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@regifukuchi
Created July 1, 2016 04:46
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T distribution and confidence interval
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Distribuição normal, distribuição t e intervalo de confiança\n",
"\n",
"Assumindo que os parâmetros abaixo foram extraídos da população que apresenta distribuição normal\n",
"\n",
"$$ \\mu = 12,6 $$\n",
"$$ \\sigma = 2,3 $$\n",
"\n",
"Podemos, criar o formato desta distribuição a partir da função de densidade da probabilidade da distribuição normal\n",
"\n",
"$$ f(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\Bigl(-\\frac{(x-\\mu)^2}{2\\sigma^2}\\Bigr) $$\n",
"\n",
"Perceba que para determinar a característica da curva de distribuição normal é necessário conhecer apenas dois parâmetros $\\mu$ e $\\sigma$\n",
"\n",
"Por exemplo, vamos primeiro criar a distribuição normal usando os dados brutos"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Parâmetros da população\n",
"mu <- 12.6\n",
"sigma <- 2.3\n",
"\n",
"N <- 1000 # número de observações"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Mostrar até 4 DP da média\n",
"xRaw <- seq(mu-4*sigma,mu+4*sigma, length = N)\n",
"\n",
"# Função de probabilidade da distribuição normal\n",
"fnRaw = (1/(sigma*sqrt(2*pi)))*exp(-(xRaw-mu)**2/(2*sigma**2)) # normal pdf"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"</g>\n",
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"</g>\n",
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"</g>\n",
"</g>\n",
"</svg>\n"
],
"text/plain": [
"Plot with title “Distribuição normal”"
]
},
"metadata": {
"image/svg+xml": {
"isolated": true
}
},
"output_type": "display_data"
}
],
"source": [
"# Visualizando distribuição normal\n",
"#graphics.off()\n",
"plot(xRaw, fnRaw, type = 'l', main = \"Distribuição normal\", xlab = \"Variável dependente\", ylab = \"Freq\", xaxt='n')\n",
"xtick <- c(mu-4*sigma,mu-3*sigma,mu-2*sigma,mu-sigma,mu,mu+sigma,mu+2*sigma,mu+3*sigma,mu+4*sigma)\n",
"axis(1, at = xtick)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Agora podemos criar uma distribuição normal N(0,1) padronizada uma vez que as propriedades da distribuição são bem conhecidas. Esta distribuição também é conhecida como Z. Assumimos então:\n",
"$$ \\mu = 0 $$\n",
"$$ \\sigma = 1 $$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Normal probability density function\n",
"xZ <- seq(-4,4,length=1000)\n",
"mu <- 0\n",
"sigma <- 1\n",
"\n",
"# Função de probabilidade da distribuição normal\n",
"fnZ = (1/(sigma*sqrt(2*pi)))*exp(-(xZ-mu)**2/(2*sigma**2)) # normal pdf"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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Q5s+GhYU1P+fR/EVVV1tamxOVL1977bUWy/fx8Wn+fqedO3c2fzhXsWLFinaKncFg+Prrr9t8hqDpnkKDwVBUVOTt7d1iBnd395UrVypvZWi+wD179ijndVrw9/c/e/asMfvCmOnGr8WYLdzZ6cZvkKstsPXCm16B1cTLy6ugoKALK83Pz29xtVGj0Sij4gkjip3B6M1r5OZq8WXro7QFM33eTh3GgFXh0AQ6oc0/LW5ubgEBAa+88krrV0q0/gNw4cKFl156KTAw0NPTU6vVenl5hYeHv/feey2GYNi2bduoUaOUJ1vbWVrriU1fLlmyZNSoUS4uLn369HnooYdOnTrV4gdzcnLGjRvn5eXl4uISHh7+7bfftrO0Jlu3bo2JiVGegvTw8Bg3btzmzZtbLPnQoUPTp0/v2bOni4vLkCFD5syZc/z4cYPB8OOPP/bq1atPnz7NZz537tyzzz47ePDgbt26eXl5hYSEzJ8/v/mLAa7man9c25xu5FqM2cJdmG7kBjGmLijzNDY2fvjhhzfddJOLi4uvr+8DDzzQYrgc41eqzHn77bd7eXl5enrGxcUpF09bh2knnjGb18jN1eaX7TDf5+3UYQxYDwYoBtBp77//fllZ2RtvvCE7iN0xZhBjAPaMYgegc86dO3f99ddrNBoPD493331XeakULINiB6B9FDsAnXbhwoWjR4+Gh4f36NFDed0nLINiB6B9jGMHoNN8fHyU11Q0DV8HALAGvFIMQOcEBgYWFBS4urpGRkYqA4MBAKwEl2IBAABUgkuxAAAAKkGxAwAAUAmKHQAAgEpQ7AAAAFSCYgcAAKASFDsAAACVoNgBAACoBMUOAABAJSh2AAAAKkGxAwAAUAmKHQAAgEpQ7AAAAFSCYgcAAKASFDsAAACVoNgBAACoBMUOAABAJSh2AAAAKkGxAwAAUAmKHQAAgEpQ7AAAAFSCYgcAAKASFDsAAACVoNgBAACoBMUOAABAJSh2AAAAKkGxAwAAUAmKHQAAgEpQ7AAAAFSCYgcAAKASFDsAAACVoNgBAACoBMUOAABAJSh2AAAAKuEoO4ANKC8vX7JkSV1dnewgAADAKjg5OT366KPdu3eXHaQlil3HPvvss+eee052CgAAYEVcXFyefPJJ2Slaoth1rL6+Xgjxz3/+MyAgQHYWAAAgWUFBwSOPPGKdl/IodsYaNmxYcHCw7BQAAECy6upq2RGuiocnAAAAVIJiBwAAoBIUOwAAAJWg2AEAAKgExQ4AAEAlVFLsHBwcHBwcZKcAAACQSSXFDgAAALY0jl2H5+Saz2AwGMwcBwAAwLrY0hm7Hj16yI4AAABgvWyp2BUUFMTGxgohvL29V69ebWhGmaH1FAAAAPthS8XOz88vNTX1jTfeuHz58owZMx566KHLly/LDgUAAGAtbKnYCSE0Gs0f//jH7OzsG2+8cfny5YGBgfn5+bJDAQAAWAUbK3aK0NDQXbt23X///UePHtXpdG+++absRAAAAPLZZLETQnh6ev7rX/9atWqVu7v7n/70J9lxAAAA5LPVYqeYOXNmQUFBVFSU7CAAAADy2dI4dm0aOHBgZmam7BQAAADy2fYZOwAAADSx+TN216ihoWHjxo3V1dXtzLNr1y4hRF1dnaVCAQAAdIUKi53yYjEjxyhOT0+fMmWKMXOuWrUqLi7uWoIBAACYlQqLXafExsampqY2NDS0M8/ChQt//PHHfv36WSwVAKtSXV1dUFCwd+/ekpISIUTfvn1HjhwZGBjYrVs32dEA4L+osNh16n1iWq02Pj6+/XlWrFghhNBouB8RsDvZ2dmLFi3atGlTZWVli2+5u7tPmDBhzpw5Op1OSjYAaE2FxQ4Arl1hYeEzzzyTlpYmhIiIiJgyZUpwcPB1110nhCgtLd2xY8f69eu//PLLL7/8Mj4+/m9/+9uoUaMkJwYAih0AtGAwGN56663XXnutsbHx0Ucffe655/z9/VvMM378+JdeeqmoqOj9999funRpUFDQa6+99vLLLyv3+AKALLZ3efHkyZPz5s2Lj4/v16+fq6uro6Nj9+7d/f3977zzzmXLlrW+XAIAxquoqLjlllv+9Kc/+fv7b9++/dNPP23d6poMHz78008/3b59+7Bhw/70pz/dcsstFRUVlkwLAC3YWLFbvHjx0KFD//znP6elpZWUlFRXVzc0NFRUVBw8eHDt2rUPP/zwsGHDNm3aJDsmAJt09uzZqKiojRs3PvTQQ/n5+WPGjDHmp8aMGbNt27aHHnpo48aNUVFRP//8s7lzAsDV2FKx27Bhw1NPPVVXVzdz5swVK1YcPnz4l19+qa+vr6ysPHr06Ndff33bbbedOXNm6tSper1edlgANqa0tDQxMbGwsHD+/PlLly51dXU1/mddXV2XLl06f/78wsLChISE0tJS8+UEgHbYUrFbuHChEGLRokWrVq26++67Bw8e7O3trdVq3dzcBg0alJyc/NVXX73wwgu1tbXz5s2THRaALTl//nxiYuKBAwc++eSTl156qWsLeemll/7xj38cOHAgMTHxwoULpk0IAMawpWKnvAHiwQcfbGeeuXPnCiHy8/MtEwmACtTW1t5222379u17//33H3300WtZ1KxZs9577719+/bddttttbW1pkoIAEaypWKnjCTX/u9KrVYreP0XgM6YNWtWdnb2s88++//+3/+79qXNmTNnzpw5WVlZs2bNuvalAUCn2FKxCwoKEkIsWLCgnXnef//9pjkBoEN///vf//3vf0+ePPndd9811TIXLlw4efLkf//73x999JGplgkAxrClYvfKK69otdp33313/PjxK1euPHToUGVlZWNjY0VFRXFx8Zo1a6ZMmfLmm29qNJqXX35ZdlgANmDHjh1z584dPHjwZ599ZsK3y2g0ms8+++zGG2987rnndu7caarFAkCHbGmA4ri4uHXr1s2ePTslJSUlJaXNeTw8PD7++OOkpCQLZwNgc65cuXLvvfcaDIYvvviiR48epl14jx49Vq9eHRkZec899+zYscPNzc20yweANtnSGTshRHJy8vHjx5csWXLXXXcNHTq0Z8+eWq3W1dV1wIABEyZMeO+9944fP37PPffIjgnABrz00ksHDhyYP39+cHCwOZYfHBz81ltvHThw4H/+53/MsXwAaM2Wztgp3NzcHnnkkUceeUR2EAA2LDMz86OPPoqNjTXJAxNXM2fOnO++++7vf//79OnTo6KizLciAFDY2Bk7ALh2NTU1s2bNcnV1XbZsmQlvrWtNo9EoYx0/+uijNTU15lsRACgodgDszoIFCw4ePPj666/fcMMN5l7XoEGDXnvttYMHD5rwqVsAuBqKHQD7UlxcPH/+/BEjRjzzzDOWWeMf/vCHm2666a233iouLrbMGgHYLYodAPsyd+7cqqqqDz74wMnJyTJrdHJy+uCDD6qqqp5//nnLrBGA3aLYAbAj6enpX3311Z133pmQkGDJ9SYmJk6fPv3LL7/MyMiw5HoB2BuKHQB7YTAY5s6d6+Li8s4771h+7QsWLHBxcXnuuecMBoPl1w7ATlDsANiLtWvXbt++/cknn7z++ustv/brr7/+iSee2L59+7p16yy/dgB2gmIHwC7U1dX96U9/8vHxefXVV2VlePXVV3v27PnHP/6xrq5OVgYA6kaxA2AXli1bdvjw4eeff97Ly0tWBm9v7+eff/7w4cPLly+XlQGAulHsAKhfXV3d22+/3bt376efflpukqeffrpXr15vv/02J+0AmAPFDoD6LVu2rLi4+Pnnn3d3d5ebxMPD4/nnnz927Bgn7QCYA8UOgMrV1dW9+eabvr6+Tz75pOwsQgjx1FNP9e7d+8033+SkHQCTo9gBULnPPvvs5MmTc+bMkX66TuHu7v7ss8+eOHHi888/l50FgNpQ7ACoWWNj48KFC728vKzkdJ3iiSee8PLyevfddxsbG2VnAaAqFDsAavbdd98VFRU98cQT3bt3l53lP7y8vB5//PGioqINGzbIzgJAVSh2ANRs4cKFLi4uc+bMkR2kpTlz5ri4uCxcuFB2EACqQrEDoFrbt2/Pysq65557fH19ZWdp6brrrrv77rszMzN37NghOwsA9aDYAVCt9957z8HB4Q9/+IPsIG1Tgr333nuygwBQD4odAHUqKSlZt25dQkLCqFGjZGdp2+jRoxMTE9euXVtSUiI7CwCVoNgBUKfFixfX19c/99xzsoO059lnn62vr//f//1f2UEAqATFDoAK1dTUfPLJJzfeeOPNN98sO0t7JkyYMGjQoE8++aSmpkZ2FgBqQLEDoEJr1qw5f/78448/rtFY9W85jUbz+OOPnzt3bu3atbKzAFADq/6VBwBds3jxYjc3t1mzZskO0rFZs2a5ubktXrxYdhAAakCxA6A2u3btys3NnTFjhpeXl+wsHfP29r7zzjv1ev3u3btlZwFg8yh2ANTmk08+EUJY1TvE2qdEVWIDwLWg2AFQlcuXL69cuTIkJCQkJER2FmONHTs2ODh4xYoVlZWVsrMAsG0UOwCqsnr16vLy8tmzZ8sO0jmzZ88uLy9fvXq17CAAbBvFDoCqLF261N3dfcaMGbKDdM7MmTPd3NyWLl0qOwgA20axA6AeBw4cyMnJueOOO7p37y47S+d07979jjvuyM7OPnDggOwsAGwYxQ6Aevzzn/8UQjz88MOyg3SFEpuTdgCuBcUOgErU1NQsW7bM398/JiZGdpauiI2N9ff3X7p0KW+hANBlFDsAKrFly5aLFy/ed999soN03b333nvx4sXU1FTZQQDYKoodAJVYvny5RqOx6WJ33333aTSa5cuXyw4CwFZR7ACowaVLlzZs2BAfH+/n5yc7S9cNGDAgLi5uw4YN5eXlsrMAsEkUOwBqsHbt2qqqqvvvv192kGt1//33X7lyZe3atbKDALBJFDsAavD555+7ublNmzZNdpBrNW3aNDc3t88//1x2EAA2iWIHwOadOnUqMzNz6tSpHh4esrNcK09PzylTpmRkZJw6dUp2FgC2h2IHwOZ9/vnnjY2NKrgOq7j//vsbGxtXrFghOwgA20OxA2Dzvvjii169eiUmJsoOYhrjxo3z8fH54osvZAcBYHsodgBsW2Fh4Z49e26//XYnJyfZWUzDycnp9ttvLygo2Lt3r+wsAGwMxQ6AbVu5cqUQYubMmbKDmJLycZSPBgDGo9gBsGEGg2H16tX9+/e30deIXU1sbGy/fv1Wr15tMBhkZwFgSyh2AGzY9u3bi4uLZ8yYodGo6reZRqOZMWPGsWPHduzYITsLAFuiql+FAOzNunXrhBDTp0+XHcT0lA+lfEAAMBLFDoANW7du3cCBA0NDQ2UHMb2wsLABAwZQ7AB0CsUOgK3avn37sWPH7rzzTgcHB9lZTM/BwWHGjBlHjx7laiwA41HsANgq5YWqqrwOq7jjjjvEbx8TAIxBsQNgq9atWzdgwICQkBDZQcxl7Nixfn5+XI0FYDyKHQCbtGPHjmPHjk2fPl2V12EVDg4O06dPP3r06M6dO2VnAWAbKHYAbJJyHmvatGmyg5jX7bffLng2FoDRKHYAbNJXX33Vt2/f8PBw2UHMKzw8vE+fPl999ZXsIABsA8UOgO3Zu3fvoUOHkpOTVTYucWsajSY5OfngwYP79u2TnQWADVD570QAqqScwVL9dViF8jE5aQfAGBQ7ALbn66+/9vHxiY2NlR3EEmJjY3v27EmxA2AMih0AG1NcXLx79+7Jkyc7OjrKzmIJTk5OkydP3r179/Hjx2VnAWDtKHYAbMy3334rhJg6darsIJajfNj169fLDgLA2lHsANiYb775xt3dfeLEibKDWM7EiRPd3NwodgA6RLEDYEvKysqysrKSkpJcXV1lZ7EcNze3pKSkzMzMsrIy2VkAWDWKHQBbsmHDhvr6+ilTpsgOYmlTp06tr6///vvvZQcBYNUodgBsyfr16zUazeTJk2UHsbRJkyZpNJXwXowAACAASURBVBquxgJoH8UOgM2oqanZvHlzeHh47969ZWexNF9f37CwsM2bN9fU1MjOAsB6UewA2Iy0tLTLly/b1fOwzU2dOrWioiItLU12EADWi2IHwGZ89913ws4GOmlO+eAbNmyQHQSA9aLYAbANBoNh/fr1/v7+w4YNk51FDuWzr1+/3mAwyM4CwEpR7ADYhr17954+fXrSpEmyg8g0adKkU6dO7du3T3YQAFaKYgfANijXYW+99VbZQWRSPr6yKQCgNYodANvwww8/eHp6RkZGyg4ik06n8/T0/OGHH2QHAWClKHYAbEBpaWlOTs6ECROcnZ1lZ5HJ2dn55ptvzs7OLi0tlZ0FgDWi2AGwAZs3b25sbLTzG+wUkyZNamxs/Omnn2QHAWCNKHYAbMB3332n1WpvueUW2UHku+WWWzQaDbfZAWgTxQ6Atauvr09JSQkODu7Vq5fsLPL17t07ODg4JSWloaFBdhYAVodiB8Da5eXl/fLLLxMnTpQdxFpMnDixrKwsLy9PdhAAVodiB8Dabdq0SQgxYcIE2UGshbIplM0CAM1R7ABYux9++MHHx2fs2LGyg1iL0NDQnj17MugJgNYodgCs2pkzZ3bu3Dlp0iStVis7i7XQarWTJk3asWPHmTNnZGcBYF0odgCs2ubNmw0GA9dhW5gwYYLBYGDQEwAtUOwAWLWNGzdqtVqenGhhwoQJWq1248aNsoMAsC4UOwDWq6GhYcuWLcHBwT169JCdxbr4+PgEBQVt2bKFQU8ANEexA2C9lIFOeOFEmyZNmlRWVpafny87CAArQrEDYL1SUlKEEElJSbKDWCNlsyibCAAUFDsA1mvTpk09evQIDQ2VHcQahYaGent7M5odgOYodgCslHKdMSEhgYFO2uTo6JiQkJCXl1dWViY7CwBrQbEDYKWU16FyHbYdSUlJyvMlsoMAsBYUOwBWSrnIyJMT7Zg8ebLg3WIAmqHYAbBSKSkpQ4cO7d+/v+wg1qt///5Dhgzh+QkATSh2AKzR3r17T506xbjEHZo4ceLJkyf37dsnOwgAq0CxA2CNlPvGEhMTZQexdsom4jY7AAqKHQBrlJKS4uzsHB8fLzuItYuPj3dycuKlsQAUFDsAVqeuri49PT0iIsLDw0N2Fmvn6ekZERGRnp5eV1cnOwsA+Sh2AKyOXq+vqKhgoBMjJSUlVVRU5Obmyg4CQD6KHQCro4zfQbEzkrKhGPQEgKDYAbBCW7Zs6dGjx5gxY2QHsQ1BQUHe3t48PwFAUOwAWJsLFy5s37593LhxvEnMSFqtdty4cdu2bbtw4YLsLAAko9gBsC4ZGRmNjY08D9sp8fHxjY2NGRkZsoMAkIxiB8C6KO9RGDdunOwgtkTZXLyCAgDFDoB1+fHHHwcNGjRkyBDZQWzJ0KFDb7jhhs2bN8sOAkAyih0AK3L69Oljx44lJCTIDmJ7EhISjh49eubMGdlBAMhEsQNgRZRzTgx00gXKRuOkHWDnKHYArMjWrVs1Gk1cXJzsILYnLi7OwcFh69atsoMAkIliB8BaGAyGzZs3BwYG9u7dW3YW2+Pr6xsYGLh582aDwSA7CwBpKHYArMX+/fvPnTvHDXZdlpCQUFpaWlRUJDsIAGkodgCsRVpamhCC67Bdpmw6ZTMCsE8UOwDWIiUlxdnZmWLXZXFxcU5OToxmB9gzih0Aq9DQ0JCRkRESEuLu7i47i63y8PAICQlJT09vbGyUnQWAHBQ7AFZhx44dZWVliYmJsoPYtsTExLKysh07dsgOAkAOih0Aq8ANdibBbXaAnaPYAbAKqampLi4ukZGRsoPYtsjISBcXl9TUVNlBAMhBsQMgX01NTWZmpk6nc3FxkZ3Ftrm6ukZGRmZkZNTU1MjOAkACih0A+fLz869cuRITEyM7iBrExMRcuXJl27ZtsoMAkIBiB0C+LVu2CCHGjRsnO4gaKJtR2aQA7A3FDoB86enp7u7uISEhsoOowdixY93d3dPT02UHASABxQ6AZNXV1bm5udHR0c7OzrKzqIGzs3NUVFRubm51dbXsLAAsjWIHQLLs7Ozq6mpeEWtCCQkJVVVVOTk5soMAsDSKHQDJMjIyhBCxsbGyg6iHsjGVDQvArlDsAEi2ZcsWb2/v4OBg2UHUIyQkxNvbm+cnADtEsQMgU2VlZX5+fnR0tFarlZ1FPbRabVRUVH5+fmVlpewsACzK5otdTU3N//zP/wwYMMDV1XXkyJELFiyoq6uTHQqAsXJzc+vq6hjBzuRiYmJqa2vz8vJkBwFgUTZW7DZu3BgSEuLq6urn5/faa681NjY++eSTb7/99qlTp6qrq/ft2/fiiy/ecsst9fX1spMCMIpyuTAxMVF2ELVRNilXYwF7Y0vFbteuXVOmTNmxY0d1dfXp06dff/313//+98uXLx8yZEheXl55efn333/v6+u7efPmxYsXyw4LwCgZGRne3t6jR4+WHURtAgICvLy8eH4CsDe2VOzeeuuthoaGpKSkkpKSEydOJCcnL168uLGx8f333w8NDfX09Jw0adKiRYuEECtWrJAdFkDHKioq8vLyYmNjucHO5LRabWxsbF5eHrfZAXbFlord9u3bhRAffPBBnz59BgwY8OGHHyrTIyIimuZJSkoSQhQVFUlJCKBTcnNz6+vrGejETGJjY+vq6vR6vewgACzHlord2bNnhRDXX3+98mX//v2V//Dx8Wmax83NTQhRW1tr6XAAOi8zM1MIERUVJTuIOkVHR4vfNjIAO2FLxU4pcMp5O4XBYDAYDM3nSUtLE0L4+flZNhqArti6dau3t3dQUJDsIOoUFBTk7e29detW2UEAWI4tFbvJkycLIR588MFNmzaVl5e3+O6FCxfWrVs3a9YsIURycrKEfAA6o7q6evv27REREdxgZyZarTY8PHzbtm28NBawH7ZU7N54441BgwYdOXJk4sSJXl5eLb7bu3fv6dOnl5SUBAQE/PGPf5SSEIDx9Hp9dXU1N9iZVVxcXHV1dW5uruwgACzEloqdr6/vrl27Xn/99VGjRnl4eLT4rouLS0BAwPz58/V6vbe3t5SEAIyXmpoqGMHOzBISEsRvmxqAPXCUHaBzunfv/uqrr7766qutv1VVVWX5PAC6LCMjo3v37oGBgbKDqNmYMWM8PT0ZzQ6wHzZW7EyuoaFh48aN7d+Acvz4cSFEY2OjhTIBdqCqqiovL2/8+PGOjvb+W8isHB0dY2JiUlJSqqurXVxcZMcBYHYq/JXq4OAghGjxtOzVpKenT5kyxZg5lXoHwCR27NhRU1PDQCcWEBUV9f3332/fvp2tDdgDFRa7TomNjU1NTW1oaGhnnoULF/74449N4+cBuHbp6elCCJ6csABlI2dkZFDsAHugwmJn5Lk6hVarjY+Pb38e5QVlGo0tPWgCWLmtW7d6enqGhITIDqJ+Y8eO9fDw2Lp168svvyw7CwCzo6wAsLS6urq8vLyxY8dyg50FODo6hoaG5ubm1tXVyc4CwOwodgAsbdu2bZcvX+7wZDlMJS4u7vLly81f2wNArWyv2J08eXLevHnx8fH9+vVzdXV1dHTs3r27v7//nXfeuWzZssrKStkBAXSAG+wsTNnUymYHoG42dh1k8eLFzz77bE1NTfOJFRUVBw8ePHjw4Nq1a1955ZUlS5ZMmDBBVkIAHcrKyurWrdvYsWNlB7EXY8eO7datW1ZWluwgAMzOls7Ybdiw4amnnqqrq5s5c+aKFSsOHz78yy+/1NfXV1ZWHj169Ouvv77tttvOnDkzdepUvV4vOyyAtjU0NGRlZYWHhzOsmsW4urqGhYVlZma2PwIAABWwpWK3cOFCIcSiRYtWrVp19913Dx482NvbW6vVurm5DRo0KDk5+auvvnrhhRdqa2vnzZsnOyyAtu3Zs6e8vFyn08kOYl90Ol15eXlhYaHsIADMy5aK3a5du4QQDz74YDvzzJ07VwiRn59vmUgAOiszM1MIERMTIzuIfVE2uLLxAaiYLRU7ZSS52tradubRarVCCJ7qB6xWenq6k5MTg+VaWFRUlJOTE89PAKpnS8UuKChICLFgwYJ25nn//feb5gRgbQwGQ3Z29pgxY9zd3WVnsS8eHh6BgYHZ2dmdGsIdgM2xpWL3yiuvaLXad999d/z48StXrjx06FBlZWVjY2NFRUVxcfGaNWumTJny5ptvajQaBlgHrFNRUVFpaWlcXJzsIPYoLi7u559/PnDggOwgAMzIloY7iYuLW7du3ezZs1NSUlJSUtqcx8PD4+OPP05KSrJwNgDGUC4FRkdHyw5ij6Kjo99999309PThw4fLzgLAXGzpjJ0QIjk5+fjx40uWLLnrrruGDh3as2dPrVbr6uo6YMCACRMmvPfee8ePH7/nnntkxwTQtqysLI1GExkZKTuIPYqMjHRwcOD5CUDdbOmMncLNze2RRx555JFHZAcB0GlpaWmjRo3q2bOn7CD2yMfHZ9SoUTw/AaibjZ2xA2C7iouLS0pKGMFOIp1Od+bMmePHj8sOAsBcKHYALER5pRUDnUik3N3I1VhAxSh2ACxE6RPKC+khhbLxKXaAilHsAFhIdnb2wIED+/btKzuI/erbt+/AgQOzs7NlBwFgLhQ7AJZQWlpaVFQUHx8vO4i9i4+PLyoqOnfunOwgAMyCYgfAErKysgwGA09OSKfT6QwGg3K/IwD1odgBsATl8h/FTjplEEGKHaBWFDsAlpCWlnbdddf5+/vLDmLvhg8f7uvry2h2gFpR7ACYXUVFRWFhofLmA9lZ7J2Dg0NkZOSePXsqKipkZwFgehQ7AGan1+vr6+sZwc5KREdH19fX6/V62UEAmB7FDoDZKQOnxcTEyA4CIX7bEYxmB6gSxQ6A2eXk5Li7uwcEBMgOAiGECAgIcHd3z8nJkR0EgOlR7ACYV21trV6vj4yMdHJykp0FQgjh5OQUERGh1+tra2tlZwFgYhQ7AOa1c+fOqqoq5S2lsBLR0dFVVVU7d+6UHQSAiVHsAJiXcsmPEeysivIgC1djAfWh2AEwr8zMTGdn54iICNlB8B8RERHOzs48PwGoD8UOgBkpb68KCgpydXWVnQX/4erqGhQUpLznTXYWAKZEsQNgRocOHbpw4YLyGitYlcjIyAsXLhw+fFh2EACmRLEDYEbKq6t4csIKKTslLS1NdhAApkSxA2BG2dnZyjusZAdBS8ob3rKzs2UHAWBKFDsAZpSVlTVkyBBfX1/ZQdCSr6/vkCFDsrKyZAcBYEoUOwDmcurUqWPHjvEmMasVExNz7NixU6dOyQ4CwGQodgDMRXnNPAOdWC1l1yi7CYA6UOwAmIsyTBpn7KyWsmsYzQ5QE4odAHPJysrq06fP4MGDZQdB2wYPHtynTx9uswPUhGIHwCwqKioKCwu5DmvlIiIiCgsLL1++LDsIANOg2AEwC71e39DQwAh2Vi46OrqhoYHb7ADVoNgBMAulKzCCnZVTdhDFDlANih0As8jJyXF3dx8zZozsIGjPmDFj3NzcGKYYUA2KHQDTq6+vz87ODgsLc3Jykp0F7XFycgoLC8vOzq6vr5edBYAJUOwAmN6ePXsqKyt5csImREREVFZW7tmzR3YQACZAsQNgesoIGtxgZxN0Op34bZcBsHUUOwCml5mZqdVqo6KiZAdBx6KiorRaLcMUA+pAsQNgejk5OSNGjOjevbvsIOhY9+7dR4wYkZOTIzsIABOg2AEwsaNHj5aUlPAmMRsSHR1dUlJy7Ngx2UEAXCuKHQATU+7WUu7cgk3gNjtANSh2AExMGRSNYmdDlJ3FaHaAClDsAJhYdna2n5+fn5+f7CAw1oABA/z8/Ch2gApQ7ACY0i+//HLgwAEGOrE5ERERRUVFv/76q+wgAK4JxQ6AKen1+sbGRq7D2hydTtfY2MhLYwFbR7EDYErKcGjR0dGyg6BzlF3GaHaAraPYATCl7OxsLy+vUaNGyQ6Czhk9erSnpye32QG2jmIHwGRqamq2bdsWFham1WplZ0HnaLXa8PDwbdu21dbWys4CoOsodgBMZufOndXV1dxgZ6N0Ol1VVdXOnTtlBwHQdRQ7ACaj3HofEREhOwi6QtlxPD8B2DSKHQCTyczMdHR0ZKwTGxUZGeno6MjzE4BNo9gBMA2DwZCVlTV69Gh3d3fZWdAVHh4eo0aN4vkJwKZR7ACYxpEjRy5cuMANdjZNp9OdO3fuyJEjsoMA6CKKHQDT4BWxKsBLYwFbR7EDYBpKG2BoYpum7D6KHWC7KHYATCM7O3vgwIF9+/aVHQRd169fvwEDBlDsANtFsQNgAhcvXjxw4ADXYVVAp9MVFRWVlZXJDgKgKyh2AEwgNzfXYDAwgp0KREREGAyG3Nxc2UEAdAXFDoAJ5OTkCCEYwU4FlJ2o7FAANodiB8AEsrKyvLy8AgICZAfBtQoMDPT09MzKypIdBEBXUOwAXKu6urrt27eHhIRotVrZWXCttFrt2LFjt2/fXl9fLzsLgE6j2AG4Vrt3775y5QpPTqhGVFRUZWXl7t27ZQcB0GkUOwDXSrlsxwh2qqHsSl4aC9giih2Aa6XX67VabVhYmOwgMI2wsDCtVsuDsYAtotgBuFYZGRnKHfeyg8A0PD09AwIC0tPTZQcB0GkUOwDX5MiRI6WlpdxgpzI6na60tPTIkSOygwDoHIodgGuiDHgWHh4uOwhMSdmher1edhAAnUOxA3BNlCcnoqKiZAeBKSk7lNHsAJtDsQNwTXJycvz8/Pz8/GQHgSkNGDDAz8+P908ANodiB6DrysrK9u/fzw12qhQZGblv376ysjLZQQB0AsUOQNfl5uYaDAZeEatKkZGRBoMhLy9PdhAAnUCxA9B1ylBnERERsoPA9JTdymh2gG2h2AHouuzsbHd398DAQNlBYHqBgYHu7u7Z2dmygwDoBIodgC6qra3V6/WRkZGOjo6ys8D0nJycIiIicnNz6+rqZGcBYCyKHYAuKiwsrKqq4gY7FYuMjKysrCwsLJQdBICxKHYAukh5SbzywniokrJzlR0NwCZQ7AB0UXZ2tqOjI++cULGwsDCtVsttdoANodgB6KLMzMxRo0a5u7vLDgJz8fT0HDVqFGfsABtCsQPQFceOHSstLWVoYtXT6XQ///xzcXGx7CAAjEKxA9AVyltEeXJC9ZRdzEtjAVtBsQPQFQxNbCcYphiwLRQ7AF2RmZnZv3//66+/XnYQmNcNN9zQv39/brMDbAXFDkCnlZeX79+/n+dh7URYWNj+/fvLy8tlBwHQMYodgE7Lzc1tbGzkyQk7odPpGhoa8vLyZAcB0DGKHYBOU26lZ2hiOxETEyN4fgKwERQ7AJ2m1+vd3d0DAgJkB4ElBAQEuLu76/V62UEAdIxiB6BzlKtyYWFhjo6OsrPAEhwdHcPCwvLy8hoaGmRnAdABih2Aztm9e3dFRQXXYe1KVFRUeXl5QUGB7CAAOkCxA9A5ypBmPBJrV5TdzWh2gPWj2AHonMzMTK1Wyzsn7IpOp9NqtYxmB1g/ih2AzsnKyho1alT37t1lB4HldO/efeTIkRQ7wPpR7AB0wokTJ86cOcMIdnZIp9OdOXPm5MmTsoMAaA/FDkAnZGdnCyEodnZI2enKAQDAalHsAHQCxc5uUewAm0CxA9AJer2+X79+AwYMkB0EljZw4MC+ffvm5OTIDgKgPRQ7AMb69ddfCwoKGMHObkVHRxcUFPz666