnG6unQ6\nrf7+fg0ODkr6zRT5nRaj2yoSiWy7/93zvB0Xp/vmm28kSb/61a/2UjJeksePH+vRo0dBl4Em6I3d\n6I+96I296I3d6I+96I296I296vmznkeflzXBPZfLqaOjQ729vf6xbDararWqmzdvqlar+avG9/T0\nNIzSS1J3d7cWFhYajq2trTVdnV6SNjY2JElff/11a98IWmZlZSXoErADemM3+mMvemMvemM3+mMv\nemMvemO3jY2N5xqgrrMiuNe3gquH9nQ6rbNnz6qvr6/hvKmpKfX19fn3v5dKJTmOI9d1FY/HG6bF\nV6tVua7bcK/8VtFoVK+//roOHz6s116z4o4BAAAAAEAb++abb7SxsfHUhdebCdWetuLbK2CM0enT\np/0V4Wu1mqLRqL788kv/HM/ztLCwoJmZGSWTSV24cEGxWEwTExM6efKkRkdHJW1+qpTNZhWLxVQo\nFDQ0NLRjcAcAAAAAYD8IPLgDAAAAAICdMUccAAAAAACLEdwBAAAAALAYwR1WyWQyQZcAAC/F1NSU\n1tfXgy4DAADsQ1asKv8q1beUc11X5XJZyWRyx73e8epkMhmtra1pampKd+/e3dXWCHg1crmcvwNE\nPp/X5OTkjtst4tXK5XKqVqtaW1vT7du3NT4+rng8HnRZ2CKXyymTyejixYv8fLPI1NSU0um0QqGQ\n4vG4rl27tm27WQQnk8moWq0qEolI0rbdhhCM06dPyxijaDSq+lJZ4+Pj/mLRCJYxRrlczv97f38/\nvxNYolQq6fPPP1d3d7fy+bzGx8d3lUMPXHCfmJjQ4uKipM3V6icmJnTjxo2Aq0L9f8ZXrlwJuBI0\n43meisWixsbGJG3+MjUyMqJbt24FXBkk6d1339U//uM/6sSJE5I2f87RG3vUtyrd7bYvePmOHTum\nu3fvShIOcusQAAAJ6UlEQVQfqFgmnU7L8zyNjo7KGKPR0VGCuyWGh4d15swZ/2fa3Nwcod0iCwsL\nmpyc9B9PTExodnY2wIogbf4ucP78ed25c0eS5Lqu3n///V315kBNlS+VSv62c5LkOI4KhYLK5XKA\nVWErNjmwU6FQ0MzMjP+4p6dHxhi+dyzxi1/8wg/tkvzRKdhhaWlJiUSCn28WqtVqCofDhHYLTU9P\n+2HQdV1/0AXB8jxPQ0NDOnr0qMLhsPL5vIaGhoIuC1tkMhkZY/zHHR0dAVaDumw229CLeDyuTCaz\nq1voDtSIe6FQ2PYfbzQalTGG/d6Bp0gkEg2/NOXzeYVCIb5vLLG1Dw8ePOCTdYvkcjn19/cHXQZ2\nUKlUtLy8LMdxdPv2bQ0NDXELkAXqAy316b7ZbFbJZJIPWCzw5LTeUqmkRCIRUDVoZmhoSKdPn9bY\n2Jg6Ozt14cKFoEuCtg+q1GfjGWOe+xatAxXcq9XqtmOO4/hfOAA72/pDJZVK6erVqwFWgycZY7Sw\nsKCVlZWmP+vw6tX/30LYsNfw8LD/wVc0Gm24nQ7BKRQKqlarcl1XsVhM3d3dGhgY4BYgy6RSKQ0P\nDwddBp4wNDSktbU1ZbNZLS8vq7u7O+iSoM1BMMdxVC6XFYvFVCgUFAqFVKlUnvsaB2qqfCQS2fbF\n8TyPxekssvVWBtgpnU6rv79fg4ODQZeCLVzX1eTkpBKJhM6fP8/q5RbIZrMql8u6efOm0um0vzjq\nyspK0KXh/2ydreK6rkqlEt87FnBdV5FIxO+P4zgyxvC9Y5nPPvuMDyYt43mePvroI12+fFmffvqp\nxsbG9O677/JzzRKffvqpstmscrmcYrGYarXarmZ5Hajg3uwTp7W1NabFWYR7QO2Wy+XU0dFBaLeI\nMUbT09P+476+PlWrVeXz+QCrgrTZi8HBQQ0ODiqZTPrHWLXcDqVSSadOnfIfO47Dh8eWiMVizByy\nXC6X4/vFQtlsVn/0R3/kP04mk0omk/xOYJFkMunfXhKNRnd12+mBCu7xeLxhWvzWaVgIVi6XUyqV\nUigU0tzcnH9fG+xR3wqut7dX0ubIO5/gBq9cLjd8v9S36PnOd74TYFXYyvM8/+fb9evXWdTREq7r\nanx83H+8tLSknp4eRhAt4Lqu4vG4/71ijFFnZycfelmkWCyy6JmFXNdtGtL5ncAOp06d8n93XlhY\n0E9+8pNdvT5UO2BDnCsrK8pms/69BUNDQwR34BmMMTp9+rT/6XqtVlM0GtWXX34ZcGWQpJs3b0ra\n7Es2m9UPf/jDhlXmATSXy+VUKpX8qdjj4+MEd0uUy2UtLCzIdV0Vi0VduHCB39cskk6nVSwW9eGH\nHwZdCp6wvLwsY4y/jldPTw8fellifn5eruvqwYMH6uzs9AfDnteBC+4AAAAAAOwnB2qqPAAAAAAA\n+w3BHQAAAAAAixHcAQAAAACwGMEdAAAAAACLEdwBAAAAALAYwR0AAAAAAIsR3AEAAAAAsBjBHQAA\nAAAAixHcAQAAAACwGMEdAIA2kc1mNTAwoHPnzqm3t1dXrlxRtVrV6dOntb6+HnR5vunpaZ06dUon\nTpzQzZs3gy4HAADrfSvoAgAAwN5ls1l98MEH+tnPfqajR49KkjKZjP74j/9YnuepUqkoHA4HXOWm\nyclJnT17VgMDA0GXAgDAvkBwBwCgDaRSKQ0NDfmhXZL6+vokSZcuXQqqrB05jhN0CQAA7BtMlQcA\noA0YY5TNZrcd7+vrk+u68jwvgKoAAEArENwBAGgD8Xhct2/f1unTp5VKpWSM8Z+7ceOGXNf1H09N\nTWlkZEQDAwP++XVb7z9Pp9OamJjQqVOnNDAwoFwuJ2OMRkZGdOLECQ0MDDT8O+l02n9tKpXSwMCA\nTp06pXPnzqlUKj3X+7h+/boGBgY0MjKi0dHRhusDAHBQhWq1Wi3oIgAAwN54nqfz58+rVCqp/r/2\nSCSiM2fO6MKFC35w/9GPfqR79+5peXlZkpTL5fTuu+/q448/Vm9vb8OxaDSq2dlZdXd360//9E9V\nKpXU2dmpjz/+WOFwWAMDA+ro6PCv9eRr/+Zv/kYnTpzQ9PS0UqmUfvGLXygWi0nanCFw+vRp/eQn\nP9Hg4KAk6aOPPtLf//3f64svvlA4HFY6ndb09LT+6Z/+yZr78wEACAIj7gAAtAHHcfTpp5/qxo0b\nGhoaUmdnpzzPUzqd1unTp1UulyVJHR0dCoVC/uveeustSWoY2Y5Go5KkoaEhfe9731M4HNbZs2cV\nCoV04cIFnThxQrFYTGfOnNk2Ir71tSdOnJAkjY+PS9ocTd+J53man5/XxYsX/ZB+5swZVatVLSws\n7OlrAwDAfsfidAAA7HOe52lubk6Tk5NKJBJKJBKSpHK5rIWFBaVSKV2/fl0ffvihrl69KmlzZPz2\n7dsqlUoKhUKqVCrbrtvd3e3/vT5iXx8xl6TOzk5J0vr6+rYR8a2vdRxHkUhEhUJhx/dQf25hYUHZ\nbFa1Wk2VSkWdnZ168ODBrr4eAAC0G4I7AAD7XKVSUTqd1uTkZMPxWCymy5cv68GDB34wXlpa0szM\njIaHh/Unf/InGh8f13e/+93n/rc6OjpaWntdtVqVJF24cMGfOg8AADYxVR4AgDZQrVYbFpnbKhqN\nqru7W8YYXbp0SWfOnNHo6Ki6urqajrS3Qj6fb6itWq3qO9/5zo7n10f0nxyVN8YonU6/lBoBANgv\nCO4AAOxz9VHwmZkZ3bx5s+G5YrGoTCajixcv+sfqK7xXq1VduXJFoVBIxhh/y7hmYb5Wq+nJ9Wyf\ntr5tOp3276ufnp5WKBTS2NiY/3x9hL0uHo+rr69P6XRamUxG0mZon5iYeGrgBwDgIDj0wQcffBB0\nEQAA4MX9+te/ViaT0RdffKEvvvhC8/Pz+uUvf6nPP/9c//Zv/6aPP/5YR48eVTQa1cbGhn75y18q\nlUrp3//93/XjH/9YjuMok8noP//zP/XrX/9af/mXfynP81QsFvVbv/VbKhaL+ulPfyrP85TNZvW7\nv/u7+od/+Ad98skn2tjY0O3bt9XZ2SnXdfVf//VfWlhY0Pvvv6/r16/rL/7iL7SxsaG//uu/1u/9\n3u9JkjKZjD766CP993//t/71X/9Vr732mt5++2319/drY2NDf/u3f6uf/vSnymazeu+99/QHf/AH\nAX+FAQAIFtvBAQCAlimVShoYGGjYXg4AAOwNU+UBAEDLMB4AAEDrEdwBAEBLZDIZXbp0SaFQSNPT\n05qfnw+6JAAA2gJT5QEAAAAAsBgj7gAAAAAAWIzgDgAAAACAxQjuAAAAAABYjOAOAAAAAIDFCO4A\nAAAAAFiM4A4AAAAAgMUI7gAAAAAAWIzgDgAAAACAxQjuAAAAAABY7P8DOp1mxeoaXKkAAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117415f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 2))\n",
    "x = range(10)\n",
    "ax.step(x,m, where='mid')\n",
    "ax.set_ylabel('Mean')\n",
    "ax.set_xlabel('Sample')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accident rate estimates can range from 24 accident per day to 27 accidents per day, depending on the sample. How can we give a unique value for the estimate?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling distribution of point estimates\n",
    "\n",
    "The most intuitive way to go about giving a value for the estimate is to simply take the *sample\n",
    "mean*. The sample mean is a point estimate of the population mean. If we\n",
    "can only choose one value to estimate the population mean, this is our best\n",
    "guess.\n",
    "\n",
    "Let's computer the sample means for a set of 10000 samples, each one composed of 200 days:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113431490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OnTq1YRz70NBQxce7ffu2hoeHCxPaSVIqlVJ7e3vRfoFAQJZlybKsLdsI7QAAYCdkMhl1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\nvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113431590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample mean: 25.908756\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115a92b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.autumn()\n",
    "\n",
    "# population\n",
    "df = accidents.to_frame()    \n",
    "N_test = 10000              \n",
    "elements = 200             \n",
    "\n",
    "# mean array of samples\n",
    "means = [0] * N_test             \n",
    "\n",
    "# sample generation\n",
    "for i in range(N_test):          \n",
    "    rows = np.random.choice(df.index.values, elements)\n",
    "    sampled_df = df.ix[rows]\n",
    "    means[i] = sampled_df.mean()\n",
    "    \n",
    "fig, ax = plt.subplots(1, 1, figsize=(12,3))\n",
    "\n",
    "plt.hist(np.array(means),bins=50)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Sample mean value')\n",
    "ax.axvline(x = np.array(means).mean(), \n",
    "           ymin = 0, \n",
    "           ymax = 700, \n",
    "           color = [1, 0, 0])\n",
    "plt.savefig(\"empiricalmean.png\",dpi=300, bbox_inches='tight')\n",
    "plt.show()\n",
    "plt.set_cmap(cmap=cm.Pastel2)\n",
    "\n",
    "print \"Sample mean:\", np.array(means).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the **sampling distribution of the mean**. From it we could estimate the most probable value of the mean and also its standard deviation, but in the real world we will not have access to this function!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard error of the mean\n",
    "\n",
    "Noe let's suppose that we have only one sample of the propulation. As comented before, the mean estimate from that sample may be close, but it will not be exactly equal to our parameter of interest (that can only be computed if we have access to the full population). For this reason it is interesting to measure its variability with respect to the sampling process. To this end we can use the *standard error of the mean*.\n",
    "\n",
    "It can be mathematically shown that given $n$ independent observations $\\{ x_i \\}_{i=1,..,n}$ from a population with a standard deviation $\\sigma_x$, the standard deviation of the sample mean $\\sigma_{\\bar{x}}$, or **standard error** is:\n",
    "\n",
    "$$ SE = \\frac{\\sigma_{x}}{\\sqrt{n}} $$\n",
    "\n",
    "This allows **to estimate the standard deviation of the sample mean** even if we cannot perform the simulation process (f.e. because we have no access to the population). Usually, $\\sigma_x$ is not known and it is substituted by its empirical estimate (that is sufficiently good of $n>30$ and the population distribution is not skewed):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Direct estimation of SE from one sample of 200 elements: 0.633985558544\n",
      "Estimation of the SE by simulating 10000 samples of 200 elements: 0.638064199328\n"
     ]
    }
   ],
   "source": [
    "rows = np.random.choice(df.index.values, 200)\n",
    "sampled_df = df.ix[rows]\n",
    "est_sigma_mean = sampled_df.std()/math.sqrt(200)\n",
    "\n",
    "print 'Direct estimation of SE from one sample of 200 elements:', \\\n",
    "       est_sigma_mean[0]\n",
    "print 'Estimation of the SE by simulating 10000 samples of 200 elements:',  \\\n",
