Soluciones/Práctica9.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4977e15f-bead-450d-b61a-5a4107b985e3",
   "metadata": {},
   "source": [
    "# Práctica 9\n",
    "\n",
    "Recomiendo ver estos videos que explican muy bien todo el tema de test de hipótesis: [parte 1](https://www.youtube.com/watch?v=hNwyqqgk7Gw) y [parte 2](https://www.youtube.com/watch?v=HLYywpjzGUo)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8a0cefc-37c4-4183-a582-38c04821f10b",
   "metadata": {},
   "source": [
    "## Ejercicio 1\n",
    "\n",
    "Un productor agropecuario cultiva una variedad de soja cuyo rendimiento por hectárea (ha.) puede considerarse una variable aleatoria con distribución $\\mathcal{N}(37,25)$. Un vendedor de granos pone a la venta una nueva variedad de soja, diciendo que tiene un rendimiento mayor. El productor agropecuario realizó una compra de esta nueva variedad y quiere asegurarse de que tienen un rendimiento mayor que las semillas que compra habitualmente. Con ese fin decide cultivar 10 parcelas de 1 ha., observar sus rendimientos y aplicar un test de hipótesis de nivel 0.05. Suponiendo que el rendimiento por ha. de la nueva variedad de soja tiene una distribución normal con varianza 25, resolver los siguientes ítems."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "394cb079-dc1c-4836-83f9-659a1e4120d5",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Definir las variables aleatorias y los parámetros involucrados en este problema y plantear el test de hipótesis que debe realizar el productor agropecuario.\n",
    "\n",
    "$X_1, \\dots, X_{10}$ una m.a. del rendimiento de las 10 parcelas cultivadas con la nueva variedad de soja. La m.a. tiene distribución $\\mathcal{N}(\\mu, 25)$.\n",
    "\n",
    "$\\mu_0 = 37$ el rendimiento promedio de la variedad de soja que usa actualmente el productor.\n",
    "\n",
    "$\\sigma^2 = 25$ para ambas variedades.\n",
    "\n",
    "$\\alpha = 0.05$\n",
    "\n",
    "$H_0 : \\mu = \\mu_0$ vs. $H_1 : \\mu > \\mu_0$\n",
    "\n",
    "Estadístico del test: $T = \\sqrt{n} \\frac{\\bar{X} - \\mu_0}{\\sigma_0}$\n",
    "\n",
    "Bajo $H_0 : \\mu = \\mu_0 \\implies T \\sim \\mathcal{N}(0,1)$\n",
    "\n",
    "Región de rechazo: $T \\geq z_\\alpha$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d160b3b-4a72-4d3b-b1f5-699067327c60",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "El productor cultiva las 10 parcelas y obtiene los siguientes rendimientos:\n",
    "\n",
    "```\n",
    "37 - 39.50 - 41.70 - 42 - 40 - 41.25 - 43 - 44.05 - 38 - 38.50\n",
    "```\n",
    "\n",
    "¿Cuál es la conclusión del test en base a estos datos observados?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fc542ee6-8643-4708-b588-94525cdb87f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = c(37, 39.50, 41.70, 42, 40, 41.25, 43, 44.05, 38, 38.50)\n",
    "n = length(X)\n",
    "mu0 = 37\n",
    "alpha = 0.05\n",
    "var0 = 25\n",
    "sd0 = sqrt(var0)\n",
    "T = sqrt(n) * (mean(X) - mu0) / sd0\n",
    "z_alpha = qnorm(alpha, 0, 1, lower.tail=FALSE)\n",
    "T >= z_alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c84c5bcd-54bf-4672-aad7-78a48f816af0",
   "metadata": {},
   "source": [
    "En base a los datos observados, se rechaza $H_0$ y se acepta la nueva $H_1$ (es decir, la nueva variedad de soja rinde más que la vieja)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18d1b20e-a8f0-473c-9e78-7fb917a296af",
   "metadata": {},
   "source": [
    "Calcular la probabilidad del error de tipo II suponiendo que el verdadero rendimiento medio de la nueva variedad de soja es de 40 toneladas por ha.\n",
    "\n",
    "$\n",
    "\\pi(\\mu) = 1 - \\beta(\\mu)\n",
    "\\iff \\beta(\\mu) = 1 - \\pi(\\mu)\n",
    "\\iff \\beta(\\mu) = 1 - \\Big( 1 - \\Phi \\big( z_\\alpha + \\sqrt{n} \\frac{\\mu_0 - \\mu}{\\sigma_0} \\big) \\Big)\n",
    "\\iff \\beta(\\mu) = \\Phi \\Big( z_\\alpha + \\sqrt{n} \\frac{\\mu_0 - \\mu}{\\sigma_0} \\Big)\n",
    "$\n",
    "\n",