+ygwC4KoodAGPl5eU1NjYygp3dCg8Pb2xszMvLkx0EwFVR7AAYS7m/ihHs7Jay67kaC1gzih0AY2VlZXl6egYFBckOAjmCgoI8PDyysrJkBwFwVRQ7AEapq6vLz88PDQ3VarWys0AOR0fH0NDQvLy8+vp62VkAtI1iB8AoBQUFlZWVUVFRsoNApqioqMrKyoKCAtlBALSNYgfAKMqdVYxgZ+eUA4Db7ACrRbEDYBS9Xq/RaEJDQ2UHgUxhYWEajUav18sOAqBtFDsARsnIyBg9erSXl5fsIJDJy8tr1KhR6enpsoMAaBvFDkDHiouLS0pKuA4LIYROpyspKSkuLpYdBEAbKHYAOqbcU8XQxBC/HQZcjQWsE8UOQMcyMzOFELxMDEKImJgY8dshAcDaUOwAdCw7O9vPz2/gwIGyg0C+gQMH+vn5Ka8hAWBtKHYAOlBWVrZv3z5GsEOTqKioffv2/frrr7KDAGiJYgegA7m5uQaDgScn0ESn0zU2NnKbHWCFKHYAOqD8/VZeAA+I3w4Gih1ghSh2ADqQmZnp5eUVEBAgOwisRUBAgJeXV0ZGhuwgAFqi2AFoT21tbX5+fnh4uEbDrwv8H41GExYWlp+fX1tbKzsLgP/Cb2oA7dm1a1dVVRUj2KGFiIiIqqqqXbt2yQ4C4L9Q7AC0R7ncxgh2aEE5JLgaC1gbY4udQ2eYNTEAS8rOznZycuKMHVoIDw93cnJiNDvA2nDGDsBVGQwGvV4/evRod3d32VlgXdzd3UePHq3X6w0Gg+wsAP7D2GJ35cqVBx54oH///itWrDh37lxtbW1JScny5ct/97vfJScnV1RUGJoxa2IAFnPgwIFz584pr5ACWoiJiTl37tyBAwdkBwHwH8YWu+eee+5f//rXihUr7r777t69ezs5OfXp0+eBBx5YtWrVN9988/TTT5s1JQApcnJyhBARERGyg8AaKQeGcpAAsBLGFrvVq1cLIUJCQlpMV+68Wb9+vWljXc0vv/zyzDPP9O3b18XFJTAwcMWKFa3n4T4/wFSUO6h4mRjapBwY3GYHWJVOPDwhhEhNTW0xfffu3U3fNbeLFy+GhYV9+OGHZ8+erampKSgouPfee19//XULrBqwTxkZGUOGDOnTp4/sILBGffr0GTJkCA/GAlbF2GI3Y8YMIcQDDzywePHikydP1tbWXrhwYc2aNcr0adOmmTHjb956663Dhw8PGDBgy5Yt5eXl33zzjY+Pz+uvv966bgK4dqWlpUePHuVNYmhHZGTk0aNHS0tLZQcB8H+MLXbvvPNOYmJiWVnZU089NXDgwG7duvXu3XvGjBknT5686aab3nnnHbOmVHz33XdCiI8++ighIcHT03Pq1Klr164VQjzxxBOMfg6YHCPYoUOMZgdYG2OLnYeHx08//bRy5cqJEyf6+vo6Ojq6u7sHBAS89tprubm5Pj4+Zk2pOHnypBCi+QN68fHxjz766KFDhz766CMLBADsCjfYoUPcZgdYG0fjZ3VwcLjrrrvuuusu86Vpn6OjY01NTYuJ8+fP//LLL//yl7/ce++9vXv3lhIMUKWsrCxfX9+hQ4fKDgLrNXToUF9f36ysLNlBAPwfWxqgeNCgQUKIH3/8sflEHx+fv/zlL7/88stDDz1UX18vKRqgNhUVFbt379bpdDxjjnY4ODjodLrdu3dXVFTIzgJAiE4Vu19++WXevHmDBg1ydXXVaDRCiCFDhnz66acWG5F4+vTpQoinnnpq3bp1v/76a9P0xx9/PDo6+vvvvx8/fvzOnTstEwZQt9zc3IaGBp1OJzsIrJ1Op2toaMjNzZUdBIAQxhe7qqqquLi4P//5z8XFxdXV1UqZO3LkyOzZs++55x7LdLu5c+cGBwefP39++vTpPXr0aJqu0WjWrVs3evTotLS04OBgCyQBVE8ZdZZHYtEh5SBhmGLAShhb7D788MM9e/aMHDmyqKioaWJGRsagQYNWrVr16aefmifef3F1dc3IyHj77bfHjBnTvXv35t/y9fXNy8v76KOPJk6c2L9/f1dXVwvkAVQsMzPTzc2t9ZjkQAshISFubm6ZmZmygwAQwvhit3LlSiHEokWL/P39myZGR0f/9a9/FUIsXbrUHOFac3Nze/HFF3fu3Hnp0qUW33JxcXnyySc3btx46tSpK1euWCYPoEr19fX5+fljx451cnKSnQXWzsnJaezYsfn5+dzlDFgDY4vdwYMHhRCtL3Qqz7rzEmhATQoKCioqKhjoBEaKioqqqKgoKCiQHQSA0cXO2dlZCKE8M9GcMv4I/6MGqIky3mxcXJzsILANsbGxgmGKAetg7Dh2gYGBGRkZWVlZkydPbj79+++/F0KMHj3a9NG6ShmdwcjnORoaGjZu3FhdXd3OPMePHxdCNDY2miIdYANycnIcHR3DwsJkB4FtCA8Pd3R01Ov1c+bMkZ0FsHfGFrvf//73GRkZc+bMuf7665UppaWl69evf/7555XvmimfuaWnp0+ZMsWYOZV6B6iewWBIT08fM2aMp6en7CywDZ6enmPGjElLSzMYDAx8CMhlbLG74447XnjhhQULFowcOVKZ8rvf/U75jyeeeELi6yha69TYK7GxsampqQ0NDe3Ms3Dhwh9//LGp0QLqdvDgwfPnz997772yg8CWREVFbdu27dChQ8OGDZOdBbBrnXil2DvvvJOUlPTRRx/l5ORcvHjR09MzKCjoscceU8YNtlFarTY+Pr79eVasWCHaur8QUCXlvZ+MYIdOiYiIWLRoUXZ2NsUOkKsTxU4IkZiYmJiYaKYoAKxBZmamg4ODcjs8YKS4uDgHB4eMjIyHH35YdhbArhl7FsrFxcXBwaGurs6saYxx8uTJefPmxcfH9+vXz9XV1dHRsXv37v7+/nfeeeeyZcsqKytlBwRsW05OzpAhQ3r37i07CGxJ7969Bw8ezPsnAOmMLXbJycnCCl4as3jx4qFDh/75z39OS0srKSmprq5uaGioqKg4ePDg2rVrH3744WHDhm3atEluSMB2nT179vDhw9HR0bKDwPZER0cfPnz4559/lh0EsGvGFrslS5bcd999999///r16ysqKsya6Wo2bNjw1FNP1dXVzZw5c8WKFYcPH/7ll1/q6+srKyuPHj369ddf33bbbWfOnJk6daper5eSELB16enpQgiKHbogJiZG/HYIAZDF2HvsmgY+UE7dtdap0cRwkQAAIABJREFUZ1G7ZuHChUKIRYsWPfPMM82nu7m5DRo0aNCgQcnJyS+++OKCBQvmzZv3ww8/mDsPoD7KWXmenEAXKIdNTk7OjBkzZGcB7JctPem5a9cuIcSDDz7Yzjxz584VQuTn51smEqAy6enpfn5+Q4YMkR0EtmfIkCH9+/fnjB0gl7HFztARs6ZUKAOO1NbWtjOPVqsVQljDQx6AzSkrKyssLOQVseiyqKiowsLCsrIy2UEA+2VLZ+yCgoKEEAsWLGhnnvfff79pTgCdotfrDQaDTqeTHQS2SqfTNTY25ubmyg4C2K/2ip2Dg4NVvRzmlVde0Wq177777vjx41euXHno0KHKysrGxsaKiori4uI1a9ZMmTLlzTff1Gg0L7/8suywgO1RLqIxgh26TDl4uBoLSNS5AYqVnmeZC6+txcXFrVu3bvbs2SkpKSkpKW3O4+Hh8fHHHyclJVk4G6AC2dnZPXr0uOmmm2QHga0aMWKEt7e38vISAFJ0rthJl5ycnJSUtGrVqi1btuzYsePChQuXLl1ydnbu3bv3TTfdNH78+AceeMDHx0d2TMD2VFVVbd++PSkpibfnocs0Gk1UVNRPP/1UVVXl6uoqOw5gj2ys2Akh3NzcHnnkkUceeUR2EEBVcnJyamtr4+LiZAeBbYuNjd2wYYNer09ISJCdBbBH/K85ACGEUC6f8eQErpFyCHE1FpCFYgdACCHS09M9PT1DQkJkB4FtGzt2rIeHB89PALJQ7ACI2tpavV4fHh7u6Gh7t2fAqjg6OoaHh+v1+vbHHAVgJhQ7AGLXrl1VVVVch4VJ6HS6K1eu7N69W3YQwB51XOwcmmk9pcW3ANgiRrCDCTGaHSARZ+wAiOzsbGdn59DQUNlBoAahoaFOTk48PwFI0d79NLIGIgZgSY2NjVlZWcHBwW5ubrKzQA3c3d2Dg4MzMzMbGxsZFhGwMP7JAfauoKCgrKwsPj5edhCoR3x8fFlZ2Z49e2QHAewOxQ6wd5mZmUKIqKgo2UGgHtHR0eK3QwuAJVHsAHuXnp7u6Oio/CUGTCI6OtrR0ZHnJwDLo9gBds1gMGRkZIwZM8bDw0N2FqiHh4dHYGBgRkYG92oDFkaxA+zaoUOHLly4wAh2MDmdTnf+/PnDhw/LDgLYF4odYNe2bt0qhODJCZicclApBxgAi6HYAXYtMzNTo9Fwxg4mp9PpHBwceH4CsDCKHWDX0tPTR4wY4ePjIzsI1KZXr14jRozg+QnAwih2gP06fPjwmTNnuA4LM4mPjz99+vSRI0dkBwHsCMUOsF/KZTIGOoGZKIdWRkaG7CCAHaHYAfYrNTXVwcEhLi5OdhCoU1xcnIODA89PAJZEsQPsV1ZW1vDhw3v16iU7CNSpd+/e/v7+WVlZsoMAdoRiB9ip48ePnzhxIiYmRnYQqFlsbKxypMkOAtgLih1gp5QLZAkJCbKDQM0YzQ6wMIodYKeUJyeioqJkB4GaKQcYo9kBFkOxA+zU1q1b/f39+/TpIzsI1Kxv377Dhg3jjB1gMRQ7wB6dOHHi+PHjsbGxsoNA/WJjY4uLi0+ePCk7CGAXKHaAPWIEO1iMcphxNRawDIodYI9SU1MFT07AIhITE8VvhxwAc6PYAfYoPT196NCh3GAHC+jTp8+QIUN4aSxgGRQ7wO6cPHny2LFj3GAHi4mNjT169OipU6dkBwHUj2IH2J0tW7aI3wYYAyxAOdiUAw+AWVHsALujvJSdJydgMcrBphx4AMyKYgfYna1btw4dOrR///6yg8Be+Pn5DRkyhNHsAAug2AH25dSpUydOnOAGO1iY8tLY06dPyw4CqBzFDrAvaWlpQoi4uDjJOWBnlENOOfwAmA/FDrAvW7ZscXBwGDdunOwgsC8JCQkODg48PwGYG8UOsC8ZGRlDhw719fWVHQT2RRnNjucnAHOj2AF25NixY8XFxcqbAAALS0xMVI5A2UEANaPYAXZEOV8SExMjOwjskXLgcdIOMCuKHWBHUlNTHRwceHICUsTFxTk4OPDSWMCsKHaAvTAYDCkpKaNGjbruuutkZ4E9+t3vfjdy5MiffvpJdhBAzSh2gL04dOjQ2bNnOV0HieLi4s6ePXvo0CHZQQDVotgB9kIZaYInJyCRMs4Og54A5kOxA+xFRkaGRqOJioqSHQT2KyoqSqPR8PwEYD4UO8AuGAyGtLS0wMDAnj17ys4C+9WzZ8+AgICtW7caDAbZWQB1otgBdmHPnj2lpaW8cALSjRs3rrS0tLCwUHYQQJ0odoBd4BWxsBK8NBYwK4odYBdSUlK6desWGxsrOwjsXVxcXLdu3VJSUmQHAdSJYgeoX0NDQ2ZmZkhIiJubm+wssHdubm4hISGZmZkNDQ2yswAqRLED1G/Hjh2XLl3iBjtYicTExF9//XXnzp2ygwAqRLED1E+57EWxg5VQDkWuxgLmQLED1C8tLc3NzS00NFR2EEAIIUJDQ93c3Hh+AjAHih2gclVVVZmZmbGxsc7OzrKzAEII0a1bt5iYmIyMjKqqKtlZALWh2AEql5eXV11dzUAnsCpxcXHV1dX5+fmygwBqQ7EDVE55L2dCQoLsIMB/KAckL40FTI5iB6jc5s2be/XqFRQUJDsI8B/BwcE9e/bcvHmz7CCA2lDsADW7dOnSzp07lTevy84C/IdGo4mOjt6xY0d5ebnsLICq8LseULOtW7fW19cnJSXJDgK0lJSUVF9fv3XrVtlBAFWh2AFqpowowQ12sELKYcmgJ4BpUewANUtJSfHz8xs2bJjsIEBL/v7+fn5+DFMMmBbFDlCt06dP79u37+abb5YdBGhbUlLS3r17T58+LTsIoB4UO0C1lLuX4uPjZQcB2qYcnFyNBUyIYgeo1ubNmzUaDU9OwGrdfPPNGo2GQU8AE6LYAaqVmpo6cuTIXr16yQ4CtK1Xr14jR45MTU2VHQRQD4odoE579+4tKSnhBjtYuaSkpDNnzuzdu1d2EEAlKHaAOvEmMdgE5RDlpB1gKhQ7QJ02bdrk7OwcHR0tOwjQnpiYGGdn502bNskOAqgExQ5QoaqqqrS0tKioKHd3d9lZgPa4u7vrdLr09PSamhrZWQA1oNgBKpSbm1tdXc11WNiEhISEK1eu6PV62UEANaDYASqkXNiaMGGC7CBAx5QDlauxgElQ7AAVSklJ8fHxGTNmjOwgQMfGjBnTs2dP3i0GmATFDlCbs2fP7tq1KykpSaPhHzhsgPb/t3fncVHVCx/Hf8MgMjCiQigqWJkLrqm5dF1RUVEM0QJ3sSy7aU/ZZre6ZvaolWLeLMkyBU1FZdNisVTEfctscV+RRRFRZJNNmOePcx8uF5QQBn7Mmc/7j152OHPO9zBzznw5Z85vtNphw4b9+uuvqampsrMAJo/jPqA2u3fvNhgM7u7usoMAleXu7m4wGJQxegBUB8UOUBvlC5qGDh0qOwhQWcoX3/HdYkD1UewAVTEYDNu3b+/UqZOLi4vsLEBlubi4dOzYcfv27QaDQXYWwLRR7ABVOXny5I0bN7gOC5Pj7u6ekpJy6tQp2UEA00axA1SFgU5gohj0BDAKih2gKjt37qxfvz7fJAaT079///r16zPoCVBNFDtAPe7evbt3796BAwfa2NjIzgI8HFtb2wEDBuzZs+fu3buyswAmjGIHqMf+/fvz8vKUGwwBkzNs2LC8vLwDBw7IDgKYMIodoB7KaBF8wA4mSnnpMugJUB0UO0A9oqKiWrZs2bFjR9lBgKro1KlTy5Yto6KiZAcBTBjFDlCJhISEs2fPMtAJTNqQIUPOnDmTmJgoOwhgqih2gEpER0cLIUaOHCk7CFB1ygtYeTEDqAKKHaASO3bs0Gq1gwcPlh0EqLrBgwdrtdodO3bIDgKYKoodoAb5+fk//fRT3759GzduLDsLUHX29vZ9+vT5+eefCwoKZGcBTBLFDlCDw4cP5+TkcD8sVMDDwyMrK+vw4cOygwAmiWIHqEFMTIwQghHsoALKy1h5SQN4WBQ7QA2ioqKcnJy6d+8uOwhQXd27d3dycmLQE6BqKHaAyUtMTDx58uSIESM0Go3sLEB1WVhYeHh4/Pnnn0lJSbKzAKaHYgeYPAY6gcow6AlQZRQ7wOT9/PPPDHQCNRkyZIhWq+W7xYAqoNgBpi0vL08Z6MTe3l52FsA4lEFPtm/fnp+fLzsLYGIodoBpO3DgAAOdQH08PDxycnIOHDggOwhgYih2gGn78ccfhRDPPPOM7CCAMSkvaeXlDaDyKHaAadu+fbuzs3PHjh1lBwGMqVOnTs7Oztu3b5cdBDAxFDvAhJ07d+7cuXNeXl4MdAKV0Wg0zzzzzNmzZ8+dOyc7C2BKKHaACWOgE6gYg54AVUCxA0xYVFSUTqdjoBOo0uDBg3U6HcUOeCgUO8BUZWZm7tu3T3nzk50FMD4bG5tBgwbt3bs3KytLdhbAZFDsAFO1c+fOgoICT09P2UGAmuLp6VlQULBz507ZQQCTQbEDTNWPP/6o0WhGjRolOwhQU0aNGqXRaBj0BKg8ih1gkoqLi6Ojo5988kkXFxfZWYCa0rJlyy5dukRFRRUXF8vOApgGih1gkg4dOpSamjp69GjZQYCa5e3tnZqaeujQIdlBANNAsQNMUlRUlBCCD9hB9Rj0BHgoFDvAJG3bts3Z2blHjx6ygwA1q2fPni1atNi2bZvsIIBpoNgBpufKlSunT5/28PDgCyegehqNxsPD49SpU/Hx8bKzACaAYgeYnoiICCEEH7CDmVBe6srLHkDFKHaA6YmMjLS2th40aJDsIEBtGDx4sLW1dWRkpOwggAmg2AEm5tatW3v37h0+fLitra3sLEBtsLW1HTZs2J49e27duiU7C1DXUewAE/Pzzz8XFRUxLjHMyqhRo4qKinbs2CE7CFDXUewAExMREaHVavmAHczK6NGjtVotH7MD/hLFDjAlBQUFP//8c+/evR0dHWVnAWpPkyZNevXq9dNPPxUUFMjOAtRpFDvAlOzatSsjI2Ps2LGygwC1bezYsRkZGbGxsbKDAHUaxQ4wJcowrXzADmZIedkzUjFQMYodYDKKi4u3bt3q6urarl072VmA2qa88rdu3VpcXCw7C1B3UewAk3H48OEbN25w2wTM1ujRo1NSUo4cOSI7CFB3UewAk7F161YhxJgxY2QHAeRQXvzcGwtUgGIHmIzw8HBnZ+devXrJDgLI0bt37xYtWlDsgApQ7ADTcPLkyUuXLo0ZM0aj0cjOAsih0WjGjBlz8eLFU6dOyc4C1FEUO8A0KNdhGegEZk7ZBZTdAUB5plTsNA9DdljAyMLCwhwdHfv37y87CCBT//79H3nkkbCwMNlBgDrKlIrdiy++2KRJE9kpAAkuXLjw22+/eXl5abVa2VkAmSwtLb28vE6cOHHx4kXZWYC6yJSK3apVq65cuTJgwAAhhOGvyA4LGFN4eLjgOiwghPj/HUHZKQCUYUrFTghhY2MzZ84c2SmA2hYREWFnZzdkyBDZQQD53N3d7ezsKHbAfZlYsRNCPP3007IjALUqISHh6NGjo0aNql+/vuwsgHz169f39PQ8evRoQkKC7CxAnWN6xc7BwYErrTAroaGhBoPBx8dHdhCgrvDx8TEYDNxCAZRnesUOMDchISENGjQYPny47CBAXeHh4aHX60NCQmQHAeocih1QpyUmJh45cmTUqFE6nU52FqCu0Ol0o0aNOnz4cFJSkuwsQN1CsQPqtJCQEIPBMH78eNlBgLpl/PjxBoOBk3ZAGZayAxifMjpxJT+HV1RUFB0dnZeXV8E88fHxQoji4mJjpAMeTnh4uF6vHzp0qOwgQN0ybNgwvV4fHh7+xhtvyM4C1CEqLHYPZc+ePV5eXpWZU6l3QG26evXqwYMHJ06cyHVYoAydTufl5RUcHJyQkNCyZUvZcYC6QoXF7qHumR04cGBsbGxRUVEF8/j7+//000+PPfZYdZMBD2nr1q0Gg4FxiYH7Gjt27MaNG7du3fraa6/JzgLUFSosdg9Fq9UOGjSo4nk2bNgghLCw4POIqG0bN25s2LChp6en7CBAXeTp6dmwYcONGzdS7IASlBWgjoqPjz927BjjEgMPYm1tPWrUqKNHj169elV2FqCuML1il5CQ8PHHHw8aNKhFixY6nc7S0tLOzs7V1dXX1zcwMDAnJ0d2QMA4goODDQbDhAkTZAcB6i7l3tiNGzfKDgLUFSZW7AICAtq2bTtv3ry4uLhr167l5eUVFRVlZWWdO3cuJCTkhRdeaNeu3fbt22XHBIwgJCSE74cFKqZ8b2xoaKjsIEBdYUrFLjIyctasWYWFhePHj9+wYcOFCxfS09Pv3buXk5Nz6dKliIiIMWPGJCcnjx49+tChQ7LDAtVy/vz5EydOjB071traWnYWoO6ytrYeM2bMr7/+ev78edlZgDrBlIqdv7+/EGLZsmXBwcETJ05s3bp1o0aNtFqtjY1Nq1atvL29w8PD58yZU1BQ8PHHH8sOC1TLpk2bhBCMSwz8JWU32bx5s+wgQJ1gSsXuxIkTQohp06ZVMM/bb78thDh69GjtRAJqyObNmx0dHQcPHiw7CFDXDRkyxNHRkWIHKEyp2CkDjhQUFFQwj1arFUIUFhbWUiagBvz++++nT5/29fWtV6+e7CxAXVevXj0fH59Tp0798ccfsrMA8plSsevevbsQYvHixRXM8/nnn5fMCZgo5RY/rsMClaTsLMqYo4CZM6ViN3fuXK1Wu2TJkqFDh27cuPH8+fM5OTnFxcVZWVlXrlzZsmWLl5fXwoULLSws3n//fdlhgSoyGAybN29u2bJl3759ZWcBTEPfvn1dXFw2b978UN88BKiSKX3zhJubW2ho6IwZM3bu3Llz5877zqPX61euXDls2LBazgYYy8GDB69evfruu+9qNBrZWQDTYGFhMXHixM8+++zQoUN9+vSRHQeQyZTO2AkhvL294+Pjv/vuuwkTJrRt29be3l6r1ep0upYtW3p4eCxdujQ+Pn7SpEmyYwJVFxgYKP7qJiEAZfj5+Yn/330Ac2ZKZ+wUNjY206dPnz59uuwggPHl5+eHhYV16dLF1dVVdhbAlLRv375z585hYWFfffUV38IHc2ZiZ+wAdYuKirpz5w5nnYEqmDRpUnp6enR0tOwggEwUO6AOCQ4OtrCw4PthgSqYMGGChYVFcHCw7CCATBQ7oK7IyMiIjIwcPHiwi4uL7CyA6WnZsuWgQYN+/PHHjIwM2VkAaSh2QF0REhKSl5c3depU2UEAUzV16tS8vLyQkBDZQQBpKHZAXbF27Vq9Xj927FjZQQBTNXbsWL1ev27dOtlBAGkodkCdcOnSpQMHDjz77LO2trayswCmSvnTaP/+/ZcvX5adBZCDYgfUCevWrTMYDFyHBarJz8/PYDBw0g5mi2IHyFdcXBwUFPToo4+6ubnJzgKYNjc3t5YtWwYFBRUXF8vOAkhAsQPki42NTUhImDx5soUFuyRQLRYWFpMnT7569eru3btlZwEk4F0EkE+5bMR1WMAolF2Jq7EwTxQ7QLLMzMywsLA+ffq0bdtWdhZADdq1a9enT5+wsLDMzEzZWYDaRrEDJNu0adPdu3dfeOEF2UEA9XjhhRdycnI2b94sOwhQ2yh2gGRr1qzR6/Xjxo2THQRQD19fX1tb2zVr1sgOAtQ2ih0g06lTp44cOeLr66vX62VnAdSjQYMGvr6+hw8fPn36tOwsQK2i2AEyKWcUuA4LGJ2yW3HSDuaGYgdIk5