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<title>Inferencia de medias con R</title>
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<h1>Inferencia de medias con R</h1>
<p><a href="http://bioinfo.cipf.es/" title="webpage of department">Francisco García García</a> <em>(2014-12-01)</em> </p>
<hr/>
<h3>0. Introducción</h3>
<h3>1. Intervalo de confianza de una media poblacional</h3>
<h3>2. Test t para una media poblacional</h3>
<h3>3. Intervalo de confianza de la diferencia de dos medias poblacionales</h3>
<h3>4. Test t para dos medias poblacionales</h3>
<h3>5. Pruebas no paramétricas: Wilcoxon</h3>
<h3>6. Ejercicios</h3>
<h3>7. Bibliografía</h3>
<hr/>
<p><br />
<br />
<br /></p>
<h2>0. Introducción</h2>
<p>Los <strong>procedimientos t</strong> son pruebas <strong>paramétricas</strong> que permiten realizar inferencia a partir de 1 ó 2 muestras:</p>
<ul>
<li>Nos proporcionan <strong>intervalos de confianza</strong> de una media poblacional o bien la media de la diferencia de 2 medias poblaciones.</li>
<li>También incluyen los <strong>contrastes de hipótesis de comparación de medias</strong>.</li>
</ul>
<p>Cuando no se verifica la <strong>normalidad</strong> en la variable respuesta, es aconsejable el uso de una prueba no paramétrica: <strong>Wilcoxon</strong>, cuyas
hipótesis nula y alternativa no se basan en el parámetro de la <strong>media</strong> sino en la <strong>mediana</strong>.</p>
<p><br />
<br /></p>
<h2>1. Intervalo de confianza de una media poblacional</h2>
<p>Comenzamos leyendo la base de datos <strong>riesgos</strong>:</p>
<pre><code class="r">datos <- read.csv("riesgos.csv", header = T, sep = "\t")
</code></pre>
<p>Echamos un vistazo a la estructura de los datos:</p>
<pre><code class="r">str(datos)
</code></pre>
<pre><code>#> 'data.frame': 91 obs. of 10 variables:
#> $ id : int 2 3 6 7 8 10 11 12 14 15 ...
#> $ contrato : int 3 1 5 1 3 2 1 3 1 1 ...
#> $ jornada : Factor w/ 2 levels "completa","parcial": 1 1 1 1 1 1 1 1 1 1 ...
#> $ turno : int 1 1 1 1 1 1 1 1 3 1 ...
#> $ carfisi : Factor w/ 2 levels "no","sí": 1 1 2 2 2 1 1 1 1 1 ...
#> $ carpsiqui : Factor w/ 2 levels "no","sí": 1 1 1 1 1 2 1 1 2 2 ...
#> $ expquímica: Factor w/ 2 levels "no","sí": 1 1 1 1 2 1 1 1 1 1 ...
#> $ edad : int 33 37 35 30 30 32 27 33 31 31 ...
#> $ peso : num 74 74 67 57 69 56 74 76 65 NA ...
#> $ talla : num 155 170 170 164 160 160 170 165 170 173 ...