    "*Ver desarrollo en el apunte de Bianco y Martínez (2004), página 197.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e70433c5-a692-44a9-8434-93dbe8184f79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.400322295453562"
      ],
      "text/latex": [
       "0.400322295453562"
      ],
      "text/markdown": [
       "0.400322295453562"
      ],
      "text/plain": [
       "[1] 0.4003223"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 40\n",
    "pnorm(z_alpha + sqrt(n) * (mu0 - mu) / sd0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ea28f74-d519-485b-89c0-32876a84c7b1",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Encontrar el test para el caso en que se cultiven $n$ parcelas (con igual nivel)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b2a785f-57c8-4493-b617-2720f90cff6e",
   "metadata": {},
   "source": [
    "### Pregunta D\n",
    "\n",
    "Determinar el número $n$ de parcelas a cultivar para que la probabilidad del error de tipo II sea menor o igual que 0.05 suponiendo que el verdadero rendimiento medio de la nueva variedad de soja es de 40 toneladas por ha.\n",
    "\n",
    "$n \\geq \\Big( \\frac{(z_\\alpha + z_\\beta) \\sigma_0}{\\mu - \\mu_0} \\Big)^2$\n",
    "\n",
    "*Ver desarrollo en el apunte de Bianco y Martínez (2004), páginas 199/200.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "500a0905-c607-400f-8a77-a0db05e2c958",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "31"
      ],
      "text/latex": [
       "31"
      ],
      "text/markdown": [
       "31"
      ],
      "text/plain": [
       "[1] 31"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = 40\n",
    "beta = 0.05\n",
    "z_beta = qnorm(beta, 0, 1, lower.tail=FALSE)\n",
    "n = ceiling((((z_alpha + z_beta) * sd0) / (mu - mu0))^2)\n",
    "n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8dc3462-dd2c-4807-8939-b02e6f8c9df7",
   "metadata": {},
   "source": [
    "### Pregunta E\n",
    "\n",
    "Calcular la función de potencia $\\pi(\\mu)$ del test planteado en c), verificar que es creciente para $\\mu \\in \\mathcal{R}$ y deducir que este test sirve también para testear:\n",
    "\n",
    "$H_0: \\mu \\leq 37$\n",
    "\n",
    "$H_1: \\mu > 37$\n",
    "\n",
    "*Ver desarrollo en el apunte de Bianco y Martínez (2004), páginas 197.*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f62f3aa4-ad7b-488b-ba76-1b5f62f77071",
   "metadata": {},
   "source": [
    "## Ejercicio 2\n",
    "\n",
    "En la construcción de un edificio debe usarse un concreto que tenga una tensión media mayor a 300 psi. Para verificar si el concreto preparado a partir del cemento \"Loma Blanca\" cumple con este requerimiento, se realizan 15 mediciones en forma independiente de la tensión de este concreto. Se observa una media muestral de 304 psi y un desvío estándar muestral de 10 psi. El constructor está dispuesto a correr un riesgo del 5% de comprar cemento \"Loma Blanca\" cuando éste produce un concreto que no cumple con las especificaciones. Suponiendo que los datos están normalmente distribuidos:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "161925e5-6cd5-40c6-88d0-eba71bb9456f",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Plantear el test correspondiente. ¿Qué decisión se toma?\n",
    "\n",
    "$n = 15$\n",
    "\n",
    "$X_1, \\dots, X_{15}$ una m.a. de la tensión del concreto \"Loma Blanca\". La m.a. tiene distribución $\\mathcal{N}(\\mu, \\sigma^2)$.\n",
    "\n",
    "$\\bar{X} = 304$\n",
    "\n",
    "$s = 10$ (desvío estándar muestral)\n",
    "\n",
    "$\\mu_0 = 300$ la tensión media requerida.\n",
    "\n",
    "$\\alpha = 0.05$\n",
    "\n",
    "$H_0 : \\mu \\leq \\mu_0$ vs. $H_1 : \\mu > \\mu_0$\n",
    "\n",
    "Estadístico del test: $T = \\sqrt{n} \\frac{\\bar{X} - \\mu_0}{S}$\n",
    "\n",
    "Bajo $H_0 : \\mu = \\mu_0 \\implies T \\sim t_{n-1}$\n",
    "\n",
    "Región de rechazo: $T \\geq t_{n-1, \\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9a24244f-704a-4338-a4c6-f484b2de1135",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 15\n",
    "Xbar = 304\n",
    "sd = 10\n",
    "mu0 = 300\n",
    "alpha = 0.05\n",
    "T = sqrt(n) * (Xbar - mu0) / sd\n",