+fv27dOldX1z59+sjOAqhN3759XV1d165dm5+fLzsLUHsodoA04eHhaWlpM2bM0Gg0srMAaqPRaF566aW0tLSIiAjZWYDaQ7EDpFm1apW1tbWfn5/sIIA6+fn5WVtbf/vtt7KDALWHYgfIce7cubi4uOeee87e3l52FkCdHBwcnn322bi4uPPnz8vOAtQSih0gx6pVqwwGw4wZM2QHAdRsxowZBoNh1apVsoMAtYRiB0iQn5+/du3atm3b9uvXT3YWQM369+/fpk0bbqGA+aDYARKEhYWlpaW98sor3DYB1CiNRvPKK6/cvHkzPDxcdhagNlDsAAkCAgJ0Op3yVeUAapRyC0VAQIDsIEBtoNgBte3kyZMHDhzw9fXltgmgFtjb2/v6+u7fv//UqVOyswA1jmIH1LaVK1cKIWbOnCk7CGAulN1N2fUAdaPYAbUqKyvr+++/79mzZ69evWRnAcxF7969e/TosW7duqysLNlZgJpFsQNqVWBgYGZmJqfrgFo2c+bMzMzMoKAg2UGAmkWxA2qPwWBYsWKFg4PDuHHjZGcBzMv48eMdHBxWrFhhMBhkZwFqEMUOqD07duw4f/789OnTdTqd7CyAedHpdC+88MK5c+d27twpOwtQgyh2QO1Zvny5Vqt95ZVXZAcBzNErr7yi1WqXL18uOwhQgyh2QC05f/58TEzM6NGjH3vsMdlZAHP0+OOPe3l5RUdHX7hwQXYWoKZQ7IBasnz58uLi4tdff112EMB8vf7668XFxZy0g4pR7IDacOfOnbVr1z711FMDBgyQnQUwXwMHDuzevfvatWszMjJkZwFqBMUOqA2rVq3Kzs7mdB0g3euvv56VlbVq1SrZQYAaQbEDalxhYeEXX3zRrFkzRjkBpBs3bpyTk9MXX3xRWFgoOwtgfBQ7oMaFhIQkJyfPnDnTyspKdhbA3NWvX3/mzJlJSUmhoaGyswDGR7EDatyyZcv0ej3fNgHUETNnzrS1tV22bJnsIIDxUeyAmrV79+5ffvll+vTp9vb2srMAEEIIBweH6dOnHzt2LC4uTnYWwMgodkDN8vf3t7S0nD17tuwgAP7jjTfesLS0XLJkiewggJFR7IAa9Pvvv8fExPj6+jIoMVCnPPbYYz4+PjExMb///rvsLIAxUeyAGvTpp58aDIa3335bdhAAZb399tsGg+Gzzz6THQQwJoodUFOuXLkSGhrq4eHRrVs32VkAlNW9e/fhw4eHhITEx8fLzgIYDcUOqCmLFy++d+/ee++9JzsIgPt777337t27t3jxYtlBAKOh2AE14vr160FBQb179+Y7xIA6a+DAgb179w4MDLx+/brsLIBxUOyAGrFkyZK8vLwPPvhAdhAAFXn//ffz8vL8/f1lBwGMg2IHGF9KSsrKlSu7d+8+atQo2VkAVOSZZ57p1q3b119/fePGDdlZACOg2AHGt2zZstzc3Hnz5mk0GtlZAFREo9HMmzcvNzeXL6KAOlDsACO7efNmQEBAly5dnnnmGdlZAPw1Ly+vzp07r1ix4ubNm7KzANVFsQOMzN/fPzs7+6OPPuJ0HWASNBrNRx99lJ2dvXTpUtlZgOqi2AHGlJqaumLFim7dunl7e8vOAqCyxowZ07Vr16+++io1NVV2FqBaKHaAMX322Wc5OTmcrgNMi3LSLicnhzHtYOoodoDRJCUlBQQE9OzZk0/XASbHy8urR48eAQEBSUlJsrMAVUexA4xm4cKFeXl58+fP53QdYHI0Gs38+fNzc3MXLVokOwtQdRQ7wDiuXLmyZs2aAQMGjBgxQnYWAFUxcuTI/v37r169+sqVK7KzAFVEsQOM48MPPywoKPj0009lBwFQdZ9++mlBQcG8efNkBwGqiGIHGMHx48c3btzo7e39t7/9TXYWAFXXp0+f0aNHb9iw4ddff5WdBagKih1gBHPmzNFoNHw0B1CBRYsWaTSaOXPmyA4CVAXFDqiun3/+OTY21s/Pr3379rKzAKiuDh06TJ06ddeuXTt27JCdBXhoFDugWoqKiubMmaPT6T766CPZWQAYx/z583U63Zw5c4qKimRnAR4OxQ6olsDAwN9///2tt95ycXGRnQWAcbi4uLz55pu//fZbUFCQ7CzAw6HYAVWXlZU1d+7cZs2avfvuu7KzADCmf/zjH82aNZs7d252drbsLMBDoNgBVbdo0aKUlJSFCxfq9XrZWQAYk16vX7BgwfXr17kpCqaFYgdU0cWLFz///PPu3bv7+fnJzgLA+KZNm9atW7elS5deunRJdhagsih2QBXNnj27sLDwiy++sLBgPwJUyMLC4osvvigsLJw9e7bsLEBl8YYEVEV0dHRUVNSUKVP69esnOwuAmtK/f//JkydHRkbGxMTIzgJUCsUOeGh5eXmzZ8/W6/WffPKJ7CwAatann35qa2v7+uuv5+Xlyc4C/DWKHfDQFixYcOHChXnz5jVv3lx2FgA1q3nz5vPmzbtw4cLChQtlZwH+GsUOeDjnz5/39/fv1q0bH7sBzMQbb7zRtWvXJUuWnD9/XnYW4C9Q7ICHYDAYXn755cLCwoCAAEtLS9lxANQGS0vLgICAwsLCl19+2WAwyI4DVIRiBzyE1atXx8XFzZgx4+mnn5adBUDt+dvf/vbSSy/FxcWtWbNGdhagIhQ7oLJSUlLeeecdJycnBiwFzNAnn3zi5OT0zjvvpKSkyM4CPBDFDqis11577c6dO19++WXjxo1lZwFQ2xo3brx8+fL09PTXXntNdhbggSh2QKWEhYWFhISMHTv2ueeek50FgBw+Pj5jxowJCQkJDw+XnQW4P4od8NfS0tJmzpzp6Oi4cuVK2VkAyLRy5cpHHnlk5syZaWlpsrMA90GxA/7aK6+8kpqaunz5ckdHR9lZAMjUpEmT5cuX37hxY+bMmbKzAPdBsQP+wsaNG0NDQ319fcePHy87CwD5JkyY4OPjExISEhwcLDsLUBbFDqhIYmLiq6++2rx584CAANlZANQVX3/9dbNmzV599dXExETZWYD/QrEDHujevXsTJ068c+fO6tWrHRwcZMcBUFc4ODisXr06PT190qRJ9+7dkx0H+A+KHfBAixYt2r9//6uvvurh4SE7C4C6ZcSIEbNmzdq3b98nn3wiOwvwHxQ74P4OHTq0YMGC7t27L1myRHYWAHWR8rWSbI//AAAgAElEQVTR//u//3v48GHZWYB/o9gB95Gamurr62tlZbV58+b69evLjgOgLqpfv/7mzZutrKx8fHxu3rwpOw4gBMUOKM9gMPj5+SUlJa1YsaJ169ay4wCou9q0abNixYqkpCQ/Pz+DwSA7DkCxA8pZsGDB9u3bX3zxRT8/P9lZANR1fn5+06dPj4mJWbhwoewsAMUO+G87duyYP39+165dly9fLjsLANPw5Zdfdu3a9aOPPtqxY4fsLDB3FDvgPy5fvjx+/Hh7e/uIiAidTic7DgDToNPpIiIiGjduPGHChCtXrsiOA7NGsQP+LSMjY9SoUXfu3Nm0adNjjz0mOw4AU/LYY49t2rQpPT3d09MzIyNDdhyYL4odIIQQRUVFEydOPHPmzJIlSwYPHiw7DgDTM2TIkMWLF585c2bSpElFRUWy48BMUewAIYSYM2dOdHT09OnT33zzTdlZAJiqt95664UXXoiKipozZ47sLDBTFDtArFq16vPPP+/bty9fCAugmr7++uu+fft+/vnn3333newsMEcUO5i7sLCwmTNntmvXbtu2bVZWVrLjADBtVlZW27Zta9eu3SuvvBIeHi47DswOxQ5m7eDBg1OmTHFwcIiJiXFwcJAdB4AaODg4REdH29vbT548+eDBg7LjwLxQ7GC+Tpw44enpqdVqIyMjH3/8cdlxAKhHq1atIiMjLSwsPD09f/vtN9lxYEYodjBTly5dGjFiRG5u7rZt23r06CE7DgC16dmz57Zt23Jzcz08PC5fviw7DswFxQ7m6NKlS25ubmlpaevXr2dwEwA1ZMiQId9//31aWtrAgQMvXbokOw7MAsUOZichIcHd3f3atWtBQUHPPfec7DgA1MzHxycwMPDatWvu7u4JCQmy40D9KHYwL1evXh0wYMDVq1cDAwMnT54sOw4A9ZsyZUpgYGDJwUd2HKgcxQ5m5OLFiwMHDkxMTAwMDJw6darsOADMxdSpU9esWZOYmOjm5nbx4kXZcaBmFDuYiz///LN///7JyclBQUF+fn6y4wAwL9OmTQsKCkpKShowYMCff/4pOw5Ui2IHsxAbG9uvX787d+6EhYVNmTJFdhwA5mjKlCmhoaHp6en9+vXbvXu37DhQJ4od1C84OHjkyJFCiJiYGC8vL9lxAJiv0aNHx8TEGAyGESNGBAcHy44DFaLYQeU+++yzyZMnOzo67tmzx83NTXYcAObOzc1t7969jo6OkydPXrx4sew4UBuKHVSroKDg+eef/8c//tGpU6cDBw507dpVdiIAEEKIrl277t+/v2PHju++++7zzz9fUFAgOxHUg2IHdUpKSho4cGBQUJC3t/eBAwdatmwpOxEA/Mejjz568ODB0aNHBwUFubm5JSUlyU4ElaDYQYXi4uJ69ux55MiR999/PywsTK/Xy04EAGXp9frw8PD333//8OHDPXv2jIuLk50IakCxg6oYDAZ/f/9hw4bl5OQEBwcvXLjQwoIXOYA6ysLCYuHChRs3bszJyRk2bNjSpUsNBoPsUDBtvOdBPVJTUz09Pd955502bdocOXJk3LhxshMBwF8bP378kSNHWrdu/fbbb3t6et68eVN2Ipgwih1UIjw83NXVNSYmZsaMGceOHWvfvr3sRABQWe3bt//ll19mzJgRExPj6uoaEREhOxFMFcUOJi8tLW3KlCnPPvushYVFWFjYN998Y2NjIzsUADwcGxubb775JiwsTAgxduzYqVOnpqWlyQ4F00Oxg2kLDQ3t3Lnz+vXrvb29T58+PXbsWNmJAKDqxo4de+bMGW9v7++//75Lly6hoaGyE8HEUOxgquLj45955hkfH5/CwsINGzZEREQ0adJEdigAqK4mTZpERESsX7++oKDAx8fHy8srPj5ediiYDIodTE9WVtY///lPV1fXqKioadOmnT17duLEibJDAYAxTZo06ezZs9OmTYuMjHR1df3nP/+ZlZUlOxRMAMUOpuTevXurV69u3779woULXV1d4+LiAgMDH3nkEdm5AMD4HnnkkcDAwN27d7u6ui5cuLB9+/arV6++d++e7Fyo0yh2MA0Gg2HLli0dO3Z88cUX8/PzV6xYcezYsQEDBsjOBQA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"text/plain": [
"Plot with title “Distribuição normal padronizada”"
]
},
"metadata": {
"image/svg+xml": {
"isolated": true