    "       np.array(means).std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could be also interested in quantifying the standard deviation of other estimates: median, standard deviation, etc., but unlike in the case of the sample mean, there is no simple formula for the standard\n",
    "error of other interesting sample estimates, such as the median."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider from now the whole accidents dataset as a sample from an hypothetical population (this is the most common situation when analyzing real data!)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bootstrapping the standard error of the mean.\n",
    "\n",
    "A modern alternative to the traditional approach to statistical inference is\n",
    "the *bootstrapping method*. In the bootstrap, we draw $N$ observations with\n",
    "replacement from the original data to create a bootstrap sample or resample.\n",
    "Then, we can calculate the mean for this resample. By repeating this process\n",
    "a large number of times we can built a good approximation of the mean\n",
    "sampling distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean estimate: 25.9026819178\n"
     ]
    }
   ],
   "source": [
    "def meanBootstrap(X,numberb):\n",
    "    import numpy as np\n",
    "    x = [0]*numberb\n",
    "    for i in range(numberb):\n",
    "        sample = [X[_] for _ in np.random.randint(len(X), size=len(X))]\n",
    "        x[i] = np.mean(sample)\n",
    "    return x\n",
    "\n",
    "m = meanBootstrap(accidents, 10000)\n",
    "print \"Mean estimate:\", np.mean(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x115b9a0d0>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5GYaxpu3KFffx8XFJUn9/v65du6YHDx5suEydYRg6dOjQlmvC9pibm9Phw4db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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116540d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Sample mean value')\n",
    "plt.hist(m, \n",
    "         bins = 50, \n",
    "         normed = True)\n",
    "ax.axvline(x = np.mean(m), \n",
    "           ymin = 0.0, \n",
    "           ymax = 1.0, \n",
    "           color = [1, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The boostrapping method can be applied to other simple estimates such as\n",
    "the median or the variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median estimate: 26.2981\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1176cb690>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115b9ab10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def medBootstrap(X,numberb):\n",
    "    import numpy as np\n",
    "    x = [0]*numberb\n",
    "    for i in range(numberb):\n",
    "        sample = [X[_] for _ in np.random.randint(len(X), size=len(X))]\n",
    "        x[i] = np.median(sample)\n",
    "    return x\n",
    "\n",
    "med = medBootstrap(accidents, 10000)\n",
    "print \"Median estimate:\", np.mean(med) \n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.hist(med, bins=5, normed=True)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Sample median value')\n",
    "ax.axvline(x = np.array(med).mean(), \n",
    "           ymin = 0, \n",
    "           ymax = 1.0, \n",
    "           color = [1, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confidence intervals.\n",
    "\n",
    "A point estimate provides a single plausible value for a parameter. However,\n",
    "as we have seen a point estimate is rarely perfect; usually there is some error\n",
    "in the estimate. That is why we have proposed to use the standard error as\n",
    "a measure of its variability.\n",
    "\n",
    "As an alternative, a next logical step would be to provide a **plausible range of\n",
    "values** for the parameter. A plausible range of values for the sample parameter\n",
    "is called a **confidence interval**.\n",
    "\n",
    "We will base the definition of confidence interval on two ideas:\n",
    "\n",
    "+ Our point estimate is the most plausible value of the parameter, so it makes sense to build the confidence interval around the point estimate.\n",
    "\n",
    "+ The plausability of a range of values can be defined from the sampling distribution of the estimate.\n",
    "\n",
    "In order to define an interval, we can make use of a well\n",
    "known result from probability that applies to normal distributions: roughly\n",
    "95% of the time our estimate will be within 1.96 standard errors of the true\n",
    "mean of the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval: [24.975156065800284, 26.8440220163915]\n"
     ]
    }
   ],
   "source": [
    "m = accidents.mean()\n",
    "se = accidents.std()/math.sqrt(len(accidents))\n",
    "ci = [m - se*1.96, m + se*1.96]\n",
    "print \"Confidence interval:\", ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is how we would compute a 95% confidence interval of the sample mean by using bootstrapping:\n",
    "\n",
    "1. Repeat the following steps a large number $M$ of times: \n",
    "    + Draw $N$ observations with replacement from the original data to create a bootstrap sample or resample; \n",
    "    + Calculate the mean for the resample.\n",
    "2. Calculate the **mean** of your $M$ values of the sample statistic. This process gives you a “bootstrapped” estimate of the sample statistic.\n",
    "3. Calculate the **standard deviation** of your $M$ values of the sample statistic. This process gives you a “bootstrapped” estimate of the **SE** of the sample statistic.\n",
    "4. Obtain the 2.5th and 97.5th centiles of your $M$ values values of the sample statistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean estimate: 25.9107663014\n",
      "SE of the estimate: 0.475388661905\n",
      "Confidence interval: [24.969863013698632, 26.835616438356166]\n"
     ]
    }
   ],
   "source": [
    "m = meanBootstrap(accidents, 10000)\n",
    "sample_mean = np.mean(m)\n",
    "sample_se =  np.std(m)\n",
    "\n",
    "print \"Mean estimate:\", sample_mean\n",
    "print \"SE of the estimate:\", sample_se\n",
    "\n",
    "ci = [np.percentile(m,2.5), np.percentile(m,97.5)]\n",
    "print \"Confidence interval:\", ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Waht is the real meaning of CI?\n",
    "\n",
    "The real meaning of \"confidence\" is not evident and it must be understood\n",
    "from the point of view of the generating process.\n",
    "\n",
    "Suppose we take many (infinite) samples from a population and built a\n",
    "95% confidence interval from each sample. Then about 95% of those intervals\n",
    "would contain the actual parameter.\n",
    "\n",
    "This can be easily showed by simulating a large number of samples and checking how many intervals contain the true parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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et6BEXZIqKiqUSCRyjnV2dqqxsbHQU/ual5MFzM2riYATc728+t6CjF4oZ/n1\n/kpvDtzixGeG8gu/i5fdpCUli3RBF2Y8tiSySLGy4HRa+JFfO5Ey9erJyUnHz205Ue/p6bF80mee\neSb0iTr8zYuJgFMJthffW9DRCwWJ3hz4G+UXfnfHopjuWhTXv3w0oIXTGpzGJse1cumdlF8X+bkT\nKVOPLimxvev5VVlO1DNz0K3ww0UF/IYE25/ohUIGvTnwM8ovguCpW3fokfd3KFnyvsZ0SYu0UDWL\nl+vp6u+6HVqoUcedneVEPRqN6rnnnlNFxbWHaY6MjOSV1ANW+XVIDMKNXihk0JsDP6P8IgiqSiu0\n6+P/oXciH+g/SlK6cbJK/736v6psQXASQurLwWE5UW9oaLC8UNw3v/lN2wEBs/HzkBiEG71QmI7e\nHPgZ5fdTLA7qb7eYN+iWiRvcDsNx1JeDxXKi3traavmktbW1toIBroYhMfAreqEwXRh6cxBclF8W\nB4W3UV8OloJWfU8mkzp48KAGBgYkSffff7+ampoUi1HxBIAMeqFwpaD25iAcwlx+WRwUyB/D8e2x\nnagPDQ1pw4YNkqbmr0vS4OCgurq69A//8A+69957nYkQAHwuDL1QfAkDCDoWBwXyx3B8+2yvI79z\n5041NTXptdde0/Hjx7P/6uvr9b3vfc/JGAEgEG4xb9AfTNypW8xg9URN/xKemJjQ6dOnZZqm22EB\ngKOsLA4KINfVhuNjbrZ71A3D0IsvvphzLBqNau/evfqjP/qjggMDAPgDc+IAhIEfFgdlkTsgOGwn\n6rFYTKdOnZoxxD2ZTGrlypXZ3zs7O9XY2Gg/QgBwGRUfWMHwfyDYvLw4KIvcAcFjO1Ffv369vv71\nr2vTpk3ZxPzEiRPq7u5Wa2urjhw5Iknq6uoiUQfgS1R8YBVz8IBw8OrioCxyBwSP7UR93759kqRn\nnnlmxmM7d+7M/kwlBYBfUfGBVQz/B8LBi4uDssgdEEy2E/VoNKqOjg5VVlZe9TmmaWrr1q12XwIA\nXEPFB8B8ykyVmJycVDQaZaqEzxR7i7prTcGyssgd31eA/9hO1FtbW5VIJCw9DwD8hooPgoR1FrzF\n6lQJ1j2AlSlYfljkDkD+bCfqDQ0NV32sv78/m8TX1tbafQkAcA0VHwQB6yy4Y64E28pUCdY9gGRt\nCpaXF7kDDW6wz/Y+6tOl0+mcf5n56wDgV5mKzyXl7vU5NjmuexZXU/GBL2Qq+SWKaLEWqUSRbCUf\n82N6gj0GVSnsAAAgAElEQVQxMaHTp0/LNM28z8Pew7AyBSvjqVt36PbJm2XK1McalynTE4vchZ1T\n9wOEU0H7qDc2NsowDCfjAQDP8OrqvoAVrLPgDhYWhFPymYLlxUXu4O/7ASMB3Gc7UW9paVEqlVJ9\nfb2qq6uzx03T1KFDhxwJDpgvzNeEFX6v+FDOw30NWGcB8Dc7U7CKvcgdgompN95gO1EfGhrSK6+8\nolhs5pf88PBwQUEB84X5mrDDS6v7SnO3clPOuQYS6ywAfsfcc7jFzyMBgsT2HPVVq1YpnU7P+tgD\nDzxgOyBgPjFf09vOnTunY8eO6dixYzp37pzb4RRdJrlsW/K8/nrRL9S25Hl99exOpS6PZp9jZb4b\n5ZxrILHOAhAEXp97/k7kA/1b6Zt6J/KB26EAgWO7R33Pnj1qbGxUc3OzYrGYqqo+7fnZt2+f1q5d\n60iAsI65JNfGfE1v8/swKyeGWFtZ3XeuVm4/lPP5Ho7uh2tQLKyzAPibV6dgMWrJ/8I8NcwvbCfq\nyWRSZ8+e1a5du3KOm6bpm4p1kPg9ySkG5mt6m1+HWTlVWXEqufRyOS9Wxc7L16DYvFrJB5Afr809\nt9KwDG+ikcU/bCfq7e3tqqmp0fr16xWPx7PHTdPU/v37HQkO1vk1ySkm5mtiPjhVWXEqufRyOS9W\nxc7L18AtXqvkS8715tArBBQXo5b8jUYW/yioR/