    "t_alpha = qt(alpha, n - 1, lower.tail=FALSE)\n",
    "T >= t_alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0ddf29f-db49-4642-9d8c-58f26b844b74",
   "metadata": {},
   "source": [
    "El estadístico $T$ no cae dentro de la región de rechazo y por lo tanto no se rechaza la hipótesis nula $H_0$. Es decir, se invalida la hipótesis alternativa $H_1$ y la decisión es no comprar cemento \"Loma Blanca\" y en cambio buscar un mejor proveedor que garantice mejor la calidad requerida."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "442069cd-9290-4319-82a3-bf84a0e9a4c2",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Acotar el p-valor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b10ba1a4-fa58-4af3-9877-3a0bb98a4145",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0718200001226106"
      ],
      "text/latex": [
       "0.0718200001226106"
      ],
      "text/markdown": [
       "0.0718200001226106"
      ],
      "text/plain": [
       "[1] 0.07182"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt(T, n - 1, lower.tail=FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb2e7ac8-f7c8-4c1c-93ec-6b615b28effc",
   "metadata": {},
   "source": [
    "## Ejercicio 3\n",
    "\n",
    "Se diseñó un nuevo sistema de riego de manera tal que el desvío del tiempo de activación sea menor que 6 segundos. Se lo prueba 11 veces, obteniéndose los siguientes tiempos de activación:\n",
    "\n",
    "```\n",
    "27 41 22 27 23 35 30 24 27 28 22\n",
    "```\n",
    "\n",
    "Suponiendo que el tiempo de activación (en segundos) es una v.a. con distribución normal:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "121a6540-9b34-4296-9ac9-f89adae63947",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "¿Usted decidiría, a nivel 0.05, que el sistema cumple la especificación?\n",
    "\n",
    "$n = 11$\n",
    "\n",
    "$\\sigma^2_0 = 6^2 = 36$\n",
    "\n",
    "$\\alpha = 0.05$\n",
    "\n",
    "$H_0 : \\sigma^2 \\geq \\sigma^2_0$ vs. $H_1 : \\sigma^2 < \\sigma^2_0$\n",
    "\n",
    "Estadístico del test: $T = \\frac{(n - 1) S^2}{\\sigma^2_0}$\n",
    "\n",
    "Bajo $H_0 : \\sigma^2 = \\sigma^2_0 \\implies T \\sim \\mathcal{X}^2_{n-1}$\n",
    "\n",
    "Región de rechazo: $T \\leq \\mathcal{X}^2_{n-1, 1 - \\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f5656919-05f3-44fe-b655-e867729786df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = c(27, 41, 22, 27, 23, 35, 30, 24, 27, 28, 22)\n",
    "n = length(X)\n",
    "var0 = 6^2\n",
    "alpha = 0.05\n",
    "T = (n - 1) * var(X) / var0\n",
    "z_alpha = qchisq(alpha, n - 1)\n",
    "T <= z_alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e869f97e-b50d-4948-8fd5-61aca6f79f25",
   "metadata": {},
   "source": [
    "No cumple con la especificación."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "623e4a12-90a0-4ee0-8d4a-c2b7bdf22a38",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Acotar el p-valor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7970397d-5ba8-4a4d-8b66-187f7db9c291",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.503428342685353"
      ],
      "text/latex": [
       "0.503428342685353"
      ],
      "text/markdown": [
       "0.503428342685353"
      ],
      "text/plain": [
       "[1] 0.5034283"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pchisq(T, n - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a4f6714-0d29-44bd-b650-cdd277df17c0",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Encontrar la función de potencia $\\pi(\\sigma^2)$, implementarla en R y graficarla. ¿Es creciente o decreciente? ¿Cuánto vale en $\\sigma = 6$?\n",
    "\n",
    "$\\pi(\\sigma^2) = F_{\\mathcal{X}^2_{n-1}} \\Big( \\frac{\\sigma^2_0}{\\sigma^2} \\mathcal{X}^2_{n-1,1-\\alpha} \\Big)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "185cb62e-fa68-4d57-9eaa-6b96018b6c97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0500000000000001"
      ],
      "text/latex": [
       "0.0500000000000001"
      ],
      "text/markdown": [
       "0.0500000000000001"
      ],
      "text/plain": [