</code></pre>
<pre><code class="r">head(datos)
</code></pre>
<pre><code>#> id contrato jornada turno carfisi carpsiqui expquímica edad peso talla
#> 1 2 3 completa 1 no no no 33 74 155
#> 2 3 1 completa 1 no no no 37 74 170
#> 3 6 5 completa 1 sí no no 35 67 170
#> 4 7 1 completa 1 sí no no 30 57 164
#> 5 8 3 completa 1 sí no sí 30 69 160
#> 6 10 2 completa 1 no sí no 32 56 160
</code></pre>
<pre><code class="r">tail(datos)
</code></pre>
<pre><code>#> id contrato jornada turno carfisi carpsiqui expquímica edad peso talla
#> 86 73 5 parcial 1 no no no 32 65 159
#> 87 75 1 parcial 1 no no no 33 87 185
#> 88 76 1 parcial 1 sí no no 30 76 178
#> 89 80 4 parcial 1 no no no 29 65 153
#> 90 82 1 parcial 1 no no no 35 78 190
#> 91 86 4 parcial 4 no no no 28 65 167
</code></pre>
<p>Con la función <strong>attach</strong> hacemos accesible la base de datos seleccionada:</p>
<pre><code class="r">attach(datos)
</code></pre>
<pre><code>#> The following objects are masked from datos (position 3):
#>
#> carfisi, carpsiqui, contrato, edad, expquímica, id, jornada,
#> peso, talla, turno
#> The following objects are masked from datos (position 4):
#>
#> carfisi, carpsiqui, contrato, edad, expquímica, id, jornada,
#> peso, talla, turno
#> The following objects are masked from datos (position 10):
#>
#> carfisi, carpsiqui, contrato, edad, expquímica, id, jornada,
#> peso, talla, turno
</code></pre>
<p>Describimos la variable <strong>peso</strong> en nuestra muestra:</p>
<pre><code class="r">summary(peso)
</code></pre>
<pre><code>#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> 50.00 62.00 69.00 70.34 76.00 98.00 2
</code></pre>
<pre><code class="r">boxplot(peso, col="pink", main ="Peso")
</code></pre>
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alt="plot of chunk unnamed-chunk-4"/> </p>
<p><em>¿Cómo determinamos un intervalo de confianza del 95% para la media poblacional del salario?</em></p>
<pre><code class="r">t.test(peso, conf.level = 0.95)$conf.int
</code></pre>
<pre><code>#> [1] 67.86330 72.81086
#> attr(,"conf.level")
#> [1] 0.95
</code></pre>
<p>¿Los datos deben cumplir algún requisito para poder obtener el intervalo de confianza anterior?</p>
<p>Redondea el intervalo de confianza a dos decimales:</p>
<pre><code class="r">round(t.test(peso, conf.level = 0.95)$conf.int,2)
</code></pre>
<pre><code>#> [1] 67.86 72.81
#> attr(,"conf.level")
#> [1] 0.95
</code></pre>
<p><br />
<br /></p>
<h2>2. Test t para una media poblacional</h2>
<p>La base de datos <strong>riesgos.csv</strong> es una muestra aleatoria de la población de trabajadores de un centro hospitalario de Valencia.</p>
<p>Se ha publicado un informe donde se indica que la media de la talla de todos los trabajadores en la Comunidad Valenciana es de 160 cm.
Sin embargo, nosotros creemos que no es cierto y por ello nos gustaría utilizar los datos de nuestro estudio. Realizaremos
los siguientes pasos:
1. Describimos la variable <strong>talla</strong> de forma numérica y gráfica.</p>
<pre><code class="r">boxplot(talla, col = "red", main = "talla en población de trabjadores")
</code></pre>
<p><img src="data:image/png;base64,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alt="plot of chunk unnamed-chunk-7"/> </p>
<pre><code class="r">hist(talla)
</code></pre>
<p><img 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alt="plot of chunk unnamed-chunk-7"/> </p>
<ol>
<li><p>Plantea el contraste de hipótesis correspondiente. ¿Dos colas o una sola?</p></li>
<li><p>Resuelve el contraste en R considerando un nivel de significación de 0.05:</p></li>
</ol>
<pre><code class="r">t.test(peso, mu = 160, alt = "two.sided", conf.level = 0.95)
</code></pre>
<pre><code>#>
#> One Sample t-test
#>
#> data: peso
#> t = -72.03, df = 88, p-value < 2.2e-16
#> alternative hypothesis: true mean is not equal to 160
#> 95 percent confidence interval:
#> 67.86330 72.81086
#> sample estimates:
#> mean of x
#> 70.33708
</code></pre>
<p><br />
<br /></p>
<h2>3. Intervalo de confianza de la diferencia de dos medias poblacionales</h2>
<p>Sospechamos que la <strong>edad</strong> de las personas que tienen <strong>exposición a carga física</strong> es menor que la edad de las personas no expuestas a
este riesgo. Nos gustaría obtener un intervalo de confianza de la diferencia de estas medias:</p>
<p>Primero exploramos la muestra:</p>
<pre><code class="r">mean(edad[carfisi == "sí"])
</code></pre>
<pre><code>#> [1] 30.88235
</code></pre>
<pre><code class="r">mean(edad[carfisi == "no"])
</code></pre>
<pre><code>#> [1] 31.78947
</code></pre>
<pre><code class="r">plot(edad ~ carfisi, col = c("red", "green"))
</code></pre>
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alt="plot of chunk unnamed-chunk-9"/> </p>
<pre><code class="r">mean(edad[carfisi == "sí"]) - mean(edad[carfisi == "no"])
</code></pre>
<pre><code>#> [1] -0.9071207
</code></pre>
<p>A partir de los datos de la muestra, ¿crees que hay diferencia de edad entre ambos grupos?</p>
<p>Determinamos el intervalo de confianza del 95% para la diferencia de estas dos medias:</p>
<pre><code class="r">t.test(edad ~ carfisi, data = datos, conf.level = 0.95)$conf.int
</code></pre>
<pre><code>#> [1] -0.5142951 2.3285366
#> attr(,"conf.level")
#> [1] 0.95
</code></pre>
<pre><code class="r">## Otra opción para obtener el mismo intervalo de confianza:
grupo1 <- edad[carfisi == "no"]
grupo2 <- edad[carfisi == "sí"]
t.test(grupo1, grupo2, conf.level = 0.95)$conf.int
</code></pre>
<pre><code>#> [1] -0.5142951 2.3285366
#> attr(,"conf.level")
#> [1] 0.95
</code></pre>
<p>¿El valor 0 está incluido en este intervalo de confianza? ¿Qué significa esto?