3VV19VeXn5jMdGRkYKCmq+MDQ83Ly+KAvl03+c\nrKw4lVx6tZwXs2Ln1WuAKU715uR7HhJ6eJXfyiajlvyLRhZ/sb2YXCKR0MDAwKyPeXG4tZUFmOA8\nry0O5tVFWSif/mSlsmKVkwt/ebGcO3mtrPDiNcAUpxb6s3oeK4s0Am7wa9nMNCzPJqyjlvyi2N/F\nQeHWoom2e9RXr16tlpYWbdq0SStXrsx57ODBg6qvry84OCcxNLz4vDhv3qvzNSmf/uT0EGunFv7y\nYjkv9nD0fK+B33q03FLodXKqNyef8zDM0z18rq7Nr2WTUUv+xdSw/Lg9n992op5ZRO6ZZ56Z8ZgX\ne9RRfF5OPr04XxP+43RlxekE20vl3K2K3VzXwO0vYb9w6jo5NWTW6nkY5ukOPldz83vZ9PKOEjQQ\nXR2NLPlxuzHNdqIejUbV0dGhysrKnOOpVEptbW0FBwYAfjAflRUvJdhO8mLFzu0vYb9w6jo51Ztj\n9TzMpXUHn6u5+b1senHkltMNREFN+L34XexFXmhMs52oNzQ0KJFIzPpYa2ur7YAAuxZ+9rP6qLJS\nC4aHJUmXKytV/tnPuhwVgs6LlRWv8tq18sKXsB84eZ2c6s2xeh6GeRaf3z9XxVrYNShl00sNy041\nEAV9RIjXvou9yguNabYXk7taMj46Oqq+vj7bAQF2RUpLpe3bNbF0qSaWLpW2b586BhTBLeYN+oOJ\nO3WL6Y0Ki5dZuVbFWLiFRXWscfo6ObXQn5XzOLlII6zx8+eqmAu7UjadZaWByCqnFrz0Ouot1+aF\nRRNt96hL0pEjR2QYhlKpVPaYYRjq7+/Xnj17Cg4OyNf19fWSxxYyBGBdMXsygtKjNd+cvk759OZc\na+ip1fMwzLO4/Py5KvbaOpRN5zjV++n3ESFwjhfm89tO1A8dOqR9+/ZJmlo8LtPiGIlE1NTU5Ex0\nCI2gzgMCkJ9izm31wpewH8zXdbrWkNl8GmzmGnrLMM/i4nNlHWXTOU41EHlhuDO8w+3GNNuJeldX\nl5599lndd9992rp1qzo6OrILya1fv97JGPGJICazQZ8HBMA6N3oy3P4S9otiX6f5aLCZK6Ev1tzk\nMHCyvITh7+Kled5+5VQDkZ9HhMB5bjem2U7UKyoqsovJ1dTUKJlMasWKFTpw4ID+4i/+Qp2dnY4F\nGXZBTmZZGRZAhhs9GW5/CftFMa+TGw020+cmS9Lp06d14403st2sTU6VF/4uyIcTDUSMCAkXq52g\nbjWm2U7Uq6o+fUOrV69WX1+fVqxYoWg0qoGBAUeCw5SgJrPMAwIwnZs9GVa+hIM4qilfxaisuNFg\nU+y5yWFRaHnh7xIeTtxfnWogYqRV8PmlE9R2oh6LxbR27VpFIhH19vZq165dSqVSGhoacjK+0Aty\nMss8IADTebUnw6tf6EEdEszQUyA85uP+WmgDkddHWtFoXDi/dILa3p5t7969uvfee/XFL35RkrRt\n2zYdPHhQv/rVr9TQ0OBYgGHn521O5uKFbQ8AeItTW3c5yYtb9RRzG6liY9sqIDy8eH/N8Nr2ZZlG\njbYlz+uvF/1CbUue11fP7lTq8qircZ07d07Hjh3TsWPHdO6c9/MSJ7fym28Fbc/25JNPZn+uq6vT\n0aNHJUnxeLywqJAV5J4Fr/aeYX7QAgwrvNaT4dVRTUEfEszQU/dwr0axePX+6lVe7AX24zoSfhrR\nW1CifiUSdOcFPZmlMhZ8Xh02DG/zyirIfvpC9wovzTWFddyrUWzcX63zaqOGHxuN/dQJajtRz6zq\nHo1GtW7dOj3++OPq7+/XqlWrtGfPHsVifLCcEuRklspY8HmxBRiwyk9f6G7z4lxTWMe9GsXG/fVT\nc605QqOGc/zUCWp7jvpvfvMbdXV1KRaL6emnn1Z/f78OHDigxsZGtbW1ORlj6GWS2d0Xv6a/HNuo\n3Re/pp9X/yBQLdxemwcEZ/hpHhAwG+ZLW+fluaZB5sT8UO7VcAP31ylW1hxhXSdneXE9nNnYTtRH\nR0d1+PBhJRIJ9fb2Kh6Pq7a2VqtWrdL58+edjBGfIJmF3wR5MUSEh1tf6O9EPtC/lb6pdyIfzOvr\nOIFEzx1OLSoYlHu1nz4zmOKXhGk+XW34+HQ0ajjLL52gtoe+RyIRlZeXa3R0VIZhaNOmTdnHpu+x\nDiC8GNaGICj2FB0/zhVmWKY7nJof6vd7tR8/M5jCFEjrgjwV1i1en15lO1E3TVPpdFovv/yypKlV\n36WpueurV692JjogAIK617EVfpgHxArHcwtzGZ6uWF/ofpwr7PdEL+z8cK++Fj9+ZpDL6wmTF9Co\nET62E/XW1lY9/PDDMgxDdXV1WrlypTZs2KChoSHdd999amxsdDLOoqLiDqe4tW2Fl8qwV1uA6YGx\nxo9br/iZV1f2nYvfEz149149l3w/M176fgTsoFEjPGwn6jU1Ndl90zM6OjoKDshNVNzhtGJvW+HF\nMuzVFmB6YKzx49YrfubnIeR+TfQwxav36rlY/cx48fsRAK6FfdSnoeIOv/NyGfZSC7Bfey0RfH4e\nQu7XRA+5vHSvtsLqZ8bL348AMBvbq74HDSvWwu8ow9YFZYVjBE8QVvZlhxIUk5XPDN+PAPyIRP0T\nVNzhd/NVhoO43Q37kcLL2K7I24J4T/S7uT4z1PEA+JGjQ9/9zM/DDQHJ+TJsZT7fws9+Vh9VVmrB\n8LAk6XJlpco/+9nC38w8Y+EreBlDyL2JOc7eNddnxs06HovXAbCLHvVPBGG4IcLN6TKcmc9XoogW\na5FKFMnO58uIlJZK27drYulSTSxdKm3fPnXMB+i1hNcxhNxbrNwT4a6rfWbcqONlGnbaljyvv170\nC7UteV5fPbtTqcujjr8WgGAqKFFPp9Pq7OxUW1ubJKm7u1snT550JDA3UHGH3zlVhvOZz3d9fb2q\n/vVfVfWv/6rr6+sdeR/FkOmB2X3xa/rLsY3affFr+nn1D+gZAzADc5z9r9h1PBp2gPkTlilItoe+\nG4ahjRs3amRkRNXV1ZKkRCKhlpYW7dixQw8++KBjQRYLww3hd06VYT9vEZUvv61wDKD4wnRPDKpi\n1vHYWQSYH2GbgmQ7Ud+9e7daW1tVV1enb3zjG5Kmtmfr6OjQ1q1b9eKLL1o+V39/vwYHByVJJ06c\nUGtra85Wb729vRoZGVE0GpUk1dbW2g3bEiru8LtCyzBrNgDhcu7cOb3++uuSpM9//vNatozP+HTc\nE4OjGHU8rzfsMG/eGX5dp8fPwrbNou2h76ZpqqGhQdFoVFVVn37Q4/G4kknrQ8BGR0c1ODiopqYm\nNTU1af369Xrssceyj3d3dyuZTKq+vl41NTXav3+/3ZABWMSaDUB4mKap06dPa2JiQhMTEzp9+rRM\n03Q7LE/hnoh8eHVnEb/Om1/42c/qcmVl9vfLlZVa6IGE2M/r9PhRGKcg2U7UU6mU0um0JCkSiWSP\n9/b2qnLah2kuAwMDOcn3qlWrZBhGNtnft2+fGhsbJU01Ahw+fNhuyNBUr8mxY8d07NgxnTvHdiS4\nOtZsCI+wzPXC7C5duqRLly5d9XdM4Z4Iq7zasOPXefNeToj9uk6PH4Vxm0XbQ9/XrVunhx56SJs3\nb5ZhGOrp6dHAwIC6u7vV1NRk+TyJRCIn+T5x4oQikYhisZgGBwcViUTU398vSerr61NDQ4PKy8vt\nhu1JxRqCNL3XRJJOnz6tG2+8MaehBchgzYbgC9tcL6AQ3BORj6du3aFH3t+hZMn7GtMlLdJCVxt2\n/D5v/vr6eolEONTynYIUhCkethP15uZmpVIptbe3S5J27twpaWr++LZt2/I614oVK7I/Hzp0SHv3\n7pUkDQ4OamRkRPF4XLFYTCtXrtSGDRt09OjRa57PMAyVXtHSlklOp3v77bdznmflOVZZOdf5yyMz\nKsk/H/q/9cR1zYpGrnM89omJiRm9Jm+88ca8XSsnr7lTfxs/v55b13z6fL6gXINiv54XY5Kkx9MH\nZsz1+veRN/TVoe+qY2mLr9+fF2MK+ut5Mab5eL257olc82C/Xj4xXdmw818mVur9376n9/XevLze\ntZ7368tDGhkb1QLl/r+xsTF9rDH989v/qskFH3vymlsV5JicPJdfY5Kkz136jE5pWAunNTiNfvyR\n7l4Q06Txsc7ojKX8ar7fn1NsJ+qStH37dm3ZskUDAwPZhLqmpsb2+bq7u7Vu3TrVf9JiFo/HFY1G\nFYtNtfBVVFTIMAydPHkyJ7m/Ujwe19KlS3OOjY+P69133805tnz5cpWVleX1HKusnKv+zHdmVJLP\nLjinH5e+kLMgglOxW31/xXw9J2Oyws+vxzWnnDv5nLfGknr3zIcqG8/tXalYfJ3e1YcqiS/WHYti\nvn1/Xowp6K/nxZiC/nr5xjS9h2nV8lWBuAbFfr18Y5resOPmNSgZW6zomQpduJzbG7lo0SKVqUwP\nLv+C5Xu+k7EXu+7t15icPJdfY5Kk5y7u0SP/njtS5T9FP69npo0EtJJfzff7c0pBibo0lTwnEomc\nY/v378+7V72/v19VVVVau3Zt9lgsFtPIyEihIXqS34cgYcr5nh5Ffjg1t8v87neZnwTf8PqqxACc\nwzQXZObN/8tHAzm9kWOT41q59E7u9/CFuaYgBS2/ipgFLO168uRJ9fX1KZVK5Rzv7u7Wr3/9a8vn\nyQxxzyT83d3dWr9+vcrLy7Vx40Z1dHQoFovJMAw1NjbqyJEjs57nwoULOnnypKTcBe4kaXJyMrv4\nXUZ5eblKSkryeo5Vc53rX8zX9UPz5yqbzC1IpSUluhgZ1/f0v+s/R+5xNHar76+Yr+dkTFY4+Xrm\nxISW/+mfauEnjUmXolG9/Td/k7PACdfcm9eg2K/nxZiS5n9oh/m0zMncr4DSkhJNRqQf65uKRW70\n7fvzYkxBfz0vxhT017Ma0/+c/KlOTyZzKq8TJZO6I3KLfhTZ7Oo1mN7Lf891twXmmnvx9YYn0/rB\n5b/L6Y28veRmfS/yP1QRWZpznmv9Xdx4f1YEOSYnz+XXmKw8z2p+NR/vr6SkRNddd51WrFgxY2S3\nXbZ71Lu7u7Vr165ZH8tncTLDMLRx48bs/zFNU5WVlWpoaJAkdXR0qKurS/F4XIODg/rZz3425zm/\n+tWvZveDzaisrNRLL72Uc+zLX/6yhj/Z+9Dqc6ya81y3lqmk/W7ddeddOc954403NDE5oeb/+XXp\n9+OOxm71/RXz9ZyMyQonX686GtXAzTdnf184MqINX/6yzk4bBcI1n59rML0C8adf/t9CVc6dfL2F\n7fco9r/cldO78vpbpzV55iP9t+/V+fr9eTGmoL+eF2MK+utZiukq9Y3fvvGW3pw8raP/81np9+NF\nvwbRW67Xf3nx4Zxe/t/9P6d0ac+bUnrC8dcLcjnI91zTeyP/9L816n8dfib7HCt/FzfenxVBjsnJ\nc/k1JkvPs5hfzff7c4rtHvWvfOUrSiQSeuSRR2bMS9+wYYMr26j5qUddmmrhPjOZzKkkT5RM6s7I\nLfqrT1q4nYzdi61jXu/dvVaLciSV0l3f+lbO/zvzt38rs6pqxnmceH9huebXel6mN2B6BWL5VXoD\nnHg9L15zJ18vn94Vv70/L8YU9NfzYkxBfz0rz3Gyh8nJa+BUL7/V5wW5HDh5Lit/FzfenxVBjsnJ\nc/k1JqvPs5JfBb5HfXh4WDt27FB5+cyt0p544omCgirUbBdofHxcfX19OcceeOCBGYsBzPUcq6yc\n6+cXfzhjQYT/XLUiZ0EEJ2O3+v4yz5uepP73B2YuOuNGTHM9by5Wz3Pu4gd65N935CSE/6nq3pz5\nfOPvvacrZ/jed999Krvppnl5f0G/5laeV3/mO3r7w9wFQt5ZfF5/u/T/ylkgJMjX3OnX29U3mTvX\nK/FfA/H+vBhT0F/PizEF/fWsPKdqbJn+5sz/qQsf5S4itmTpUi3WEv3JnX+cXUSsWNfgrbGk/uPM\nqMo+ym08qFwa1fsaVdWdyyzHZDWuIJcDp85l9e/ixvuzIsgxOXkuv8Zk9XlW8qv5fn9OsZ2oNzQ0\n6OWXX86u0D7d4OBgQau/h4VX92Rl0Rnpz37/4xkrRp78+G1tOfvDnBX5UTxBWyDES6avSgwgWJxc\nRGzhwoVauHBhdqvXzO/5YjFLb+LvgiDwan5lh+VE/coF3B544AH99Kc/1eDgoO677z5VVlZmHzt4\n8OCsCTxm57VKspeT1Om9/PMlLAlhMa6lk6hAAIA9T926Q4+8n9vDVLN4uZ6u/m5e54lEIrr77ruz\n6wDdfffdea1LlBEvu0lLShbpgi7MeGxJZJFiZcvyPicKF4a/i1ONTfA+r+VXdlhO1B9//HFFIhFd\nOaV9cHBwxnPt3LThDV5NUovZy+/1hLDQBNuvIybCUIFA8FFJhBuc7GFatmyZli0r7H7LVmHeNF9/\nFy91DDjV2AQUg+VEPRqNqqOjI6fnfDapVEptbW0FBxYUXro5WZFvklqs91fMXn6vJoROJdheHjFx\nLVTscCW/3V8lKolwl5d6mJzq5YeznPy7eLVjwInGJqAYLCfqdXV12X3OryaZTKqmpkatra0FB+Z3\nXr05zcVqklrM91fsXn6vJoROJNheHTFhVT4VCC8lcfSiOsuv99cMKolAsOaRBomTfxe/dgwAXmF5\nn4G9e/fm/N7Z2Znzu2EYam9v18aNG1VdXe1MdD6WuTmVKKLFWqQSRbI3Jy/LJKmXdCnn+NjkuO5Z\nXJ1N4or5/qz08jvtqVt36PbJm2XK1McalynT1ZZ+Kwm2FW5cSydlKhC7L35Nfzm2Ubsvfk0/r/5B\nTnKWSeLaljyvv170C7UteV5fPbtTqcujrsWd6UUtLS1VaWkpvagF8uv9FcBMt5g36A8m7tQtpjd6\n+jGl0L+LU/UWIMzy3xDwE1cuQx+Px9XR0aEDBw6opaWl4MD8zO83p7mS1GK/v0wv/2zmayi6lYSw\nmJxKsN24lvPhWhUIryZxy5Yt05o1a7RmzRp6Uwvg9/srAISB3zsGAC+wPPQ9nU7LMIzs76lUSqdO\nncpZXC6VSmloaEjDw8PORukzXl+MbC5zDXsq9vtzcyi6V+bzOTVv3qvD+p3i96H9mJvf768AEAZe\nXe8nLLw0/S/DSkxejNtNlhP1EydO6IUXXlB/f79GR6eGkD788MM5z8kk7Zs2bXIwRP8Jys3pakmq\nG+8v7IvOOJlgB/laksQFX1DurwAQZEHvGMhXsRJQL67hYiUmL8adr/+IDOs6XefoOS0n6olEIruY\nXHt7u44cOTJj0bhoNKpYLKZ4PO5okH4T9JuTG++PRWecS7CDfC1J4oIv6PdXAAiKIHcMWFXsBNSL\nC/hZicmLcVuV+RuXlizQj7TZ0XNbTtSn2759uyKRiGprax0NJkiCfnNy6/15ZSi6G5xOsIN4LUni\nwiHo91cACIIgdwxYVcwE1IvT/6yuK+O1uPOR+RvfI+c7qm0l6pJCvwXb+Z4eRX44tTiV+d3v6vr6\n+pzHg35zCvr787IgJthOIolzT7GG9nH/AQD/CGu9pdiJsxen/1mJyZTpubitutrf2Cm2E/UwMycm\npPZ2lV6YGl57ub1d5oYNipSWznhu0G9OQX9/8B+SuOJza24Z9x8AmLJw4UItXLhQly5dyvkd7il2\n4uzF6X9WY/Ja3FZd62/sBNvbs4XZpfff14JpK9svGB7WpfffdzEiAFdib97i8eqWeG54J/KB/q30\nTb0T+cDtUACESCQS0d13363S0lKVlpbq7rvvViQScTusUCv2lriZ6X+XdCnn+NjkuO5ZXO1Kr7SV\nmLwYt1XX+hs7gUQdAGAb+5pPyYwqaFvyvP560S/UtuR5ffXsTqUuj7odGgAfu7Jn/Fo95cuWLdOa\nNWu0Zs0aLVvm3V7IsHAjAX3q1h26ffJmmTL1scZlynR9+p+VmLwYtxVX+xs7paCh7+l0WuXl5U7F\nAgDwGS/OiXODV1esZTise9gzOJiK/ZnK9JS//vrrkkRPuc8Ue90cL07/sxKTF+O2KvM3NktMx89t\nO1F/7LHH1N/fr46ODq1du9bJmAAAPuHFOXHF5sWVdjOo5BdfWPYMDis3PlPLli2jh9yn3EpAvbiG\ni5WYvBj3XDJ/4w9KR6Wlzp67oB71+vp6rVixwqlYAAA+w5Z43h9VQCW/uIK+ZzD4TCF/fkxAkZ8b\nzUrHz2l7jnpdXZ3WrVuneHzmnnH79+8vKCgA8IJ85gaGmV/nljml2AsGwbusjK7Id10HFigE4Bbu\nP+6y3aMej8fV19enffv2adWqVaqurlYsFtPo6Kh6e3u1bds2J+MEgKJj2LA1fp5b5gRGFSDDyT2D\nGR4PwC3cf7zBdqL+6KOPZn8eHByUNFWpNU2TiiyAwGCIo3VhHtpX7AWD4E1O7hnM8HgAbuH+4w22\nE/VoNKqOjo4Zx03TVFtbW0FBIVhY1Rb5oLzAj8I+qgBTrI6umOs5Xl6gEECwcf/xDtuJekNDgxKJ\nxKyPtba22g4IwcGwGeSD8oIgCPOoAkyxMrpirud4fYFCAMHF/cc7bCfqmWS8p6dHv/rVryRJq1ev\nVn19vWpra52JDr7mxWEz7CnsXV4sL8VG+QT8z4k9g9n2EIBbuP94h+1EfXR0VBs2bJBhGNljv/zl\nL3Xo0CG9+OKLKi8vdyRA5Mcrw4a9OmyGxcG8yavlxQonk2vKJxAchewZzAKFANzC/cc7bCfq3//+\n95VIJNTR0aF4PK6KigoNDg6qq6tL3//+93