       "[1] 0.05"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAYAAAD958/bAAAEDmlDQ1BrQ0dDb2xvclNwYWNl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\nAgQIECBAgAABAgQIEFgggX8BGR3z0aKE1HoAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pi = function(var) pchisq(var0 / var * z_alpha, n - 1)\n",
    "curve(pi, from=16, to=256, xname='var')\n",
    "pi(36)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "377ce4b8-77a1-4187-8e7c-3db104d8c2bb",
   "metadata": {},
   "source": [
    "## Ejercicio 4\n",
    "\n",
    "Se supone que 1 de cada 10 fumadores prefiere la marca A. Después de una campaña publicitaria en cierta región de ventas, se entrevistó a 200 fumadores para determinar la efectividad de la campaña. El resultado de esta encuesta mostró que 26 personas preferían la marca A."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7bf5b59-41ec-44f4-836a-c1a89b92bcaa",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "¿Indican estos datos, a nivel aproximado 0.05, un aumento en la preferencia por la marca A?\n",
    "\n",
    "$H_0 : p = p_0$ vs $H_1 : p > p_0$\n",
    "\n",
    "$\\bar{X} = \\tfrac{26}{200} = 0.13$\n",
    "\n",
    "$p_0 = \\tfrac{1}{10} = 0.1$\n",
    "\n",
    "$s_0 = \\sqrt{p_0(1 - p_0)}$\n",
    "\n",
    "$\\alpha = 0.05$\n",
    "\n",
    "$T = \\sqrt{n} \\frac{\\bar{X} - p_0}{s_0}$\n",
    "\n",
    "Región de rechazo: $T \\geq z_{\\alpha}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a7bdcb45-4202-4a19-ae84-c8ac0d2e2b08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 200\n",
    "Xbar = 0.13\n",
    "p0 = 0.1\n",
    "s0 = sqrt(p0 * (1 - p0))\n",
    "alpha = 0.05\n",
    "T = sqrt(n) * (Xbar - p0) / s0\n",
    "z_alpha = qnorm(alpha, 0, 1, lower.tail=FALSE)\n",
    "T >= z_alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c17fbcff-51d5-4a68-8308-62ed4f6e1350",
   "metadata": {},
   "source": [
    "No se rechaza la $H_0$ y por lo tanto no se puede concluir en base a la muestra tomada si aumentó la preferencia por la marca A."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe1eb213-644e-4dc1-b866-59448c7db397",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Calcular el p-valor aproximado."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "af7d1f90-cb6e-4f6f-a889-59e634617727",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0786496035251426"
      ],
      "text/latex": [
       "0.0786496035251426"
      ],
      "text/markdown": [
       "0.0786496035251426"
      ],
      "text/plain": [
       "[1] 0.0786496"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pnorm(T, 0, 1, lower.tail=FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fde657d-fbbe-4a91-a462-9b6521a6beff",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "¿Cuál es la probabilidad aproximada de decidir que la campaña publicitaria no fue efectiva, cuando en realidad la proporción de preferencia por la marca A después de la campaña es 0.15?\n",
    "\n",
    "$\\sigma = \\sqrt{p(1 - p)}$\n",
    "\n",
    "$\n",
    "\\begin{align*}\n",
    "\\pi(p) = P_{p_0 = p}(T \\in R)\n",
    "&= P(T \\geq z_\\alpha) \\\\\n",
    "&= 1 - P(T \\leq z_\\alpha) \\\\\n",
    "&= 1 - P(\\sqrt{n} \\frac{\\bar{X} - p_0}{s_0} \\leq z_\\alpha) \\\\\n",
    "&= 1 - P(\\sqrt{n} \\frac{\\bar{X} - p + p - p_0}{s_0} \\frac{\\sigma}{\\sigma} \\leq z_\\alpha) \\\\\n",
    "&= 1 - P(\\sqrt{n} \\frac{\\bar{X} - p + p - p_0}{\\sigma} \\frac{\\sigma}{s_0} \\leq z_\\alpha) \\\\\n",
    "&= 1 - P \\Big( \\sqrt{n} \\big( \\frac{\\bar{X} - p}{\\sigma} + \\frac{p - p_0}{\\sigma} \\big) \\frac{\\sigma}{s_0} \\leq z_\\alpha \\Big) \\\\\n",
    "&= 1 - P \\Big( \\sqrt{n} \\big( \\frac{\\bar{X} - p}{\\sigma} + \\frac{p - p_0}{\\sigma} \\big) \\leq z_\\alpha \\frac{s_0}{\\sigma} \\Big) \\\\\n",
    "&= 1 - P \\Big( \\sqrt{n} \\frac{\\bar{X} - p}{\\sigma} \\leq z_\\alpha \\frac{s_0}{\\sigma} - \\sqrt{n} \\frac{p - p_0}{\\sigma} \\Big) \\\\\n",
    "&= 1 - P \\Big( Z \\leq z_\\alpha \\frac{s_0}{\\sigma} - \\sqrt{n} \\frac{p - p_0}{\\sigma} \\Big) \\\\\n",
    "&= 1 - \\Phi \\Big( z_\\alpha \\frac{s_0}{\\sigma} - \\sqrt{n} \\frac{p - p_0}{\\sigma} \\Big)\n",