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},
"output_type": "display_data"
}
],
"source": [
"# Visualizando distribuição normal padronizada\n",
"#graphics.off()\n",
"plot(xZ, fnZ, type = 'l', main = \"Distribuição normal padronizada\", xlab = \"Variável dependente\", ylab = \"Freq\", xaxt='n')\n",
"xtick <- seq(-4,4,1)\n",
"axis(1, at = xtick)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Portanto, a partir desta padronização da distribuição é possível calcular a proporção da população em uma faixa de valor, por meio da área sob a curva de distribuição. Por exemplo, suponha que você deseja saber qual a probabilidade de que um indivíduo desta população tenha valor maior que 12,6. Bom para isto é fácil pois sabemos que a área total da curva é 1 e que a média corresponde a 50% da distribuição. Portanto, a probabilidade é 0.5. \n",
"Mas suponha que agora você queira calcular a probabilidade de obter um valor maior que 13. Primeiro, precisamos converter este valor para um medida padronizada que é o escore Z.\n",
"\n",
"$$ z = \\frac{x - \\mu}{\\sigma} $$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"0.173913043478261"
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"[1] 0.173913"
]
},
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],
"source": [
"# Calculando o escore Z\n",
"z <- (13 - 12.6)/2.3\n",
"z"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Portanto, podemos dizer que a probabilidade é um pouco menor que 0.5 uma vez que este valor é maior que a média. Porém para determinarmos a probabilidade correta é necessário obter a área sob a curva da distribuição. Em geral, nas disciplinas de estatística isto é feito por meio de tabelas mas vamos usar o R para fazer isto."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"0.430966900814878"
],
"text/latex": [
"0.430966900814878"
],
"text/markdown": [
"0.430966900814878"
],
"text/plain": [
"[1] 0.4309669"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Assumindo distribuição normal padronizada podemos obter a proporção\n",
"pZ <- pnorm(z, mean = 0, sd = 1)\n",
"1-pZ"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Portanto, concluímos que a proporção da população que apresenta valores maiores que 13 é de 43%.\n",
"\n",
"O gráfico abaixo mostra a área da curva de distribuição que corresponde a esta proporção."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"</g>\n",
"</svg>\n"
],
"text/plain": [
"Plot with title “Distribuição normal padronizada”"
]
},
"metadata": {
"image/svg+xml": {
"isolated": true
}
},
"output_type": "display_data"
}
],
"source": [
"# Visualizando distribuição normal padronizada\n",
"#graphics.off()\n",
"plot(xZ, fnZ, type = 'l', main = \"Distribuição normal padronizada\", xlab = \"Variável dependente\", ylab = \"Freq\", xaxt='n')\n",
"xtick <- seq(-4,4,1)\n",
"axis(1, at = xtick)\n",
"\n",
"# Obtendo o indice da região com maior que o valor crítico\n",
"ipZ <- xZ > z\n",
"\n",
"# Preenchendo a área sob a curva\n",
"polygon(c(z,xZ[ipZ],4),c(0,fnZ[ipZ],0), col = \"red\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Intervalo de confiança\n",
"Na maioria das situações não é possível obter os parâmetros da população e temos de usar estimativas de amostras extraídas desta população. De fato, na maioria dos casos de apenas uma única amostra. Uma questão óbvia que surge quando realizamos uma pesquisa é qual é o tamanho da amostra? A resposta mais usada é quanto mais melhor. Vamos entender qual é a associação entre o tamanho da amostra e a validade da estatística inferencial.\n",
"\n",
"Suponha que você esteja interessado em saber qual é o comprimento médio das pernas da população de São Bernardo do Campo que está por volta de 817 mil habitantes. Obviamente, você não vai medir todos os habitantes mas provavelmente obter as medidas de uma amostra desta população. Então a média desta amostra é chamada de estimativa pontual, ou seja, é o valor que estima o parâmetro da população.\n",
"\n",
"A pergunta seguinte é \"Quão boa é esta estimativa?\"\n",
"\n",
"Infelizmente, é impossível saber com exatidão quão perto esta estimativa pontual está do verdadeiro parâmetro da população. Portanto, os estatísticos preferem estimar o intervalo ao invés de um ponto. \n",
"\n",
"O grau de confiança de um intervalo estimado é a probabilidade que este intervalo inclua o verdadeiro parâmetro (ex. a média da população) e considerando que uma amostra grande seja usada e que o processo para obter a estimativa do parâmetro sejam repetidas. Portanto, o intervalo de confiança é usada para indicar a precisão da estimativa obtida pela amostra.\n",
"\n",
"\n",
"Por exemplo, suponha que você obtenha a média de 100 habitantes escolhidos aleatoriamente de SBC. Se você repetir este processo 30 vezes, você vai obter um distribuição das médias destas amostras que muito provavelmente terá distribuição normal."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Intervalo de confiança para sigma conhecido\n",
"\n",
"$$ \\left[\\bar{x} - Z_{\\alpha/2}\\:\\sigma/\\sqrt{n},\\quad \\bar{x} + Z_{\\alpha/2}\\:\\sigma/\\sqrt{n}\\right] $$\n",
"\n",
"\n",
"O termo $Z_{\\alpha/2}\\:\\sigma/\\sqrt{n}$ também é conhecido como **margem de erro da média** e representa o máximo erro da estimativa ou a máxima diferença entre o ponto estimado pela amostra e o valor real do parâmetro.\n",
"\n",
"Exemplo retirado do livro do Bluman\n",
"\n",
"A survey of 30 emergency room patients found that the average waiting time for treatment\n",