XgwAEn48QcvDZs2MvDZry8OJhXGlqKzcvlZS5OJ9de\nLp8AiocFCgG4hfuPN9hO1NPp9IzF5O677z7t3btXjY2NBQeG/Hht2DDDZvLjtYaWYvN7eSG5BuA0\nFigE4BbuP95QYvc/nj9/3tZjcJ6VYcPFlhk2c0mXco6PTY7rnsXVnu0ddUumoaVEES3WIpUokm1o\nCQPKCwDM7hbzBv3BxJ26xfTPIoVXTgHy23ob70Q+0L+Vvql3Ih+4HQrgKqv3Hz4z88N2j/q6deu0\ndu1aPfLII4rFpirRhmGoq6tLmzZtcixAzM2rw4YZNmONn+dnO4nyAgDB4Nf1Noo9uo0FROF3YR8R\nOt/yStTT6XR2kbjm5mYZhqEf//jHikQiMk1T0tS2bQx9Ly6vDhtm2Iw1Xm1oKTbKi3Oo/AFwmx+n\nBBV7GqFfGzSADK9NvQ0ay4n6rl271NPTo8OHD2vFihWSpL1796q5uVlDQ0OSpJqaGsXj8fmJFFfl\n9dUZ2Vf42rza0OIWykvhqPzRWBEG/I3hJLdGt/mxQQOQGBFaDJYT9YGBATU2NmYT8UzvejweJzn3\nAIYN+5fXG1rgTXPtEBD2yh+NFcE3H3/jsO68AUa35YuGMvCZmX+WE/Wqqiq1trZmf29paVFnZ+es\nz92/f7+2bdtWeHSwjGHD/kZDC6zy83ywYlfswt5YEQZO/Y39/LmCMxjdlh8aQ8FnZv5ZTtQrKirU\n2Niouro6VVZWyjAMHT16NDs3fbre3l7PJupBby1n2LA/0dACq/w8H8xKxY5eGjjNSpny8+cKzmB0\nW/5oDPUnp75n+czMP8uJ+hNPPKGvf/3r2rlzp6SpCtef//mfz/pcL7ao0VoOP6ChBdcShPlgc1Xs\npifzk5OT9NKgYHM1EAXhcxV0xepkYXQbwsDJ0RB8ZuZXXj3qhw8f1ujoqM6ePaudO3fqiSeemPG8\nVCqltrY2R4N0Aq3lAPwuLPPBMsn8mTNn6K0JIDdGTVyrgSgsnys/KnYnC6Pbio9RVO5wajQEn5n5\nlfc+6hUVFbrvvvu0fv161dTUzPqc6XPZvYDWcgBBwHwwBIHX5rbyufIutzpZGN1WPF67H8AePjPz\nI+9EPaOpqemqj9XW1to97bygtdy7aEkFrGM+GILCS3Nb+Vx5E50s4eGl+wHgJSVuB1AMmdby2dBa\n7q5MS2ppaalKS0tpSQXm8NStO3T75M0yZepjjcuUyXywEHsn8oH+rfRNvRP5YF5f58pG1KA1qvK5\n8h4rnSzAdEG/TyF8bPeo+wmt5d5GSypgHfPBnOXXUT3Fnrsb9OGpfK68hykJyFfQ71MIn1Ak6hKr\nEgIIFuaDOcOvFTs35u4Ws1HVrQYUPlfeQScL7PBz50/Qt5D2I7cb80OTqNNaDgCYjd8qdmGYu+vX\nBhQ4i04WuKHYyRlbSHuX299FoUnUM2gtBwB42VyVxLAskOq3BhQ4j04WuKHYyZnVEVJu9+6GlZvf\nRcD/AyMAACAASURBVPOymFxnZ+d8nDa0WBwDAMJjrkU2WSAVYXOLeYP+YOJO3WLS0YLiWLZsmdas\nWaM1a9bMa5JmZYRUBgswh4/lHvWenh7LJ33mmWfU2NhoKyDM5PawCwBAcV2rBZ+5uwAQDPmOkGKk\nkTP8MjrBcqK+c+dOyycliXQeH0wAQMZ8zN1lISMAKC52N3CHXzpBLSfq0WhUzz33nCoqrr2owcjI\nSF5JPQAAyI+Tc3edWsjILz0UQUQjC+BPjJByjx86QS0n6g0NDaqpqbH03G9+85u2AwIAwEu8nIA6\nsUCqU1u9+aWHIkicXC3ay+UcCDJ2N8DVWE7UW1tbLT1vdHRUfX19qq2ttR0UAABeEeQE1Omt3vzQ\nQxEkTjWySMEu54CXsbsBrqag7dmOHDkiwzCUSqWyxwzDUH9/v/bs2VNwcEBQMCwRfhf2MhzUBDQs\nW70FkdONLFJwyzngB2whjSvZTtQPHTqkffv2SZpqhTVNM/tzU1OTM9EBPufksETADZThYGMhI/+i\nkQUAgs32PupdXV169tlndfz4cSUSCb322ms6evSoEomE1q9f72SMgG9lhiWWKKLFWqQSRbLDEuGu\nK+dfMh9zdpThYMssZHRJl3KOj02O657F1SR6HpZpZJlN2BpZuJ8DCCLbiXpFRYUSiYSi0ahqamqU\nTCYVj8d14MCBbE+733Cjh5OsDEuEezLzMUtLS1VaWsp8zFlQhsPhqVt36PbJm2XK1McalymThYx8\ngEaWT1m5n1PHA+A3toe+V1V9Ok9x9erV6uvr04oVKxSNRjUwMOBIcMXGQipwEsMSp3h5JWHmY14b\nZTgcWMjIv1gt+lNz3c+p4wHwG9uJeiwW09q1axWJRNTb26tdu3YplUppaGjIyfiKjoo7nMLczylU\njvyLMhwuLGTkPzSy5Ic6HgA/sZ2o7927V48//ni2Z33btm3aunWrJKm5udmZ6DAvwr56c7FkhiX+\ny0cDWjht6PDY5LhWLr0zVD2RVI78iTIM+AONLAAQPAVtz/bkk09mf66rq9PRo0clSfF4vLCoMC9Y\nvbn4GJYIv6MMA0D+vDztC4A/2E7U29raZuyVToLubZnVm8u0UIs1tVJsZvXmF+74K5ejCyaGJcLv\nKMPAFBIv5INpXwAKZTtR7+rqUmVlpTZv3qzy8nInY8I8sLJ6M8NY50+xhiU6WZGkUorpGFqLsCPx\nQr6Y9gWgELYT9Wg0qsnJSX3ta1/T/fffr0ceeUQrVqxwMjY4iNWbw8HJiiSVUgDIReIFACgW24n6\nD37wA9XW1kqShoaG9Pd///caHBzUI488ovr6escChDNYvXn+vL0sot9/pkS3fjipe90ORs5WJKmU\nAgAAAMVXYvc/ZpJ0SaqpqdHq1as1MjKinTt36otf/KIjwcE5mdWbL+lSzvGxyXHds7ia3nQbUpNp\nfePbi/W1liXa2rhIX2tZoq9+8COlLo+6HRoAAFlXTl1iKhOAoArS/c52or5161al02nt379fX/zi\nF7Nbs+3du1e//vWvHQsQznnq1h26ffJmmTL1scZlymT15gL82fmf6GSsRCWmdN2YVGJKJy+d1Zaz\nP3Q7NAAAsjJTmUpLS1VaWspUJgCBFaT7ne2h77/85S/V29sr0zS1atUqNTc3K5FIOBkbHMbqzc55\nayypM5ff0eLLuccXRRayOB8AwHOYygQgLIJyvytoH/X6+no1NzezLZvPsHpz4Yzx93TRHNPSWR5j\ncT74BSv7AwAAeJPtoe8NDQ3asWOHI0l6f3+/Dh06pEOHDqmlpUWGYcz6vF27dimdThf8ekCh4mU3\naUlk0ayPsTgf/CJIw8MAAECwBWn+uRW2E/VkMqk//MM/1JEjRwoKYHR0VIODg2pqalJTU5PWr1+v\nxx57bMbz+vv71dvbq1QqVdDrAU64Y1FMdy24RR9fMSZlzLzE4nzwlWXLlmnNmjVas2ZNIIaJAQBm\nF7YkB8ETtg4G24m6NDX0vdC90wcGBrR///7s76tWrZJhGEomk9ljo6NTq2hXVlYW9FqAk566/tta\nkZzUZET6qEyajEg1C29jcT4AAOA5YUtyEExh6mCwPUe9rq5O8Xh81qHv+/fv17Zt2yydJ5FI6PDh\nw9nfT5w4oUgkoljs0x7JX/7yl6qvr5dpmnbDBfJiZe5uVUm5nvvJx3p7WUTvfKZEt3w4qXt/8R2V\nLahwI2QAAIBrCsoiW0AY2E7U4/G4+vr6tG/fPq1atUrV1dWKxWIaHR1Vb2+v5URdUk6v/KFDh7R3\n797s7/39/Vq3bp3dMD2NhZy8K9Pq/Prrr0vSNVudl58ztfzcRDHDAwAAcBx1U8A7bCfqjz76aPbn\nwcFBSVPJjWmatofRdHd3a926daqvr5f06ZD38vJyu2F6Wj7JYNi58cVBqzMAAAgT6qaAd9hO1KPR\nqDo6OmYcN01TbW1teZ+vv79fVVVVWrt2bfZYX1+fRkZG1NPTI9M0ZRiGent7tWrVqmvOjTcMQ6Wl\npTnHJiZm9ni+/fbbM55nhfnhh7r5imO/+93vFPmkYSHf1/vc5z4nSRoZGdHIyEje8Vh9PasxOXUu\nJ6+5JFVUVOj8+fPZn998801b53GKk+WgmNfT6b+LU7xa7rym2O/PzWv+0Ucf6cyZM7ZiKjYv/l3c\nOJdfFft6cr/z5vvz8/V0WrHqpkFX7HJe7Loi97LZY3eK7US9oaFBiURi1sdaW1vzOlemRz6TpHd3\nd2v9+vWqra3Ned6uXbtUW1ubM399NvF4XEuX5u5wPT4+rnfffTfn2PLly1VWVpZXrJI0/t57Grvi\n2G233aaym26al9ezFJOF17Mak1PnKvY1KDYny0Exr6dX/y6UO2v8fG/J15kzZ3TXXXfZiqnYvPh3\nceNcflXs68n9bqpj5/33388ZKXfPPffk9N76+XMFrqdU/HJe7Loi97LZY3eK7US9tbVV6XRaXV1d\nOnv2rPbs2aPu7m7df//9MxLsazEMQxs3bswWWNM0VVlZqYaGhuxzRkdH1dXVpUgkooMHD6q5uXnO\nZB0AAADexBBrhAHlHIWwnahnEuyRkRFVV1dLmlrBvaWlRTt27NCDDz5o6TzxeFynTp265nMqKiqy\n+6wDKAwLxQAAvIC1YBAGlHPYZXsf9d27d6u1tVXHjx/PLvYWj8fV0dGh9vZ2xwIEMOXKhNpugs0+\nqgAAAIC32e5RN00zOzy9qqoqezwejyuZTBYeGVxDj6s3TR8+NTk5WVCC7dfWXcomAAAAwsB2j3oq\nlVI6nZaknGSht7dXlZWVhUcG19Dj6l3Lli3TmjVrdOutt/oy0S4UZRMAAABhYLtHfd26dXrooYe0\nefNmGYahnp4eDQwMqLu7m7nkAeDXHlcEH2UTjKwAAABBZztRb25uViqVys5H37lzpySptrZW27Zt\ncyY6j3t7WUS//0yJbv1wUve6HQwAhASr6AIA4A80rttnO1GXpO3bt2vLli0aGBjQyMiIysrK9KUv\nfcmp2DwrNZnWt769WG9+rkQXy6Ql49LdH/xIB2/Yq6oFFZIolAAwnxhZAQDeRl0YEo3rhbA9R72z\ns1PS1NZpiURCNTU1eumll7Rx48Y5t1vzuz87/xOdjJWoxJSuG5NKTOnkpbPacvaH2ecwlxYAAABh\nNb0unPmZunA4ZdZYWrNmDY3sebDdo97X16fGxsbs75mt2QzDUGNjo44cOeJIgF7z1lhSZy6/o8WX\nc48viizUGx+f1VtjSd2xKCaJHh8AAACEV6YufObMGerERcAohmCxnKin02kZhpH9PZVK6dSpUzJN\nM+fY0NCQhoeHnY3SQ4zx93TRHNPSWR67aI4pOX4um6gHGTcCeBVlEwAAhBHDzIPFcqJ+4sQJvfDC\nC+rv79fo6Kgk6eGHH855TiZp37Rpk4Mheku87CYtiSya9bElkUWKlYWjtZAbAbyKsgkAAMKKEb3B\nYTlRTyQSSiQSkqT29nYdOXJEra2tOc+JRqOKxWKKx+PORukhdyyK6a4Ft2hwwRs5w9/HzEtauXh5\nKHrTM7gRwKsom8XFKAYAAGAX9YjZ2Zqjvn37dkUiEdXW1jodjy88df239a3kq1Orvi+UllySahbe\npqerv+t2aABQdIxioJKBT1EWACA/1CNmZ3sxuSt706fbv39/oPdSryop13M/+VhvL4vonc+U6JYP\nJ3XvL76jsk+2ZgOAsAn7KAYqGcigLABA/vxaj8g0xk5MTDh+7oL2UT958qT6+vr0/7d3P0Ft3Pf/\nx1+Km6TTQYhOU/c3Ey3pt1MPWODMtDN2jZwc0hgD6UxngovknpIAsnPpyFPAJwM2dnMIkIbUh8aA\n038HI4b0FhCeTE5ISdomMzWCpONDwyqHb+p+IySa1kmT/R0YbRD/LIRshPR8nNDuh903+/lY3vd+\n/mwikcjYHgqFijpRT/ufjyz9z0f5r5RiQa8CgFKyW28ykH+3awv8/wgAxSH9cPZvf/tb3o+dc6Ie\nCoXU09Oz7j6eHEOiVwEAgPWs/P/xiy++4P9HALsSDx2X7d27V2VlZZqfn8/rcXNO1IeHh+Xz+XTi\nxAl5PJ6Mfc3NzdsODMWBHiYAANbi/dIAdjs65e6snBP1xcVFnTlzRmVlZWv2Xbx4cVtBAQAAAADu\nvq30lNMpd+fck+svNjY2anJyct19sVgs54AAAAAAADsj3VO+Z88e7dmzh57yHZJzj/qRI0d0+vRp\nxWIx1dTUyOVy2fuGh4fV0tKSlwABlAbmOQHAl/hOBLCT6CnfeTkn6sFgUJJ09erVNft44gJgq5jn\nBABf4jsRAEpbzol6eXm5hoaGMnrSJSmRSKi3t3fbgQEoPTy9BYAv8Z14dzGKAUAhyTlRP3nypOrq\n6tbd19nZmXNAAAAAwN3GKAYAhSTnRL29vX3DfbOzs2poaMj10AAAAMBdxygGAIUi60R9enpaknTs\n2DFJ0vj4+LrlksmkQqGQOjo68hAessVwrd2N+gMAAACQlnWifvbsWVVUVNiJend394ZlGSZ09zFc\na3ej/gAAAACkZZ2oT0xMqKKiwv5cXl6uiYmJdcumV4TH3cVwrd2N+gMAAAAgbSFRNwwj43NjY+Oa\nbWldXV3biwoAAOAuYfoRAKDQ3JPrL/b19W24b6PV4AEAAApNevrRnj17tGfPHqYfAQB2XM6rvgMA\nABQLph8BAApJzj3qAAAAAAAg/0jUAQAAAAAoICTqAAAAAAAUEBJ1AABK2OoVzlnxHIWCtgmglG0r\nUV9aWtLo6Kh6e3slSaFQSPPz83kJDAAA3HmseI5CRdsEUMpyXvXdNE0dP35cyWRSlZWVkpZfyxYM\nBnXmzBkdPnw4b0ECAIA7hxXPUahomwBKVc496ufOnVNnZ6fefvttlZWVSZIMw9DQ0JD6+/vzFiAA\nAAAAAKUk5x51y7Lk8/kkSRUVFfZ2wzAUj8e3HxkAAAAAFLH02gufffZZxmcg5x71RCKhpaUlScqY\nLxQOh+VyubYfGQAAWBeLbAFAcWAtBmwk5x71pqYmPf744zp58qRM09T4+LhmZ2cVCoXU3t6ezxjz\ngqdVAIBikb6xe//99yWJGzsA2MVYiwHryTlRDwQCSiQS9nz07u5uSVJDQ4M6OjryE10ecVMDoBjw\n0BFp3NgBAFC8ck7UJamrq0vPPvusZmdnlUwmZRiGPB5PvmLLO25qAOx2PHQEAAAoftt6Pdu5c+dk\nGIbOnTsnafk96mNjYzp//ny+4gMArMJDRwAAgOKW82Jyvb29un79uiYnJ+1tPp9PhmGot7c3L8EB\nAAAAAFBqck7UHQ6H3n77bb311lsZ2/1+v0Kh0LYDAwAAAACgFOWcqH/88cf269lWikQiKi8v31ZQ\nAAAAAACUqm2/ns3v96u2tlaLi4v269l8Pl8+YwQAAAAAoGRs6/Vspmnq8uXLcjgcsixLkuT1ellM\nDgAAAACAHG3r9Wx9fX0KBAKam5vT4uKiamtrC/r1bAAAAMXi3nvv1b333qvPPvss4zMAYPfbVqIu\nSYZhyDCMjG2Dg4Pq6OjY7qEBAACwAYfDoX379un999+XJO3bt08Oh2OHowIA5MO2EvX5+XlFIhEl\nEomM7aFQiEQdAIoAPXZAYdu7d6/27t2702EAAPIs50Q9FAqpp6dn3X08zQWWkeRgt6PHDgAA4O7L\nOVEfHh6Wz+fTiRMn1sxLb25u3nZgyD+SxruPJAfFgB47AACAuyvnRH1xcVFnzpxRWVnZmn0XL17c\nVlC4M0gadwZJDgAAAICtuCfXX2xsbNTk5OS6+2KxWM4B4c7au3evHn30UT366KMkjwAAAABQgHLu\nUT9y5IhOnz6tWCymmpoauVwue9/w8LBaWlryEiAAAAAAAKUk50Q9GAxKkq5evbpmH8OpAQAAAADI\nTc6Jenl5uYaGhjJ60iUpkUiot7d324EBhe7eBx7Qv1wufWVxUZL0X5dLZQ88sMNRAQAAANjtck7U\nT548qbq6unX3dXZ25hwQsFs49uyRurr0+XPPLW/o6lreBgAAAADbkHOi3t7erqWlJY2NjWlhYUHn\nz59XKBTSgQMH1NDQkM8YgYL19ZYWifUYAAAAAORRzom6aZo6fvy4ksmkKisrJUl1dXUKBoM6c+aM\nDh8+nLcgAQAAAAAoFTm/nu3cuXPq7OzU22+/bb9L3TAMDQ0Nqb+/P28BAgAAAABQSnLuUbcsSz6f\nT5JUUVFhbzcMQ/F4fPuRAQAAAABQgnLuUU8kElpaWpKU+Tq2cDi8ZiV4AAAAAACQnZx71JuamvT4\n44/r5MmTMk1T4+Pjmp2dVSgUUnt7ez5jBAAAAACgZOScqAcCASUSCXs+end3tySpoaFBHR0d+YkO\nAAAAAIASk3OiLkldXV169tlnNTs7q2QyKcMw5PF48hUbAAAAAAAlZ1uJuiQ5nU7V1dVlbIvH43K7\n3ds9NAAAAAAAJSfnxeQ2c/z48TtxWAAAAAAAil7WPerHjh3LqpxpmjkHAwAAAABAqcs6UV9YWJDX\n683YFolEJC2/O93pdCoej8uyLB05cmRLQUSjUcViMUnS9evX1dnZKcMwbrsPAAAAAIBik3WibhiG\nrly5Yn8eGRmRx+NRZ2dnRrmxsTHF4/GsA0ilUorFYvYr3cLhsFpbW3Xt2rVN9wEAAAAAUIyynqO+\nOiEPhUJrtkmS3+/X3Nxc1gHMzs5qcHDQ/uz1emWapuLx+Kb7AAAAAAAoRlkn6g0NDRmfE4mE3nzz\nzTXl4vH4luap19XV6dVXX7U/X79+XQ6HQ263e9N9AAAAAAAUo5xfzxYIBPTMM8/I6/XK7XarsrJS\nCwsLCoVC9lD1bO3fv9/+eWRkRH19fVnt24hpmtqzZ8+WYtgK6//+T/9v1bYPPvhAjlTqjp0TWOlf\n//qXbty4sdNhAHcU7RylgHaOUkA7R7H7/PPP837MbSXqiURCo6OjGdt9Pp86OjpyOmYoFFJTU5Na\nWlq2tG81wzD0ta99LacYsvHp//6vbq3a9tBDD+m+b33rjp0TWOnGjRv67ne/u9NhAHcU7RylgHaO\nUkA7R7H75JNPND8/n9dj5pyoS1JXV5e6urrsOenp1d9zEY1GVVFRse5r4DbbBwAAAABAMcl6jvpm\nPB6PPB6PnaSv7mW/nfTr19KJeCgU0tLS0m33AQAAAABQbLbUox6NRlVXVydp82T88uXLamtry+qY\npmnq+PHjcjgckiTLsuRyueTz+Tbdt5PufeAB/cvl0lcWFyVJ/3W5VPbAAzsaEwAAAACgOGSdqAeD\nQU1PT+vKlSuqq6tTf3//hmXTiXU2DMPQe++9t+V9O8mxZ4/U1aXPn3tueUNX1/I2AAAAAAC2KetE\n3TRNtbS06MCBA5KWk+grV66ooqIio1wikVAwGMxvlAXo6y0tUhYL2wEAAAAAsBVZJ+qVlZUZr0Yz\nDEOGYawp53Q61dXVlZ/oAAAAAAAoMVkvJpdMJvXhhx/anzcb3p5eBR4AAAAAAGxN1j3qPp9Pzc3N\n8vv9MgxDpmlqfHx83bJbWUwOAAAAAAB8KetEvbGxUaZpanBw0N7W3d29btmtLCYHAAAAAAC+tKXX\nswUCAQUCASWTST399NMaGhpaUyaZTG6YwAMAAAAAgM1tKVFPKy8vl9frXXcxOUksJgcAAAAAQI6y\nXkxutc7Ozg33RSKRXA8LAAAAAEBJy6lHPW1+fl6RSESJRCJjeygUUkdHx7YCAwAAAACgFOWcqIdC\nIfX09Ky7j8XkAAAAAADITc6J+vDwsHw+n06cOCGPx5Oxr7m5eduBAQAAAABQinJO1BcXF3XmzBmV\nlZWt2Xfx4sVtBQUAAAAAQKnKeTG5xsZGTU5OrrsvFovlHBAAAAAAAKUs5x71I0eO6PTp04rFYqqp\nqZHL5bL3DQ8Pq6WlJS8BAgAAAABQSnJO1IPBoCTp6tWra/axmBwAAAAAALnJOVEvLy/X0NBQRk+6\nJCUSCfX29m47MAAAAAAASlHOifrJkydVV1e37r7Ozs6cAwIAAAAAoJTlnKi3t7dLksbHxzUzMyNp\ned56S0uLGhoa8hMdAAAAAAAlJudEPZVKqbm5WaZp2tumpqY0MjKiiYmJdV/bBgAAAAAANpfz69nO\nnj2ruro6vfrqq/rTn/6k9957TxMTE/rBD36gs2fP5jNGAAAAAABKRs6J+tLSkvr6+uTxeOR0OiVJ\nNTU16uvrUyqVyluAAAAAAACUkpwT9Y8//jinfQAAAAAAYGM5z1FvamrSsWPHdOLECbndbkmSaZoa\nGxuT3+/PW4AAAAAAAJSSnBP1QCAg0zT1/PPPy+FwyLIsSZLP51NbW1veAgQAAAAAoJTknKhLUl9f\nnwKBgObm5iRJHo9HhmHkJTAAAAAAAErRthJ1STIMg+QcAAAAAIA8yTpRDwaDWlpakiQlEgkZhqEX\nX3xR0vLc9NbWVjU2Nqqjo+PORAoAAAAAQAnIetX3pqYmzczMaGFhQX6/307SpeVe9WvXrsntduvY\nsWN3JFAAAAAAAEpB1j3qDodDXq9XV65c2bBMerX3wcFBetYBAAAAAMhB1j3qly9f1ksvvXTbcn6/\nX5FIZFtBAQAAAABQqrJO1C3LUllZ2Z2MBQAAAACAkpd1og4AAAAAAO68rOeo19bW6oUXXtDPf/7z\nTcuNjo7K7XZvO7BcfPHFF5Kkf//73ztyfuBu+fzzz/XJJ5/sdBjAHUU7RymgnaMU0M5R7NL5Zzof\nzQeHZVlWNgVTqZQef/xxHTlyRD6fTwcOHLCHwi8tLck0TV29elWhUMheAf5u++c//6m///3vd/28\nAAAAAIDS9u1vf1vf+MY38nKsrBN1SYpEImptbZXD4diwzPnz5+Xz+fIS3Fb997//1eLiou6//37d\ncw+j+gEAAAAAd9YXX3yhW7duyeVy6StfyXrQ+qa2lKhLUjKZ1NmzZzU9PZ2x3ePx6OLFi/J4PHkJ\nDAAAAACAUrTlRH0l0zQlSYZh5C0gAAAAAABK2bYSdQAAAAAAkF9M5AYAAAAAoICQqAMACkZPT4+W\nlpbsz6ZpamRkROFwWKOjo0qlUjsYHQAAKEXhcHjNts3uUfJx/1IUQ99N01Q4HJZhGIrH4/L5fHI6\nnTsdFrBt0WhUsVhMknT9+nV1dnbaa0LQ7lFsotGoTp8+rYmJCfsVn83NzXr11VclLb8mNBgM6sqV\nKzsZJpCzcDisZDKp8vJySVJDQ4Mkvs9RPEzTVDQatX9uamqyF5qmnWM3CofDWlxcVE9Pj/785z/b\nryeXNr9Hycf9S37Wjt9hwWCQGzkUnVQqpVgspvb2dknLXxStra26du2aJNo9ikv6SbPL5bK3zc3N\nZbwO1Ol0anZ2VvF43E7kgd0iFAoplUqpra1Npmmqra3NTtT5PkexGBsbU2dnp/05GAxqaGjI/pl2\njt0m/T3d29ubsX2ze5RkMpmX+5ddP/R9s4sE7Gazs7MaHBy0P3u9XpmmqXg8TrtH0ZmamlJdXZ1W\nDvKanZ1VRUVFRjmXy2W/cQTYTQYGBtTW1iZp+W056YSF73MUk3A4nPEdnf4Op51jt1s9CH2ze5R8\n3b/s+kSdGzkUq7q6OvtGTloe+u5wOOR2u2n3KCrRaFRNTU1rtieTyTXbnE4n89Sx66STlGg0qmg0\nqsHBQX388ceSuI9BcfH7/aqvr9fAwIBCoZACgYAk2jmKz2b3KPm6f9n1Q9+5kUMx279/v/3zyMiI\n+vr6JNHuUTzSbXblnK+08vJyJRKJNeWZ04jdZnZ2VslkUoZhyO12q7a2Vs3Nzbp27Rrf5ygqfr9f\ni4uLikQimp6eVm1trSTuW1B8NrtHydf9y67vUedGDqUgFAqpqalJLS0tkmj3KB6RSETxeFzj4+MK\nhUL2YkPz8/P2Dd5Ki4uL9oKKwG5hGIbKy8vtuYlOp1OmaWp+fp7vcxSNVCql/v5+dXR0aGJiQu3t\n7XrmmWe0tLREO8eut3LqhqRN71Hydf+y6xN1buRQ7KLRqCoqKuwkXaLdo3g0NDSopaVFLS0t8vl8\n9rb9+/fL4/Fk9Las7JEEdhO3271uj6LE9zmKRyQS0SOPPGJ/9vl88vl8un79umpra9fM8aWdYzdZ\n3X43u0fJ1/3Lrh/6zo0ciln61WzHjh2TtNyz/sQTT9DuUXRSqZTGxsbkcDg0PDysQCAgt9utoaEh\njY6O2mszpFcPBnYTwzDk8XjsFX9N01RlZaU9vYnvcxQDwzA0OTlp37OkHThwQGVlZVpaWrK30c6x\nW6RflexwOPTyyy/L6/Wqrq5Okja9R8nH/UtRvEd9fn5ekUjEvhB+v59/+Nj1TNNUfX29PdTGsiy5\nXC699dZbkmj3ALCbxONxjY2NyTAMxWIx+2GUxPc5isf09LRM07Tnn3u9XvuBFO0c2JqiSNQBAAAA\nACgWu36OOgAAAAAAxYREHQAAAACAAkKiDgAAAABAASFRBwAAAACggJCoAwAAAABQQEjUAQAAHa0v\n2wAADR5JREFUAAAoICTqAAAAAAAUEBJ1AAAAAAAKCIk6AAAAAAAFhEQdALCuSCSi5uZmHT9+XMeO\nHVNvb6+SyaTq6+u1tLS00+HZBgYGdOjQIVVXV2t8fPyunDMcDm/7XKZp6tChQ5qens7YHo1GM65v\nT0+P/fetLruVc/X39+vQoUPr7k+lUgoGg2ptbVVbW5ui0WhOZbaqtbVV1dXV2r9//7aPVQhW1520\ncT3fLcFgUKZp7si5AQC5I1EHAKwRiUR07tw5/epXv9LExISmp6fl9Xp19OhRxeNxJRKJnQ7R1tnZ\nqd/85jd37XxjY2OanJxUS0vLto5TUVGhioqKNduvXr2akVj19fVpaGhIDodjy+eYm5tTfX29fvKT\nn2h0dHTdY6RSKTU3N+uRRx7RlStX1NHRoWeeeSYjEc+mTC6uXLkin8+3rWMUktV1J21cz3dLZ2en\nWltbC+rhGgDg9kjUAQBrjIyMyO/368EHH7S3NTQ06MKFCzsY1cacTuddOU8ymdTg4KAuXry47WM5\nnU5NT0/r2LFjGdvXS35dLpcsy9ryOTwej65du6a33npLhmHI5XKtKfPrX/9aDofDfvDg8Xjk9Xo1\nMDCwpTJYv+42que7xTAMeb1ePf/88ztyfgBAbkjUAQBrmKapSCSyZntDQ4MMw1AqldqBqHbe2bNn\ndeDAAZWVld2R4/f399+xa7vRw4zx8XF5PJ6MbV6vV3Nzc4rH41mXKXV3su62y+/3KxQKUVcAsIt8\nZacDAAAUHo/Ho3A4rPr6evn9fjtBl5aHK68cytvT02MPh0+lUvL7/Wpvb5e0PH88FAopmUyqr69P\nMzMzikajcrvd6urqktvtVm9vryKRiDwej4aGhuzzhEIhDQwMKJlMqrOzU6+99pri8bgMw9CFCxfW\nJI7rGR4e1uTkpCoqKuRwOHTu3Dn7+HNzcxoYGJDD4ZBlWXI6nXr44YfV1ta24fGmp6cVCAQyto2M\njNg9y+m/PRgMam5uTjU1Ners7LSvk2ma6urq0gcffKCpqSklk0lduHBBLS0tGhgYsOcxnz17VhUV\nFfJ6vWviSV9Tl8ulQCCwraHjqVRKyWRyTU97eXm5fY1cLtdty7jd7k3Pk66Hr3/96yorK9PFixfX\nPDiIRqPq7+/Xhx9+qJqaGg0NDdllsqmrjep6ZRt85ZVXZJqmpqamJElut1uhUEiS1NjYqBdffFHh\ncFjd3d1KJpPy+/06f/68pNu38/Xqbr16zua6jIyM6PLly0omkxoaGtLMzIympqbWrfNsrk3638rY\n2Jg6Ojo2rSsAQIGwAABYJZlMWs3NzVZ1dbVVVVVlVVVVWQcPHrS6u7uthYUFu9zPfvYzq76+3v4c\niUSsqqoqKxwOr9l26NAhKxqNWqlUynryySetqqoqq76+3pqfn7dM07QOHjyYcazVvzs/P29ZlmX1\n9/dbVVVVlmmadrmFhQWrqqrKCoVC9rbnn3/eOnTokJVKpSzLsqyxsTHr4MGD9uejR4/aP6dSKau+\nvt4aGRnZ8Jqsd4607u5uq7q62j6eZVlWVVWVNTAwYH8eHh62BgcHNz3e1NSUVV1dbf+tabFYzKqq\nqrKam5utUChkpVIpq7u726qqqrLm5uY2jHmlJ598cs31TR93ZZzpOKqqqqyRkZGsymymu7s747zd\n3d3W0aNHMz5XVVVZPT09G8Z6u7q6XV2n29HAwIAViUQy6mu9uuvv78+oq2za+UZ1t1G7ud11SZ+j\nurp60zrPth0fPXrUam1tXbMdAFCYGPoOAFjD6XRqYmJCV65ckd/vV2VlpVKplEKhkOrr6+0htOne\ny7SamhpJylhQK90T6/f7dfjwYZWVlemJJ56Qw+FQIBBQdXW13G63Ghsb1yzEtfJ3q6urJUmnTp2S\ntNwbuZFUKqXR0VGdPHnSHqbe2NioZDKpsbExO8bXXntNqVRKZWVlOn/+vN1LvJ65uTk5HI5153mf\nOHFClmVpcnJSkuxpA+neWkl67bXXdPLkyQ2Pv5K1wXz0AwcOqKWlRWVlZTpx4kTGubYjmUzmpcxq\npmkqFArZsUrL18o0zYxV8x0OR8a1OXXqlBYWFuxe6s3qKpu6TotEIqqrq1MgENDQ0JDKysoUCARk\nWZZefvnljHIr48mmnadtVHdbvS4r2/5mdZ5tO3Y6naz+DgC7CIk6ACBDKpWyh3LX1dXp/Pnzmp6e\n1rVr1xQIBORwOOwkua+vT+FwWNFoVAMDAzp9+rQcDse6q8LX1tbaP6eHn68cMl1ZWSlJ665OvfJ3\nnU6nysvLNTs7u+HfkN43NjamtrY2tba26umnn1ZlZaWdrDQ2Nqqnp0cHDx5UfX29ZmZm1NTUlN1F\nWsXj8cjj8djXZWxsTBcuXFAymVQ0GpVpmvbw5u1IJ4jpc0ra1gr8G81bX1xclMPhkGEYWZXZSPrh\nxsp6TpefmZnJKLty4cL033b9+nVJm9fVZnW9sLCQcQ6v12vHkF7cLb3YWvqhytzc3Jp1CLbSzrOx\nletyuzrPth0X6vx5AMD6mKMOAMiQSCQUCoXsudVpbrdbHR0dWlhYsJOjqakpDQ4O6sSJE/rRj36k\nU6dO6eDBg1mf6069tird+xsIBDZ8jdqFCxfk9/s1NTWlaDSq0dFRzc/Pa3R0dN3yHo9HlmVpcXFx\n3f0nTpxQb2+votGo4vG4WlpadPnyZV29elWGYcjv92/57zBNMyMRXq83fzsMw1B5efmavyl9/Sor\nK29bZrNEXVrbw7w68d/oeq60WV1lU9dp6YdBqwUCAbW2tiocDmtmZkY//elPM/bn0s5X191qt7su\naber82zb8eLiov2gAgBQ+OhRBwCskUwmNTIysu4+l8ul2tpamaap06dPq7GxUW1tbdq/f/8de796\numc1HVsymdSBAwc2LJ9OkFb3uqeHHJumqaeeeipjxMCLL7646TDy9DFX99KmNTU1ybIsBYNBe4iy\n3+9XOBzO+vVc5eXlsizLvo4DAwN3fKVun8+35rVif/3rX+XxeOzpBpuV2b9//4bHTvcArxxyHYvF\nJElHjhyR9GVP78qRFOnyDz/88G3r6nZ1nba6B3uluro6ud1uDQwMKBaLZfxN2bbzrdRdNtclG1tp\nx8lkUg8//HDWxwYA7CwSdQBAhnQv9+DgYMY8Ymk5mQiHwxnzd+fm5iQtJwK9vb1yOBwyTdNOwNZL\naizLWtOjuNnc3pWvlkqvcJ1ecTt97pU8Ho8aGhoUCoUUDoclLSc1wWDQTvDn5uYyeh2dTudtexzb\n29s3TOadTqcaGhqUSqXsocfpXvTNjrsy9nQiOTc3J9M0FY/H5Xa78/IAJJlMrtt7nZ7zn67rWCym\na9euqaura0tl1mMYhnw+X8Zc8bGxMT300EN273cikVB5ebn6+/vtMiMjI6qtrVV9fb2kzesqm7pO\nt7fNhn8HAgGZppkxb3yl27XzjeoubWU9Z3tdspFNO45EInI4HBkPi/r7+1VdXb3uVBMAwM7bc+7c\nuXM7HQQAoHB8+umnCofDev311/X6669rdHRUb7zxhiYnJ/XOO+/opZde0oMPPiiXy6Vbt27pjTfe\n0MjIiN599111dXXJ6XQqHA7ro48+0qeffqrnnntOqVRKsVhMX/3qVxWLxXTp0iWlUilFIhF961vf\n0h//+Ef94Q9/0K1btzQzM2MPuf7HP/6hsbExnT17VsPDw/rFL36hW7du6fLly/rOd74jSQqHw+rv\n79fNmzf1l7/8Rffcc4++//3vq6mpSbdu3dLvf/97Xbp0SZFIRGfOnNH3vvc9JZNJvfPOO9q3b58u\nXbqk3/72t5qfn7/tgnJer1cvvPCCHnnkEX3zm99cs7+iokL/+c9/9OMf/1iSdP/99+vdd9/VyZMn\nM8pHo1F1d3fr5s2bmp2dVTKZlNfrlcvlsv/m9N/1zjvvrLmGDodDp06d0s2bN3Xjxg3791eLRqMK\nBoMaGRnRhx9+aF+PqakpHTlyROXl5br//vvV1NSkq1evanx8XG+++ab6+vp0+PBh+zjZlNnIY489\npk8//VQXL160F4d7+eWXdd9990lafgjzyiuv6ObNm7p06ZJ+97vfad++ferv79d9992XVV1tVtfh\ncDjj+n300UfrXquamhr9/ve/1y9/+cuM7dm088cee2zdurtx48a69Xy767I65o3qvKamJqt2PDAw\noB/+8IdqaGiwt83PzysWi+mpp56y6wIAUDgcVjbLkwIAsAPm5ubU3Nysl156Kauh43dDNBrVyMjI\nhnPZgUISiUQ0ODioiYmJnQ4FALAFLCYHAChYhfgsua6uTtLyMPDbLV4G7KRUKqVwOEySDgC7ED3q\nAICCFA6H7QW50qumt7W17XRYAAAAdxyJOgAAAAAABYRV3wEAAAAAKCAk6gAAAAAAFBASdQAAAAAA\nCgiJOgAAAAAABYREHQAAAACAAkKiDgAAAABAASFRBwAAAACggJCoAwAAAABQQEjUAQAAAAAoIP8f\n4TID/60P82gAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1165c4f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = accidents   \n",
    "\n",
    "n = 100                                               # number of observations\n",
    "N_test = 100                                          # number of samples with n observations\n",
    "means = np.array([0.0] * N_test)                      # samples' mean\n",
    "s = np.array([0.0] * N_test)                          # samples' std\n",
    "ci = np.array([[0.0,0.0]] * N_test)\n",