    "\\end{align*}\n",
    "$\n",
    "\n",
    "$p \\in H_1 \\implies \\pi(p) = 1 - \\beta(p) \\iff \\beta(p) = 1 - \\pi(p) \\iff \\beta(p) = \\Phi \\Big( z_\\alpha \\frac{s_0}{\\sigma} - \\sqrt{n} \\frac{p - p_0}{\\sigma} \\Big)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3505eeb9-3fef-410a-a3e2-8ffa436f0fd3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.274806005211727"
      ],
      "text/latex": [
       "0.274806005211727"
      ],
      "text/markdown": [
       "0.274806005211727"
      ],
      "text/plain": [
       "[1] 0.274806"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 0.15\n",
    "sd = sqrt(p * (1 - p))\n",
    "pnorm(z_alpha * (s0 / sd) - sqrt(n) * (p - p0) / sd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc2a154e-5295-4f20-a237-0d5f462d104f",
   "metadata": {},
   "source": [
    "### Pregunta D\n",
    "\n",
    "Implementar la función potencia y graficarla. ¿Qué características tiene esta función? Interpretar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e968ec8b-d5cb-409e-85ea-54c1211a1069",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAYAAAD958/bAAAEDmlDQ1BrQ0dDb2xvclNwYWNl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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pi = function (p) {\n",
    "    sd = sqrt(p * (1 - p))\n",
    "    return(1 - pnorm(z_alpha * (s0 / sd) - sqrt(n) * (p - p0) / sd))\n",
    "}\n",
    "curve(pi, from=0, to=1, xname='p')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a44baa8-8cf1-46f0-8d9c-d65ec28565f6",
   "metadata": {},
   "source": [
    "A medida que aumenta el verdadero valor de $p$, aumenta la probabilidad de rechazar la $H_0$ que planteaba $p = p_0 = 0.1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76ce8dbf-474e-4a4c-bfd9-6091b914f14e",
   "metadata": {},
   "source": [
    "### Pregunta E\n",
    "\n",
    "¿Qué tamaño de muestra debería tomarse para que la probabilidad de c) fuese a lo sumo 0.05?\n",
    "\n",
    "$\n",
    "\\begin{align*}\n",
    "&\\Phi \\Big( z_\\alpha \\frac{s_0}{\\sigma} - \\sqrt{n} \\frac{p - p_0}{\\sigma} \\Big) \\leq 0.05 \\\\\n",
    "&\\iff z_\\alpha \\frac{s_0}{\\sigma} - \\sqrt{n} \\frac{p - p_0}{\\sigma} \\leq \\Phi^{-1}(0.05) \\\\\n",
    "&\\iff z_\\alpha \\frac{s_0}{\\sigma} - \\Phi^{-1}(0.05) \\leq \\sqrt{n} \\frac{p - p_0}{\\sigma} \\\\\n",
    "&\\iff z_\\alpha \\frac{s_0}{p - p_0} - \\Phi^{-1}(0.05) \\frac{\\sigma}{p - p_0} \\leq \\sqrt{n} \\\\\n",
    "&\\iff \\Big( z_\\alpha \\frac{s_0}{p - p_0} - \\Phi^{-1}(0.05) \\frac{\\sigma}{p - p_0} \\Big)^2 \\leq n\n",
    "\\end{align*}\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dccbe7e4-6264-43ee-a0c3-76f337e4f6a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "468"
      ],
      "text/latex": [
       "468"
      ],
      "text/markdown": [
       "468"
      ],
      "text/plain": [
       "[1] 468"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 0.15\n",
    "sd = sqrt(p * (1 - p))\n",
    "ceiling((z_alpha * s0 / (p - p0) - qnorm(0.05) * sd / (p - p0))^2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdbbfa73-cbe7-48ee-8ac6-22128ef7e389",
   "metadata": {},
   "source": [
    "### Pregunta F\n",
    "\n",
    "Decidir si las siguientes afirmaciones son V o F. Justificar."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "226da386-201d-4549-b53a-5c6bd4d87d9d",
   "metadata": {},
   "source": [
    "#### Item i\n",
    "\n",
    "Si la verdadera proporción de fumadores que prefieren la marca A es mayor que 0.15, la probabilidad de que este test rechace $H_0$ es mayor que 0.725.\n",
    "\n",
    "**Verdadero**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "895e7fee-4698-4856-9765-30a05613e99d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pi(0.15) >= 0.725"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86c2459e-0336-427b-90bb-903d3c660928",
   "metadata": {},
   "source": [
    "#### Item ii\n",
    "\n",
    "Cuánto más pequeña es la verdadera proporción de fumadores que prefieren la marca A más improbable es que el test rechace $H_0$.\n",
    "\n",