"was 174.3 minutes. Assuming that the population standard deviation is 46.5 minutes, find the\n",
"best point estimate of the population mean and the 99% confidence of the population mean"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"2.5758293035489"
],
"text/latex": [
"2.5758293035489"
],
"text/markdown": [
"2.5758293035489"
],
"text/plain": [
"[1] 2.575829"
]
},
"metadata": {},
"output_type": "display_data"
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],
"source": [
"m <- 174.3 # média da amostra\n",
"sigma <- 46.5 # desvio padrão da população\n",
"n <- 30 # tamanho da amostra\n",
"\n",
"# Obtendo Z para alpha/2\n",
"alpha <- 0.01\n",
"Zalpha <- qnorm(1-alpha/2, mean = 0, sd = 1)\n",
"Zalpha"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<ol class=list-inline>\n",
"\t<li>152.4</li>\n",
"\t<li>196.2</li>\n",
"</ol>\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 152.4\n",
"\\item 196.2\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 152.4\n",
"2. 196.2\n",
"\n",
"\n"
],
"text/plain": [
"[1] 152.4 196.2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Intervalo de confiança de 99%\n",
"ic99 <- m + (Zalpha*(sigma/sqrt(n)))*c(-1,1)\n",
"round(ic99, digits = 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Portanto, podemos ser 99% confiantes que a média do tempo de espera para o tratamento está entre 152.4 a 196.2 minutos."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Intervalo de confiança para sigma desconhecido\n",
"\n",
"Na maioria dos casos não é possível conhecer a variância da população e, portanto, é necessário usar o desvio padrão da amostra. Nestes casos não é possível usar a distribuição Z, principalmente quando a amostra é pequena. Então usamos uma outra família de distribuição conhecida como distribuição Student t. Na prática, a distribuição t vai levar em conta o tamanho da amostra e ajustar os valores de probabilidade para aumentar o intervalo de confiança.\n",
"\n",
"O cálculo do intervalo de confiança para estes casos é feito da seguinte forma.\n",
"\n",
"$$ \\left[\\bar{x} - T_{n-1}\\:s/\\sqrt{n},\\quad \\bar{x} + T_{n-1}\\:s/\\sqrt{n}\\right] $$\n",
"\n",
"Onde s é o desvio padrão da amostra. Como a distribuição T leva em conta os graus de liberdade, o tamanho da amostra deve ser informado.\n",
"\n",
"Exemplo\n",
"\n",
"Ten randomly selected people were asked how long they slept at night. The mean time\n",
"was 7.1 hours, and the standard deviation was 0.78 hour. Find the 95% confidence\n",
"interval of the mean time. Assume the variable is normally distributed."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<ol class=list-inline>\n",
"\t<li>6.54</li>\n",
"\t<li>7.66</li>\n",
"</ol>\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 6.54\n",
"\\item 7.66\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 6.54\n",
"2. 7.66\n",
"\n",
"\n"
],
"text/plain": [
"[1] 6.54 7.66"
]
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"metadata": {},
"output_type": "display_data"
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],
"source": [
"# Calculando o intervalo de confiança\n",
"m <- 7.1 # média da amostra\n",
"sd <- 0.78 # desvio padrão da amostra\n",
"alpha <- 1-0.95\n",
"n <- 10 # tamanho da amostra\n",
"df <- n - 1 # degrees of freedom\n",
"\n",
"tAlpha <- qt(1-alpha/2,df) # valor critico\n",
"\n",
"icT95 <- m + (tAlpha*(sd/sqrt(n)))*c(-1,1)\n",
"round(icT95, digits = 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Therefore, one can be 95% confident that the population mean is between 6.54 and\n",
"7.66 inches."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tamanho da amostra\n",
"Uma pergunta constante em estatística e pesquisa em geral é \"qual é o tamanho da amostra para que eu tenha uma estimativa exata de um parâmetro?\"\n",
"\n",
"Para isto é necessário saber:\n",
"* o quanto a sua estimativa pode estar distante do valor desejado (1, 2, 3 unidades)\n",
"* quão confiante você pretende ser com esta estimativa\n",
"\n",
"Então será necessário informações a respeito da margem de erro, do desvio padrão da população e do grau de confiança.\n",
"\n",
"O cálculo amostral pode ser feito a partir da margem de erro\n",
"\n",
"$$E = Z_{\\alpha/2}\\:\\sigma/\\sqrt{n}$$\n",
"\n",
"Rearranjando obtemos\n",
"\n",
"$$n = \\left(Z_{\\alpha/2}\\:\\sigma/E \\right)^2 $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exemplo:\n",
"\n",
"A scientist wishes to estimate the average depth of a river. He wants to be 99%\n",
"confident that the estimate is accurate within 2 feet. From a previous study, the standard\n",
"deviation of the depths measured was 4.33 feet."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"32"
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"text/latex": [
"32"
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"text/markdown": [
"32"
],
"text/plain": [
"[1] 32"
]
},
"metadata": {},
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}
],
"source": [
"E <- 2 # margem de erro\n",
"sigma <- 4.33 # standard deviation\n",
"alpha <- 1-0.99\n",
"\n",
"# Z-score\n",
"zAlpha <- qnorm(1-alpha/2, mean = 0, sd = 1)\n",
"\n",
"# Sample size\n",
"n <- ((zAlpha*sigma)/E)^2\n",
"ceiling(n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Therefore, to be 99% confident that the estimate is within 2 feet of the true mean depth, the scientist needs at least a sample of 32 measurements. "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.3.0"
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