    "tm = df.mean()                                        # \"true\" mean\n",
    "\n",
    "for i in range(N_test):                               # sample generation and CI computation\n",
    "    rows = np.random.choice(df.index.values, n)\n",
    "    sampled_df = df.ix[rows]\n",
    "    means[i] = sampled_df.mean()\n",
    "    s[i] = sampled_df.std()\n",
    "    ci[i] = means[i] + np.array([-s[i] *1.96/np.sqrt(n), s[i]*1.96/np.sqrt(n)])    \n",
    "\n",
    "out1 = ci[:,0] > tm                                   # CI that do not contain the \"true\" mean\n",
    "out2 = ci[:,1] < tm\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 5))\n",
    "ind = np.arange(1, N_test+1)\n",
    "ax.axhline(y = tm, \n",
    "           xmin = 0, \n",
    "           xmax = N_test+1, \n",
    "           color = [0, 0, 0])\n",
    "ci = np.transpose(ci)\n",
    "ax.plot([ind,ind], \n",
    "        ci, \n",
    "        color = '0.75', \n",
    "        marker = '_', \n",
    "        ms = 0, \n",
    "        linewidth = 3)\n",
    "ax.plot([ind[out1],ind[out1]], \n",
    "        ci[:, out1], \n",
    "        color = [1, 0, 0, 0.8], \n",
    "        marker = '_', \n",
    "        ms = 0, \n",
    "        linewidth = 3)\n",
    "ax.plot([ind[out2],ind[out2]], \n",
    "        ci[:, out2], \n",
    "        color = [1, 0, 0, 0.8], \n",
    "        marker = '_',\n",
    "        ms = 0, \n",
    "        linewidth = 3)\n",
    "ax.plot(ind, \n",
    "        means, \n",
    "        color = [0, .8, .2, .8], \n",
    "        marker = '.',\n",
    "        ms = 10, \n",
    "        linestyle = '')\n",
    "ax.set_ylabel(\"Confidence interval for the samples' mean estimate\",\n",
    "              fontsize = 12)\n",
    "ax.set_xlabel('Samples (with %d observations). '  %n, \n",
    "              fontsize = 12)\n",
    "plt.savefig(\"confidence.png\",\n",
    "            dpi = 300, \n",
    "            bbox_inches = 'tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis testing\n",
    "\n",
    "To give a measure of variability of our estimates is a way of producing a\n",
    "statistical proposition about the population, but not the only one. R.A.Fisher\n",
    "(1890-1962) proposed an alternative, known as *hypothesis testing*, that is\n",
    "based on the concept of *statistical significance*.\n",
    "\n",
    "Let's suppose that a deeper analysis of traffic accidents in Barcelona results\n",
    "in a difference between 2010 and 2013. Of course, the diference could be caused only by chance, because of the variability of both estimates. But it\n",
    "could also be the case that traffic conditions are very diferent in Barcelona\n",
    "during these two periods and, because of this, data from these two periods can\n",
    "be considered as belonging to two diferent populations. Then, the relevant\n",
    "question is: Are the observed effects real or not?\n",
    "\n",
    "The process of determining the statistical significance of an effect is called\n",
    "**hypothesis testing**. This process starts by simplifying the options into two\n",
    "competing hypotheses:\n",
    "\n",
    "+ $H_0$: The mean number of daily traffic accidents is the same in 2013 and 2010 (there is only one population, one true mean, and 2010 and 2013 are just different samples from the same population).\n",
    "\n",
    "+ $H_A$: The mean number of daily traffic accidents for 2010 and for 2013 is different (2010 and 2013 are two samples from two different populations).\n",
    "\n",
    "We call $H_0$ the *null hypothesis* and it represents a skeptical point of view:\n",
    "the effect we have observed is due to chance (due to the specific sample bias).\n",
    "\n",
    "$H_A$ is the *alternative hypothesis* and it represents the other point of view:\n",
    "the effect is real.\n",
    "\n",
    "The general rule of frequentist hypothesis testing is: We will not discard $H_0$\n",
    "(and hence we will not consider $H_A$) unless the observed effect is implausible\n",
    "under $H_0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing hypotheses using confidence intervals.\n",
    "\n",
    "We can use the concept represented by confidence intervals to measure the\n",
    "plausibility of an hypothesis.\n",
    "\n",
    "We can illustrate the evaluation of the hypotheses setup by comparing the\n",
    "mean rate of traffic accidents in Barcelona during 2010 and 2013 using a point estimate from the 2013 sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2010: Mean 24.8109589041\n",
      "2013: Mean 25.9095890411\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv(\"files/ch04/ACCIDENTS_GU_BCN_2010.csv\", encoding='latin-1')\n",
    "#Create a new column which is the date\n",
    "data['Date'] = data['Dia de mes'].apply(lambda x : str(x)) + '-' +  \\\n",
    "               data['Mes de any'].apply(lambda x : str(x))\n",
    "data2 = data['Date']\n",
    "counts2010 =data['Date'].value_counts()\n",
    "print '2010: Mean', counts2010.mean()\n",
    "\n",
    "data = pd.read_csv(\"files/ch04/ACCIDENTS_GU_BCN_2013.csv\", encoding='latin-1')\n",
    "#Create a new column which is the date\n",
    "data['Date'] = data['Dia de mes'].apply(lambda x : str(x)) + '-' +  \\\n",
    "               data['Mes de any'].apply(lambda x : str(x))\n",
    "data2 = data['Date']\n",
    "counts2013 = data['Date'].value_counts()\n",
    "print '2013: Mean', counts2013.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This estimate suggests that during 2013 the mean rate of\n",
    "traffic accidents in Barcelona **was higher** than 2010. But is this effect statistically significant?\n",
    "\n",
    "Based on our sample, the 95% confidence interval for the mean rate of\n",
    "traffic accidents in Barcelona during 2013 can be calculated as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2010 accident rate estimate: 24.8109589041\n",
      "2013 accident rate estimate: 25.9095890411\n",
      "CI for 2013: [24.975156065800284, 26.844022016391499]\n"
     ]
    }
   ],
   "source": [
    "n = len(counts2013)\n",
    "mean = counts2013.mean()\n",
    "s = counts2013.std()\n",
    "ci = [mean - s*1.96/np.sqrt(n),  mean + s*1.96/np.sqrt(n)] \n",
    "print '2010 accident rate estimate:', counts2010.mean()\n",
    "print '2013 accident rate estimate:', counts2013.mean()\n",
    "print 'CI for 2013:',ci"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because 2010 accident rate estimate does not fall in the range of plausible values of 2013, we say the\n",
    "alternative hypothesis cannot be discarted. That is, it can not be discarted that during 2013 the mean rate of traffic accidents in Barcelona was higher than during 2010."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing hypotheses using P-values.\n",
    "\n",
    "A more advanced notion of statistical significance was developed by R.A.Fisher\n",
    "in the 1920's when looking for a test to decide whether variation in crop yields\n",
    "were due to some specific intervention or merely randon factors beyond experimental control.\n",
    "Fisher first assumed that fertilizer caused no difference (null hypothesis)\n",
    "and then calculated $P$, the probability that an observed yield in a fertilized\n",
    "field would occur if fertilizer had no real effect. This probability is called\n",
    "p-value.\n",
    "\n",
    "The p-value is the probability of observing data at least as favorable to\n",
    "the alternative hypothesis as our current data set, if the null hypothesis is\n",
    "true.\n",
    "\n",
    "To apply a test of hypotheses to our problem, the first step is to quantify the size of the apparent effect by choosing a test statistic. In our case, the apparent effect is a difference in accident\n",
    "rates, so a natural choice for the test statistic is the difference in means\n",
    "between the two periods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "m: 365 n: 365\n",
      "mean difference:  1.09863013699\n"
     ]
    }
   ],
   "source": [
    "m = len(counts2010)\n",
    "n = len(counts2013)\n",
    "p = (counts2013.mean() - counts2010.mean())\n",
    "print 'm:',m, 'n:', n\n",
    "print 'mean difference: ', p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second step is to define a null hypothesis, which is a model of the\n",
    "system based on the assumption that the apparent effect is not real. In\n",
    "our case the null hypothesis is that there is no diference between the two\n",
    "periods. The alternative hypothesis is that during 2013 the mean rate of traffic accidents in Barcelona was higher than 2010.\n",
    "\n",
    "The third step is to compute a p-value, which is the probability of seeing\n",
    "the apparent effect if the null hypothesis is true. In our case, we would\n",
    "compute the absolute difference in means, then compute the probability\n",
    "of seeing a difference as big, or bigger, under the null hypothesis.\n",