    "**Verdadero**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c08e896a-f8f5-4a7c-a2e8-8d2b8ddd8295",
   "metadata": {},
   "source": [
    "#### Item iii\n",
    "\n",
    "$\\pi(0.1) = 0.05$\n",
    "\n",
    "**Verdadero**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0204b6da-f18d-44ef-b1b5-809c8339fb3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.05"
      ],
      "text/latex": [
       "0.05"
      ],
      "text/markdown": [
       "0.05"
      ],
      "text/plain": [
       "[1] 0.05"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pi(0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fff095dd-f49e-48f1-a73a-c40fcc974cf5",
   "metadata": {},
   "source": [
    "#### Item iv\n",
    "\n",
    "La probabilidad de error de tipo II es una función creciente de $p$, donde $p$ es la verdadera proporción de fumadores que prefieren la marca A.\n",
    "\n",
    "**Falso**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89c7d4d1-b709-46ab-9070-943f2e9152a6",
   "metadata": {},
   "source": [
    "## Ejercicio 5\n",
    "\n",
    "Se supone que el tiempo de duración de cierto tipo de lamparitas tiene distribución exponencial. Una fábrica garantiza que el tiempo medio de vida de las lamparitas que produce es mayor que 50 días, y la empresa vendedora quiere asegurarse que la producción satisface las especificaciones antes de sacarla a la venta. Para ello toma al azar una muestra de 40 lamparitas y observa el tiempo de duración de las mismas, obteniendo un promedio de 53 días."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46203d26-ebf1-4f8e-84c0-0fc9152c22fd",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Proponer un test de nivel exacto con hipótesis nula simple para este problema de manera tal que la probabilidad de que la empresa decida no vender si no se satisfacen los requerimientos sea del 0.95.\n",
    "\n",
    "$n = 40$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2683c4e5-0d08-45b9-8900-821cdd3782d1",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "¿Qué decisión se toma en base a los tiempos observados?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b00be7d-a77e-4cac-a65b-bd1a9c547134",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Repetir a) usando un nivel aproximado."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e435a03-5854-43d7-b20d-c968b5e52807",
   "metadata": {},
   "source": [
    "### Pregunta D\n",
    "\n",
    "Calcular la función de potencia aproximada para el test del ítem anterior. ¿Este test conserva el nivel aproximado 5% si ampliamos la hipótesis nula, reemplazándola por una hipótesis compuesta?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "889e062c-f5c9-4ad5-804b-d44fa5027345",
   "metadata": {},
   "source": [
    "### Pregunta E\n",
    "\n",
    "Utilizando el test aproximado, ¿qué probabilidad tiene la empresa de no sacar la producción a la venta, si el promedio de vida verdadero es 52 días?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed5d9b37-e2b3-42c8-aca6-6045c6fc8fa5",
   "metadata": {},
   "source": [
    "### Pregunta F\n",
    "\n",
    "¿Cuál debería ser el tamaño de la muestra para que la probabilidad de d) fuese 0.1?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fb212dc-0bff-49f1-9ac6-29a008faf3c2",
   "metadata": {},
   "source": [
    "## Ejercicio 6\n",
    "\n",
    "Se desea determinar si un dado de seis caras está cargado o no. Para ello se arroja el dado 1000 veces obteniéndose los resultados contenidos en el archivo dado.txt, que se encuentra en la página web de la materia.\n",
    "\n",
    "Estamos interesados en testear las hipótesis $H_0$ : El dado es equilibrado vs. $H_1$ : El dado está cargado. Para ello consideramos distintos tests:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "38df0649-242a-4eb4-91c7-7b2e8cecd8f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "dado = scan('./datasets/p9/dado.txt')\n",
    "n = length(dado)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd7dbb75-4d49-4bfc-8b16-70a5b95f6cea",
   "metadata": {},
   "source": [
    "Todas las preguntas tienen la misma estructura de tests:\n",
    "\n",
    "$H_0 : p = p_0$ vs $H_1 : p \\neq p_0$\n",
    "\n",
    "$p_0 = 0.5$\n",
    "\n",
    "$s_0 = \\sqrt{p_0(1 - p_0)}$\n",
    "\n",
    "$p$ = proporción de la v.a. de cada pregunta en cuestión\n",
    "\n",
    "$\\alpha = 0.05$\n",
    "\n",
    "$T = \\sqrt{n} \\frac{p - p_0}{s_0}$\n",
    "\n",
    "Región de rechazo: $|T| \\geq z_{\\alpha/2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6938169e-f35a-474c-9b7d-55ded5a0a3e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.05\n",
    "\n",
    "calcularT = function(p, p0) sqrt(n) * (p - p0) / sqrt(p0 * (1 - p0))\n",
    "\n",
    "rechazar = function(p, p0) {\n",
    "    T = calcularT(p, p0)\n",
    "    z_alpha2 = qnorm(alpha / 2, 0, 1, lower.tail=FALSE)\n",
    "    return(abs(T) >= z_alpha2)\n",
    "}\n",
    "\n",
    "pValor = function(p, p0) {\n",
    "    T = calcularT(p, p0)\n",
    "    return(2 * pnorm(abs(T), 0, 1, lower.tail=FALSE))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a5da2c9-31d0-4442-988b-8fd308fa1fd5",
   "metadata": {},
   "source": [
    "### Pregunta A\n",
    "\n",
    "Sea $X$ = cantidad de veces que el resultado del dado es par. Plantear las hipótesis y determinar la región de rechazo para un test de nivel aproximado $\\alpha = 0.05$ basado en $X$. Para el conjunto de datos obtenido, ¿cuál es el p-valor aproximado?, ¿cuál es la decisión?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "bb0ace94-1462-4c54-8dea-c8c8aea154e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.342781711147911"
      ],
      "text/latex": [
       "0.342781711147911"
      ],
      "text/markdown": [
       "0.342781711147911"
      ],
      "text/plain": [
       "[1] 0.3427817"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p0 = 0.5\n",
    "p = sum(dado %% 2 == 0) / n\n",
    "rechazar(p, p0)\n",
    "pValor(p, p0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfe95187-947a-4c59-b044-2308c0cbfb9c",
   "metadata": {},
   "source": [
    "### Pregunta B\n",
    "\n",
    "Sea $Y$ = cantidad de veces que el resultado del dado es menor o igual que 3. Plantear claramente las hipótesis y determinar la región de rechazo para un test de nivel aproximado $\\alpha = 0.05$ basado en $Y$. Para el conjunto de datos obtenido, ¿cuál es el p-valor aproximado?, ¿cuál es la decisión?."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "02313672-c0fe-4dd3-a3bd-ec0c1689e38a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.704336413488452"
      ],
      "text/latex": [
       "0.704336413488452"
      ],
      "text/markdown": [
       "0.704336413488452"
      ],
      "text/plain": [
       "[1] 0.7043364"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p0 = 0.5\n",
    "p = sum(dado <= 3) / n\n",
    "rechazar(p, p0)\n",
    "pValor(p, p0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1d6b58d-85e7-4f90-a4fd-7625e607e07a",
   "metadata": {},
   "source": [
    "### Pregunta C\n",
    "\n",
    "Sea $W$ = cantidad de veces que el resultado del dado es exactamente 3. Plantear claramente las hipótesis y determinar la región de rechazo para un test de nivel aproximado $\\alpha = 0.05$ basado en $W$. Para el conjunto de datos obtenido, ¿cuál es el p-valor aproximado?, ¿cuál es la decisión?."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b4017644-f0db-420f-88e8-53e461406a64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.820988186801895"
      ],
      "text/latex": [
       "0.820988186801895"
      ],
      "text/markdown": [
       "0.820988186801895"
      ],
      "text/plain": [
       "[1] 0.8209882"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p0 = 1 / 6\n",
    "p = sum(dado == 3) / n\n",
    "rechazar(p, p0)\n",
    "pValor(p, p0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fe2ab21-b780-44da-81a0-a64514782ac6",
   "metadata": {},
   "source": [
    "### Pregunta D\n",
    "\n",