    "\n",
    "Usually, if P is less than 0.05 (the chance of a \n",
    "fluke is less than 5%) the\n",
    "result is declared statistically significant.\n",
    "\n",
    "To approximate the p-value, we can follow the following procedure:\n",
    "1. Pool the distributions, generate samples with size $n$ and compute the difference in the mean.\n",
    "2. Generate samples with size $n$ and compute the difference in the mean.\n",
    "3. Count how many differences are larger than the observed one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1165103d0>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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V20ql0rIT263VthLgJckwDKVSKc3Nza06vN40Te3evXs9LwHY1j777DPduXPH7jKATcVx\nDrtsp1F/pmnK4/HYXQawLpzP0ew+//zzde/D9hDf2dmpiYmJqm2FQkGGYdTVNpVK6YUXXtD7778v\naf4K/cL751diGIb27t27jlcAbG937tzRI488YncZwKbiOIddlhslaBfDMPjvAI7H+RzN7u7du0qn\n0+vah+0h3u/3Vw2dLxaLMgzDuqqeSqXkdrtlGMaqbUulkk6fPm09Nj09ra6uLia5AwAAAAA0DdtD\nvCRFIhGNj4+rra1NyWRSkUjEeuzy5cs6ePCg+vv7V23rdrvl9/s1Pj4ut9st0zSr9gMAAAAAgNNt\nixDv8/nk8/kkSd3d3VWPLQ7iq7UNBAIKBAKbWCkAAAAAAPaxfYk5AAAAAABQG0I8AAAAAAAOQYgH\nAAAAAMAhCPEAAAAAADjEtpjYDgAAoFGZTEa5XM6Wvte71i8AAPUixAMAAMfKZDLav9+ne/fu2l0K\nAABbghAPAAAcK5fLfRng35Xks6GC65KGbOgXALBTEeIBAEAT8El6zIZ+GU4PANhaTGwHAAAAAIBD\nEOIBAAAAAHAIQjwAAAAAAA5BiAcAAAAAwCEI8QAAAAAAOASz0wOAw2QyGeVyOVtr2Ldvn9rb222t\nAUC1dNremfI5LwDA1iDEA4CDZDIZ7d/v+3JdbPvs2bNXn3yS5gM7sC38WtIuHT9+3NYqOC8AwNYg\nxAOAg+RyuS8D/LuaXxfbDmndu3dcuVyOD+vAtpCX9IU4LwDAzkCIBwBH8kl6zO4iAGwrnBcAYCdg\nYjsAAAAAAByCEA8AAAAAgEMQ4gEAAAAAcAhCPAAAAAAADkGIBwAAAADAIQjxAAAAAAA4BCEeAAAA\nAACHIMQDAAAAAOAQhHgAAAAAAByCEA8AAAAAgEMQ4gEAAAAAcIhtEeJN09TY2JhisZjGx8dVKpXW\n3TYcDmtubm6zSgYAAAAAYMs9YHcBkhQKhTQ1NSVJKpVKCoVCunr1asNtE4mEYrGYTp06pZaWls0t\nHgAAAACALWL7lfhUKiWXy2X97na7lUwmlc1mG2pbuTLv9Xo3sWoAAAAAALae7SE+mUyqtbW1apvX\n65Vpmg21nZ6eViAQULlc3pyCAQAAAACwie0hvlgsLtnmdruXvdd9rbaJREJHjhzZ+CIBAAAAANgG\nGg7xw8PDG1KAx+NRPp+v2lYqleR2u+tqWwny3AMPAAAAAGhWDU9sNzExIZfLpcHBwXUF587OTk1M\nTFRtKxQKMgyjrrbxeFzFYlGTk5Mql8syTVOxWExdXV3y+Xwr9m+apnbv3t1w/cB299lnn+nOnTt2\nl4ENstytRnYxTVMej8fuMiRxnO9k2+m/CWyv8wKcifM5mt3nn3++7n00HOINw1BbW5u+//3vq729\nXX19fQoEAnXvx+/3Vw2dLxaL1r6l+cns3G63DMNYtW2lfUU4HFZ3d/eS7cu9jr1799ZdN+AUd+7c\n0SOPPGJ3Gdggy91WZBfDMLbNscVxvnNtp/8msL3OC3Amzudodnfv3lU6nV7XPhoeTn/x4kUNDAxo\nampKZ8+e1Xvvvafnn39ek5OTde8rEolofHxcsVhMV65cUSQSsR67fPmyZmZmamorzQ+vHxsbk8vl\n0pUrV5ad5R4AAAAAACdq+Er8gQMHrJ+/8Y1vqL29XdPT0xoaGtJPf/pTffe731V/f39N+/L5fNaQ\n9+7u7qrHFof01dpK8xPdDQwMaGBgoK7XAwAAAADAdtfwlfhQKKR0Oq0zZ87o8ccf12uvvaZAIKCp\nqSldu3ZNDz30kJ5//nmuhAMAAAAAsEEavhJ/8+ZNxeNxlctlBYNBnTx5smoyup6eHj366KMaHh7W\n+Pj4hhQLAAAAAMBO1nCIl6SzZ8+qr69v2eXgSqWS+vv7VSgU1tMFAAAAAAD4UsMhvpb7zsvlsk6d\nOtVoFwAAAAAAYIGGQ/zg4OCqj7vdbt24caPR3QMAAAAAgEUaDvHZbFbDw8MyDEPnz5+XJEWjUc3O\nzurChQsbVR8AbCuZTEa5XM62/te7rigAAACcreEQHw6HlUwmlUwmrRAfDAY1Njam4eFhgjyAppPJ\nZLR/v0/37t21uxQAAADsUA2HeJfLpffff3/J9r6+Pj3xxBOEeABNJ5fLfRng35Xks6mK65KGbOob\nAAAAdms4xP/ud7/T3NycWlpaqrbH43F5PJ51FwYA25dP0mM29c1wenzF7ts7JGnfvn1qb2+3tQYA\nAHaShkP8kSNH9Oyzz6qvr0+dnZ0qFApKJpOKRqMKBoMbWSMAAFhku9zesWfPXn3ySZogDwDAFmk4\nxJ88eVKmaerNN9+Uy+VSuVyWJHV1dTGUHgCATbY9bu9I696948rlcoR4AAC2SMMhXpIuXryokydP\nKpVKqVAoqLOzU36/f6NqAwBgRQuHkpumqWKxuKX9b59h5Hbe3gEAALbaukK8JBmGIcMwqra99tpr\nOnv27Hp3DQDAsrbDUHKGkQMAADusK8Sn02nF43Hl8/mq7dFolBAPANg09g8lZxg5AACwR8MhPhqN\nKhwOL/uYy+VquCAAAGrHUHIAALCzNBzir1y5omAwqGPHji25D/7o0aPrLgwAAAAAAFRrOMQXCgW9\n/PLLS9aJl6RLly6tqygAAAAAALDUrkaf2NPTo/fee2/Zx2ZnZxsuCAAAAAAALK/hK/FPP/20zpw5\no9nZWT366KPyer3WY1euXFFvb++GFAgAAAAAAOY1HOJDoZAk6ac//emSx5jYDgAAAACAjddwiPd4\nPIpEIlVX4CUpn89reHh43YUBAAAAAIBqDYf4U6dOKRAILPvY4OBgwwUBAAAAAIDlNTyx3cDAgObm\n5jQ+Pm5deY9Go0qn0+ru7t6wAgEAAAAAwLyGr8Sbpqnnn39exWJR7e3tkqRAIKBQKKSXX35ZTz31\n1IYVCQAAAAAA1nEl/vz58xocHNT7779vrRVvGIYikYhGRkY2rEAAAAAAADCv4Svx5XJZwWBQktTa\n2mptNwxD2Wx2/ZUBAAAAAIAqDYf4fD6vubk5tbS0VC0pF4vFlsxYDwBAM0qn0zuybwAAYJ+GQ/yR\nI0f07LPP6tSpUzJNU5OTk0omk4pGoxoYGNjIGgEA2GZ+LWmXjh8/bnchAABgh2k4xJ88eVL5fN66\n/31oaEiS1N3drbNnz25MdQAAbEt5SV9IeleSz6YarksasqlvAABgl4ZDvCSdO3dOL730kpLJpIrF\nogzDkN/v36jaAADY5nySHrOpb4bTAwCwE60rxEuS2+1WIBCo2tbf36/x8fGa92GapmKxmDUpXjAY\nlNvtrrttIpFQsVhUoVDQzZs3dfr0ab5UAAAAAAA0jYZD/OTk5LLbi8Wi4vF4XfsKhUKampqSJJVK\nJYVCIV29erXuti+++KJ+/vOfq6Ojw2p748aNumoBAAAAAGC7ajjEV+6BX2jhLPW1SqVSVc9zu91K\nJpPKZrNqa2urq+0vfvGLqud4PJ666wEAAAAAYLtqOMR7PB7967/+qzWUPZvNKpPJaGJiQj/+8Y9r\n3k8ymaxaZ16SvF6vTNNcEuLXaruwfSaTUSQSqfdlAQAAAA3JZDLK5XK21rBv3z61t7fbWgOAzdVw\niO/p6am639wwDAUCAR05ckThcFivv/56TfspFotLtrndbpVKpYbamqapiYkJpdPpZdsDAAAAGy2T\nyWj/fp/u3btrax179uzVJ5+kCfJAE2s4xF+8eHHZ7R6PR6Zp1rwfj8ejfD5fta1UKi07sV0tbQ3D\n0ODgoMbGxvTCCy/oP//zP9XS0rJi/6Zpavfu3TXXCzjNZ599pjt37thdRlOo59y2E5imadttS/wt\ntheOBVTYeSzYbXZ29ssAb+fSk2ndu3dcH374of7whz/YVMP68LkFze7zzz9f9z4aDvGJRGLZ7fF4\nfNmr6Cvp7OzUxMRE1bZCoSDDMOpqW7kCPzg4KGl+vfrR0VF99NFHS2bPX8gwDO3du7fmegGnuXPn\njh555BG7y2gKjO6pZhiGbccWf4vthWMBFXYeC3b76li0c+nJeU7+O/C5Bc3u7t27SqfXt0xswyH+\nxRdfXDKRXblclsvlqutedL/fXxX6K+vNV+5vT6VScrvd1hr0K7VNJBJVXyyYpimv16sDBw40+hIB\nAAAAANhW1jWx3auvvrpkW2dn54prvK8kEolofHxcbW1tSiaTVV8CXL58WQcPHlR/f/+qbQOBgI4d\nO6bJyUmVy2XF43G9/fbbqw6lBwAAAADASRoO8cFgUN3d3RtShM/nk883f+/Q4n0uvqq/Wtve3t6q\n+gAAAAAAaCa7Gn1i5d7ztZw5c6bRLgAAAAAAwAINX4k/evSo5ubm1hw6n0qlGu0CAAAAAAAs0HCI\nn5qa0uOPP65MJmPNJF9Z5mXh+vEAAADAZstkMsrlcrb1v97ZpgGgVg2H+OHhYZ07d27JvecjIyP6\nkz/5E2siulAotL4KAQAAgFVkMhnt3+/7cp12AGhuDYf4bDarCxcuLNl+7tw5HT582Arxtd47DwAA\nADQil8t9GeDf1fw67Xa4LmnIpr4B7CQNh/jf/e53mpubW7KEm2mayufz1u+VofYAAADA5vJJesym\nvhlOD2BrNBzijxw5omeffVZ9fX1WUM9kMopGozpy5MiGFQgAAAAAAOY1HOJPnjypfD6vN998s2p7\nV1fXssPsAQAAAADA+jQc4qX5+99feuklJZNJFYtF+f1+hs8DAAAAALBJdq3nyXNzc4pGo5qenlZ3\nd7cSiQTLawAAAAAAsEkavhJvmqaef/55FYtFtbe3S5ICgYBCoZBefvllPfXUUxtWJAAAAAAAWEeI\nP3/+vAYHB9XT06MXXnhB0vxM9JFIRGfOnNG1a9c2qkYAsGQyGeVyOVv6ZqQRAAAA7NZwiC+XywoG\ng5Kk1tZWa7thGMpms+uvDAAWyWQy2r/f9+VawAAAAMDO03CIz+fz1jrxLpfL2h6LxeT1ejekOABY\nKJfLfRng39X8WsBb7bqkIRv6BQAAAOate534U6dOyTRNTU5OKplMKhqNamBgYCNrBIBFfJIes6Ff\nhtMDAADAXuteJ35kZESSNDQ0f3Wqu7tbZ8+e3ZjqAAAAAACAZV3rxP/N3/xN1TrxhmHI7/dvVG0A\nAAAAAGCBhkP8iRMnlEgkFIlEdPjw4Y2sCQAAAAAALGPXep7c29srn8+OyaUAAAAAANh5Gg7xPT09\nOnLkiAzDWPLYa6+9tq6iAAAAAADAUg0PpzcMQ/F4XKOjo+rq6lJ7e7va2tpUKpUUi8WY3A4AgB0i\nnbZv5QY7+wYAwA4Nh/gXX3zR+nl2dlaS5HK5VC6Xq9aNBwAAzerXknbp+PHjdhcCAMCO0XCI93g8\nikQiS7aXy2UNDw+vqygAAOAEeUlfSHpXkl1z5FyXNGRT3wAAbL2GQ3wwGFQgEFj2scHBwYYLAgAA\nTuOT9JhNfTOcHgCws9Qc4icnJ1UsFpXP51UsFnXhwoUV23Z3d29IcQAAAAAA4Cs1h/ihoSG5XC71\n9vbqyJEjm1kTAAAAAABYRl3D6SORiA4fPrxZtQAAAAAAgFXUHOI9Ho8V4EOh0JIZ6Pv6+la8Rx4A\nAAAAAKzfrlober1e6+fTp0+rUCgoFoupWCyqr69PnZ2d1uPZbHZjqwQAAAAAAPVdia/w+/166623\n1NHRoatXry5pGwqFdO3atZqLME1TsVhMhmEom80qGAzK7XbX3TaRSFhr1n/00UcaHByUYRg11wEA\nAAAAwHZWc4jPZrP69NNPVS6XrW3t7e1LthWLxbqvxIdCIU1NTUmSSqWSQqHQsl8OrNa2VCppdnZW\nAwMDkqRYLKYTJ07oxo0bddUCAAAAAMB2VXOILxQKeu6555ZsX25bPVKpVNX99W63W8lkUtlsVm1t\nbTW3NU1Tr732mhXiu7q6ZJrmsvsBAAAAAMCJ6pqd3ufzqbW1ddU2+Xxe6XS65n0mk8kl+/R6vTJN\nc0n4Xq1tIBCwrtBL88PpXS4XAR5NI5PJKJfL1f080zRVLBY3pIZ9+/apvb19Q/YF56vnXN9MfQPA\ndmf3OZLPC8DmqjnEG4ZRFZJXc+jQoZoLWC5cuN1ulUqlutv6fD5r+9jYmC5evFhzHcB2lslktH+/\nT/fu3bULflJnAAAW/UlEQVS1jj179uqTT9L8j3nH+7WkXTp+/LjdhQAAqmyP8zOfF4DNVXOIP3ny\nZM07raetx+NRPp+v2lYqlZad2K7WttFoVEeOHFFvb++a/Zumqd27d9dcL2CH2dnZLwP8u5J8azXf\nJGndu3dcH374of7whz/YUoFpmrb0i8Xykr6QvcfjdUlDNvUNYCWmaVZNhryV/ULaHufn9X1e+Oyz\nz3Tnzp1NqAvYHj7//PN176PmEB8MBmveaT1tOzs7NTExUbWtUCgsO6t8LW0TiYRaW1utNe3XYhiG\n9u7dW3O9gB2+GoXik/SYnaXIMAw98sgjtvS9UbcFYKPYeTwynB7Yjuz6fwT/f1jMuZ8X7ty5Y9vn\nDGAr3L17d923vNS8Tvxm8fv9VUPni8WiDMOw7mVPpVLWt6trta0sL1cJ8NFoVHNzc1vyOgAAAAAA\n2Gx1TWy3WSKRiMbHx9XW1qZkMqlIJGI9dvnyZR08eFD9/f2rtjVNU88//7w1e325XJbX661rVAAA\nAAAAANvZtgjxPp/PmpSuu7u76rGFgX61toZh6OOPP97kSgEAAAAAsI/tw+kBAAAAAEBtCPEAAAAA\nADgEIR4AAAAAAIcgxAMAAAAA4BCEeAAAAAAAHIIQDwAAAACAQxDiAQAAAABwCEI8AAAAAAAOQYgH\nAAAAAMAhCPEAAAAAADgEIR4AAAAAAIcgxAMAAAAA4BCEeAAAAAAAHIIQDwAAAACAQxDiAQAAAABw\nCEI8AAAAAAAOQYgHAAAAAMAhCPEAAAAAADgEIR4AAAAAAIcgxAMAAAAA4BCEeAAAAAAAHIIQDwAA\nAACAQxDiAQAAAABwiAfsLgAAAADNIZ1O76h+AcAOhHgAAACs068l7dLx48ftLgQAmh4hHgAAAOuU\nl/SFpHcl+Wzo/7qkIRv6BYCtR4gHAADABvFJesyGfhlOD2Dn2BYh3jRNxWIxGYahbDarYDAot9vd\ncNtYLKbu7u6tKB0AAAAAgC2zLUJ8KBTS1NSUJKlUKikUCunq1at1t43FYioUCgqHw7p9+7ZaWlq2\n5gUAAAAAALAFbA/xqVRKLpfL+t3tdiuZTCqbzaqtra2utpWr78PDw1tTPLAD2TkDMLMPAwAAYKez\nPcQnk0m1trZWbfN6vTJNc0mIr7VtuVzevIKBHYuZhwEAAAC72R7ii8Xikm1ut1ulUmldbQFsNLtn\nHpaYfRgAAAA7ne0h3uPxKJ/PV20rlUrLTmxXT1sAm8WumYclZh8GAADATmd7iO/s7NTExETVtkKh\nIMMwGm678L75tZimqd27d9dRMbD1TNO0uwQAAICamaYpj8dT9/M+++wz3blzZxMqAraHzz//fN37\nsD3E+/3+quHwxWJRhmFY97inUim53W4ZhrFm24p67ok3DEN79+5d56sANtdyt5IAAABsV4Zh6JFH\nHqn7eXfu3GnoeYBT3L17d92TNdse4iUpEolofHxcbW1tSiaTikQi1mOXL1/WwYMH1d/fv2bbRCKh\n2dlZuVwuXb58WV1dXQoEAlv+egAAAAAA2AzbIsT7fD75fPMTZVWWiatYGNLXahsIBBQIBDQwMLCJ\n1QIAAAAAYI9ddhcAAAAAAABqsy2uxAMAAADARshkMsrlcrbWsG/fPrW3t9taA5oXIR4AAABAU8hk\nMtq/36d79+7aWseePXv1ySdpgjw2BSEeAAAAQFPI5XJfBvh3JflsqiKte/eOK5fLEeKxKQjxAAAA\nAJqMT9Jjtlaw3mXE1osh/c2LEA8AAAAAG+bXknbp+PHjtlbBkP7mRYgHAAAAgA2Tl/SFGNKPzUKI\nB2pg9yyndg/HAgAAQL0Y0s+Q/s1BiAfWsF1mOQUAAABqw5D+ZkaIB9awPWY5vS5pyKa+AQAA4CwM\n6W9