    "Sea $U$ = cantidad de veces que el resultado del dado es exactamente 2. Plantear claramente las hipótesis y determinar la región de rechazo para un test de nivel aproximado $\\alpha = 0.05$ basado en $U$. Para el conjunto de datos obtenido, ¿cuál es el p-valor aproximado?, ¿cuál es la decisión?."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c40fe176-a1b4-45a2-80ac-84e7c4029579",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "3.45063384340428e-14"
      ],
      "text/latex": [
       "3.45063384340428e-14"
      ],
      "text/markdown": [
       "3.45063384340428e-14"
      ],
      "text/plain": [
       "[1] 3.450634e-14"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p0 = 1 / 6\n",
    "p = sum(dado == 2) / n\n",
    "rechazar(p, p0)\n",
    "pValor(p, p0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "429d4ea1-34b9-402f-aa49-7ee7ffbb1396",
   "metadata": {},
   "source": [
    "### Pregunta E\n",
    "\n",
    "En base a los resultados obtenidos. ¿Qué decisión tomaría? ¿Está cargado el dado?\n",
    "\n",
    "Podemos concluir que el dado está cargado.\n",
    "\n",
    "Por el test D, se observa directamente que el 2 está cargado. Pero el 1 y 3 no están cargados por el test B.\n",
    "\n",
    "Por el test A, como no pudimos rechazar $H_0$ pero ya sabemos que el 2 está cargado, entonces el 4 o el 6 podrían estar cargados o ninguno está cargado (y en cierto sentido están \"descargados\").\n",
    "\n",
    "Como la media es 3.683, y el 2 está cargado, esto nos dice que hay algún número > 3 que está cargado y está \"balanceando\" la media hacia el centro (o sea, la media real que es 3).\n",
    "\n",
    "También podemos mirar el histograma y ahí se observa que el 5 está cargado de forma similar al 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3222ea31-3674-4588-b313-462e381e194c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  1.000   2.000   4.000   3.683   5.000   6.000 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAYAAAD958/bAAAEDmlDQ1BrQ0dDb2xvclNwYWNl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",
      "text/plain": [
       "Plot with title “Histogram of dado”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(dado)\n",
    "hist(dado, col='lightblue')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09801fcb-00cf-404d-9168-afecb284bb9b",
   "metadata": {},
   "source": [
    "## Ejercicio 7\n",
    "\n",
    "En cada caso indique si la afirmación es verdadera o falsa y justifique:\n",
    "\n",
    "### Pregunta A\n",
    "\n",
    "El nivel de significación de un test es igual a la probabilidad de que la hipótesis nula sea cierta.\n",
    "\n",
    "**Falso**\n",
    "\n",
    "Solo podemos rechazar la $H_0$ pero no podemos afirmar si es verdadera o no.\n",
    "\n",
    "### Pregunta B\n",
    "\n",
    "Un error de tipo II es más grave que un error de tipo I.\n",
    "\n",
    "**Falso**\n",
    "\n",
    "Esto es más por convención que por algún argumento lógico, por lo general se acepta que es peor difamar que no decir nada, pero depende de cada caso particular.\n",
    "\n",
    "### Pregunta C\n",
    "\n",
    "Si el p-valor es 0.3, el test correspondiente rechazará al nivel 0.01.\n",
    "\n",
    "**Falso**\n",
    "\n",
    "La regla es al revés: p-valor $ \\leq \\alpha \\iff $ rechazamos $H_0$\n",
    "\n",
    "### Pregunta D\n",
    "\n",
    "Si un test rechaza al nivel de significación 0.06, entonces el p-valor es menor o igual a 0.06.\n",
    "\n",
    "**Verdadero**\n",
    "\n",
    "### Pregunta E\n",
    "\n",
    "Si un intervalo de confianza de nivel 0.99 para la media $\\mu$ de una distribución normal calculado a partir de una muestra da como resultado $(2.1, 3.3)$, entonces el test para las hipótesis $H_0 : \\mu = 3$ vs. $H_1 : \\mu \\neq 3$ basado en los mismos datos rechazará la hipótesis nula al nivel 0.01.\n",
    "\n",
    "**Falso**\n",
    "\n",
    "La propiedad es al revés. Si el $\\mu_0$ utilizado en el test de hipótesis **no** pertenece al intervalo de confianza, entonces podemos afirmar que esa probabilidad es de 0.01, y por lo tanto, podemos afirmar que vamos a rechazar la $H_0$ con esa misma probabilidad."
   ]
  }
 ],
 "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": "4.1.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}