mhHigZnYOiWI4PQAAAOpl/5B+bLxddhcAAAAAAABqQ4gHAAAAAMAhCPEAAAAAADgEIR4AAAAA\nAIcgxAMAAAAA4BDMTg8AAABgQ6XTja2sY5qmisXilvcLOAkhHgAAAMAG+bWkXTp+/LjdhQBNixAP\nAAAAYIPkJX0h6V3Nr1G+1a5LGrKhX2DrEOIBAAAAbDCfpMds6Jfh9Gh+TGwHAAAAAIBDEOIBAAAA\nAHAIhtPDETKZjHK5nC19M8spAAAAgO2CEI9tL5PJaP9+n+7du2t3KQAAAABgK0I8tr1cLvdlgGeW\nUwAAAAA7GyEeDsIspwAAAAB2Nia2AwAAAADAIQjxAAAAAAA4BMPpsaoPPvhAly9ftrWGubk5W/sH\nAAAA0Bg7V3rat2+f2tvbbet/sxDisar//b//Xjdu/Ld2737Ethr++MfbtvUNAAAAoBG/lrRLx48f\nt62CPXv26pNP0k0X5LdFiDdNU7FYTIZhKJvNKhgMyu121922nv2gNuVyWeXyc/rjHydtrGK3pC9s\n7B8AAABAffKa/wxv1wpTad27d1y5XI4QvxlCoZCmpqYkSaVSSaFQSFevXq27bT37AQAAAABsNrtW\nmGpetk9sl0ql5HK5rN/dbreSyaSy2WxdbevZDwAAAAAATmR7iE8mk2ptba3a5vV6ZZpmXW3r2Q8A\nAAAAAE5k+3D6YrG4ZJvb7VapVKqrbT37kaQvvpi/x/r3v/99vSXvKH/2Z3+m/ftNSRdsrOLbX/77\n/5FUtqH//0/Sfhv7p4btU4Pd/VPD9qnB7v6pYfvUYHf/1LA9+qeG7VOD3f1Tw/ap4f+VtF/lcll3\n7961of/lVfJnJY82wvYQ7/F4lM/nq7aVSqVlJ6RbrW09+5Gk+/fvS5J+9atfraP65vfDH/5f+uEP\n7a7i/7S5/6e//IcaqMHu/qlh+9Rgd//UsH1qsLt/atge/VPD9qnB7v6pYfvU8H9I+r8l2bvM3Uru\n37+vlpaWhp5re4jv7OzUxMRE1bZCoSDDMOpq6/V6a96PND/U/lvf+pYefPBB7dpl+10FAAAAAIAm\n98UXX+j+/fvyer0N78P2EO/3+6uGvBeLRRmGoba2Nknzk9m53W4ZhrFm29UeW+yBBx7QN7/5zc14\nSQAAAAAALKvRK/AVrnK5bNdNEpZ0Oq14PK62tjYlk0n19fVZ4TsUCungwYPq7+9fs+1qjwEAAAAA\n4HTbIsQDAAAAAIC1cTM4AAAAAAAOQYgHmkgsFluyzTRNjY2NKRaLaXx8fMVlFwEAAOwQDoc1Nzdn\n/c5nF2B1O244vWmaisViMgxD2WxWwWBwxWXoAKeIxWIqFAoKh8O6fft21WQZR48e1dTUlKT5yR9D\noZCuXr1qV6nAuiQSCc3OzkqSPvroIw0ODlqrkHB+R7NIJBIqFosqFAq6efOmTp8+Lb/fL4njHM0n\nkUjozJkzunbtmjWXFZ9d0CzC4bCi0ahcLpf8fr8uXbokn88naX3nc9tnp99qoVCIkwKaTnd3tyRp\neHi4ansqlZLL5bJ+d7vdSiaTymazTPoIxymVSpqdndXAwICk+S+vTpw4oRs3bkji/I7m8eKLL+rn\nP/+5Ojo6JM0f2xznaEaVK+wLl9riswuaycMPP6zbt29LWjoj/XrO5ztqOP1qJwWgGSweWJNMJtXa\n2lq1zev1yjTNrSwL2BDJZFKvvfaa9XtXV5dM01Q2m+X8jqbyi1/8wgrwkuTxeCTxOQbNZ3p6WoFA\noOrzC59d0EzK5bJaWlqWBPj1ns93VIjnpICdplgsLtnmdru5twyOFAgErG+spfnh9C6Xy1pWlPM7\nmsXCq42ZTEaRSEQSn2PQXBKJhI4cObJkO59d0Ezy+bxmZmaUSCQ0Ojpqna/Xez7fUcPpOSlgp/F4\nPMrn81XbSqUS90/CsSr3kUnS2NiYLl68KInzO5qPaZqamJhQOp22jm+OczSLyjG7+OqkxGcXNJdj\nx45ZX8x6vV5rCP16z+c76ko8JwU0u4XDciSps7NzSZtCoWBNBAY4VTQa1ZEjR9Tb2yuJ8zuaj2EY\nGhwcVCAQ0AsvvKC5uTmOczSNeDyubDaryclJRaNRa4KvdDrNZxc0lYUjqwzDUDqd3pDz+Y4K8ZwU\n0OwW3xPv9/urvtErFosyDIOJYeBoiURCra2tVoCXOL+jeZimqdHRUev37u5uFYtFffTRR+rs7Fxy\nnuc4hxN1d3ert7dXvb29CgaD1jafz8dnFzSNVCqlJ554wvp9YUBf7+eWHTWcnpMCmlVl2S2Xy6XL\nly+rq6tLgUBAkhSJRDQ+Pm7dN1y5txJwosrycocPH5Y0f0X+u9/9Lud3NI1sNqtEImH9bpqmvF6v\nDhw4oJaWlqq1tDnO4XSlUkkTExNyuVy6cuWKTp48qba2Nj67oCkYhqHTp09bv09PT6urq0stLS3r\n/tyy49aJT6fTisfj1kmhr6+P//kBgAOYpqlDhw5Zt42Uy2V5vV7dunVLEud3NI/JyUlJ88d4PB7X\nSy+9ZM1Wz3EOAM6RSCSUSqXkdrtlmqZOnz5tzQWxnvP5jgvxAAAAAAA41Y66Jx4AAAAAACcjxAMA\nAAAA4BCEeAAAAAAAHIIQDwAAAACAQxDiAQAAAABwCEI8AAAAAAAOQYgHAAAAAMAhCPEAAAAAADgE\nIR4AAAAAAIcgxAMAdqzR0VE98cQT6ujoUEdHh7LZbNXjY2Nj1mMdHR06fPjwkjab5cSJE+ro6JDP\n59uS/upRKpUUCoV04sQJHT16VOFweEv7N01TTzzxhGZmZpZ9PBaL6dChQ9bfbLMkEgnNzc1t2v4B\nAFgOIR4AsGMNDg7q/fffl9/vl8vl0okTJ6oeHxgY0O3bt+XxeHTs2DHNzMyora1tS2q7evWqgsHg\nlvRVrx/84Aeam5vT1atX1dXVpcnJyS0Ns62trWptbV3x8e7ubt24cUNdXV2bWsdPf/pTmaa5qX0A\nALAYIR4AAEl+v1+maWp4eLhqe0tLizo7O9Xd3W1TZdtLqVRSKpVST0+PJOmll17S1NSUWlpatqwG\nt9utmZmZTb3KXotEImFr/wCAnYkQDwDY8Vwuly5duqS2tjZFo9Elw7TdbrdNlW0/mUxGkuT1eiXN\nf8mxHYf8b7aRkRGVSiW7ywAA7EAP2F0AAAB2K5fLcrvdunr1qg4dOqRQKKQbN26sOHR+dHRU0WhU\nxWJRb731lgKBgMLhsKanp1UsFvXqq6+qt7e3qt3Fixd18+ZNJRIJtbW16dy5c2pra9Pw8LDi8bj8\nfr8ikYgMw1jSXyKR0MjIiD799FM9+uijikQiVV8sXLlyRe+9955aW1vlcrl0/vx5GYaxpE7TNDU9\nPS1pfrj+Sir7+8Y3vqGWlhZdunRJbrdbY2Njun79ulwul0ZHRzUxMaFIJLLiVfhwOKxsNqt8Pq9S\nqaS+vj4NDAys2Fe5XNaFCxes92Dh65KkCxcu6MqVK0ve54X7unLlilpbW1e9FWGl92tsbExvvvmm\nisWiIpGIbt68qenpaXm9Xp08edLa5+joqPVFzyuvvKLW1lZ1dXWpv79fkpRKpTQ6OiqXy2UdWwcP\nHrQeBwBgXcoAAOxw3/ve98qmaZbL5XJ5YmKivH///vKhQ4esx3/0ox+V4/F41XOmp6fLHR0dVdtn\nZ2fL+/fvL0ejUWtbPB4v79+/v/zEE0+UE4lEuVQqlb/3ve9ZfaTT6bJpmuXHH3+8qs9yuVweGhoq\n79+/vxwOh6tqXdjuJz/5SfmJJ54ol0olq/7HH3/c+r3S/+joaDkej5eHhobKHR0d1uOLDQ0NVe1/\naGio/Nxzzy15jTMzM6u+pz/84Q+r9lOpIxaLVe17Ye2PP/54+cSJE2s+lslklrzPP/nJT8odHR3l\nRCJRLpfL5ZGRkSV/x3rer46OjnI0Gi2XSiXr75BKpaz9VP7+6XR6yWt/7rnnrP2VSqXyoUOHymNj\nY6u+XwAA1Irh9AAALBAMBhUMBpXJZJbcH7+W5YbdV4ad9/X16amnnlJLS4u++93vyuVy6eTJk+ro\n6FBbW5t6enqWnSTN5XLp1KlT1u+nT5+WaZqamZlRqVTS+Pi4Tp06ZV0N7+npUbFY1MTERNV+4vG4\nAoGATp48ueLVc9M0FY1GdezYMWvbsWPHZJqmJicnq9qWy+VV34vKVe6KRx991OpjYV99fX1WLS6X\nS4ZhrPrYSsbHx9XV1aWnnnpK0vykhYvV8n4t/Hv19vaqpaXFej/i8fiSfS73PpimqevXr6tUKqml\npUUXLlyQx+NZ7e0CAKBmDKcHAGCRixcvKpFIKBqNbtgM552dndbPlTC6cLh+e3u7JGlubm5JwH7o\noYesn/1+v8rlsj766CPrS4OJiQnF43GVy2Xl83m1t7db965XVF6HYRgrhuFUKiWXy1VVV6XtzZs3\nq4aur+XixYuS5m8FuHnzprXvfD5f1dfC9+XWrVuS5peIW+mxleqWtOT2h8WvM5lMSqrt/ap86SDN\nv+eSrNrX0tPTo3A4rHA4LMMw1N3drZdeeqmm5wIAsBZCPAAAy1h4f/zCQLeaeteQX22ZNEkqFAqr\nPl4sFiVJJ0+eXDNgV74kWMviK8uNTuo3PT2t1157TceOHdNf/uVf6vTp03r88cetxwuFgsrl8rKv\ncbXHVrP4Nbrd7qql7+p5vypX5Gtlmqb1pcGrr76qvr4+TU9PK5FIaHx8XOl0WuPj43XtEwCA5TCc\nHgCw45VKpSUzjRuGoX/6p3+S9NWV3oU8Hs+SwJvJZKqGkG9EXZKqgmhlOPrBgwet0Fi5wrywTTQa\ntX5ffHV9JZUrzguH9c/OzkqSnn766ZrrNk1TZ86cUU9Pj/r7++Xz+ZZcxa5cZV9cezQaXfWx5VTe\nh8VX0xd/qVLr+1WLyt+/8rpGR0eVzWZlmqZ+8IMfKBAI6MKFC5qZmdHrr7++7FB8AAAaQYgHAOxo\npmla9zAvdvjw4RVnOe/s7JTL5bLC2cL7qitXfKXlh2CXy+UlXwAsd291Pp+Xx+PRyMiItW1sbEyd\nnZ06dOiQ/H6/uru7FY1GFYvFrNcTCoV04MCBqr5qWQ7NMAwFg8Gq++knJib08MMPW1euax1SLn31\n5UexWNTw8LBcLpdM09Tc3Jz8fr+6urqs2kulksbGxjQ7O7vqYwtV3me3261gMKhoNGoF94mJCRWL\nxaovJGp5v2p9fZUvRVKplEzTVDabrdq28Kq72+3esNsyAADYff78+fN2FwEAgB3C4bD+7u/+Ti6X\nSx988IHeeecdnTx5sqrNM888o1/+8pfq6uqqusf6wQcf1P/6X/9L77zzjn7+85/rgw8+0Msvv2zd\nb/3hhx9qz549+od/+AeVSiXNzs5qz549mp2d1RtvvKFSqaR4PK4//dM/1c9+9jO9++67un//vm7e\nvKn29nYZhqFoNKq33npLuVxOb7zxhv7t3/5N3/72tzUyMqKvfe1rkqQjR47o/v37euedd/TGG28o\nHo/r5Zdf1p//+Z8rFotV9f+b3/xmzTD5zDPP6A9/+IMuXbpkLaN2+fJlfe1rX6t5f16vV/fv39cv\nf/lLjY2N6cMPP9S5c+fkdrsVi8X0m9/8Rs8884z+6q/+Sr/97W915coVvfHGGzIMQxcuXJCkJY+1\nt7frwoULSiQSGhoaUi6XUzKZVLFYVFdXl5555hndv39f//iP/6j/+q//0oMPPqivf/3rMk1T77zz\njo4cOSKPx1PX+7Vnzx65XC6dPn1auVxOd+7csfrzer367W9/q4mJCcViMY2Ojmrfvn0qFov64IMP\n9O1vf1tvvPGG3n77baXTaSa3AwBsGFd5rellAQAAAADAtsBwegAAAAAAHIIQDwAAAACAQxDiAQAA\nAABwCEI8AAAAAAAOQYgHAAAAAMAhCPEAAAAAADgEIR4AAAAAAIcgxAMAAAAA4BCEeAAAAAAAHIIQ\nDwAAAACAQxDiAQAAAABwCEI8AAAAAAAO8f8DKItwAoJHTkYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1045b13d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = counts2010\n",
    "y = counts2013\n",
    "pool = np.concatenate([x,y])\n",
    "np.random.shuffle(pool)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.hist(pool, \n",
    "         bins = 25, \n",
    "         normed = True)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Number of accidents')\n",
    "plt.title(\"Pooled distribution\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1155aa950>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DBCW9auP4tJyF+sd9V1dHlMvlCOcAXEU4B4AqZDIZ5XI52/2YKgkAjWQ31APA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\n8bo8ZwCA1sXIOQAATyhtcS/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113f7cb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10000 # number of samples\n",
    "diff = range(N)\n",
    "for i in range(N):\n",
    "    p1 = [random.choice(pool) for _ in xrange(n)]\n",
    "    p2 = [random.choice(pool) for _ in xrange(n)]\n",
    "    diff[i] = (np.mean(p1)-np.mean(p2))\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 3))\n",
    "plt.hist(diff, \n",
    "         bins = 50, \n",
    "         normed = True)\n",
    "plt.ylabel('Frequency')\n",
    "plt.xlabel('Difference in the mean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "492"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# counting how many differences are larger than the observed one\n",
    "diff2 = np.array(diff)\n",
    "w1 = np.where(diff2 > p)[0]      \n",
    "len(w1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If there are $k$ sample pairs where the difference in mean is as big as or bigger than 0.05, the p-value is approximately $k/N$. In or case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value (Simulation)= 0.0492 ( 4.92 %) Difference = 1.09863013699\n",
      "The effect is likely\n"
     ]
    }
   ],
   "source": [
    "print 'p-value (Simulation)=', len(w1)/float(N), '(', len(w1)/float(N)*100 ,'%)', 'Difference =', p\n",
    "if len(w1)/float(N)<0.05:\n",
    "    print 'The effect is likely'\n",
    "else:\n",
    "    print 'The effect is not likely'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have defined the effect as a difference in mean as\n",
    "big or bigger than the observed difference, taking into account the sign. A test like this is called *one-sided*.\n",
    "\n",
    "If the relevant question is whether accident rates are different, then it\n",
    "makes sense to test the absolute difference in means. This kind of test is called *two-sided*\n",
    "because it  counts both sides of the distribution of differences."
   ]
  }
 ],
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   "pygments_lexer": "ipython2",
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