<br />
<br /></p>
<h2>4. Test t para dos medias poblacionales</h2>
<p>En ocasiones nos gustaría comparar dos poblaciones. Una opción sería comparar las <strong>medias</strong> de ambos grupos pero
antes debemos tener claro si las muestras son <strong>relacionadas</strong> o <strong>independientes</strong>. Comenta un ejemplo de cada tipo.</p>
<p>¿Hay diferencias de <strong>peso</strong> entre las personas que tienen <strong>carga psíquica</strong> y las que no están expuestas?</p>
<p>Vemos que ocurre en nuestra muestra:</p>
<pre><code class="r">summary(peso[carpsiqui == "sí"])
</code></pre>
<pre><code>#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> 50.00 64.50 69.00 71.51 78.00 96.00 2
</code></pre>
<pre><code class="r">summary(peso[carpsiqui == "no"])
</code></pre>
<pre><code>#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> 50.00 59.00 69.00 69.24 76.00 98.00
</code></pre>
<pre><code class="r">boxplot(peso ~ carpsiqui, col= c("pink", "red"), main = "peso vs. carga psíquica")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-11"/> </p>
<p>Con esta información, ¿crees que hay diferencias entre ambos grupos? Comprueba si estas diferencias estadísticamente
son estadísticamente significativas mediante la utilización del correspondiente test estadístico.
t de comparación de 2 medias:</p>
<pre><code class="r">t.test(peso ~ carpsiqui, data = datos, conf.level = 0.95)
</code></pre>
<pre><code>#>
#> Welch Two Sample t-test
#>
#> data: peso by carpsiqui
#> t = -0.9096, df = 85.665, p-value = 0.3656
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#> -7.239123 2.694128
#> sample estimates:
#> mean in group no mean in group sí
#> 69.23913 71.51163
</code></pre>
<p>Comenta los resultados obtenidos.
<br />
<br /></p>
<h2>5. Pruebas no paramétricas: Wilcoxon</h2>
<p>Los procedimientos t exigen el cumplimiento de normalidad de la variable de estudio.
Sin embargo, si no se verifican los requisitos exigidos, no será aconsejable el uso de estas pruebas paramétricas y
utilizaremos procedimientos no paramétricos, que no suelen exigir ningún requerimiento a nuestros datos. </p>
<p>El test de <strong>Wilcoxon</strong> es una opción no paramétrica que nos permite comparar dos poblaciones.</p>
<p>Vamos a evaluar si hay diferencias de <strong>peso</strong> entre las personas que presentan exposición a <strong>carga física</strong>
y las que no están expuestas, utilizando el <strong>test de Wilcoxon</strong>:</p>
<pre><code class="r">summary(peso[carfisi == "sí"])
</code></pre>
<pre><code>#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> 50.00 59.00 68.00 69.52 76.00 93.00 1
</code></pre>
<pre><code class="r">summary(peso[carfisi == "no"])
</code></pre>
<pre><code>#> Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#> 50.00 64.75 69.00 70.82 76.50 98.00 1
</code></pre>
<pre><code class="r">boxplot(peso ~ carfisi, col= c("blue", "red"), main = "peso vs. carga psíquica")
</code></pre>
<p><img 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b81L5MDtpsWPYv1yYbXvZ9R3VDdYte2sxqOvo+Xl8kt28VTDwAT8jLR5dr6l8ldWd2loTV/UvV3dm372pTj0KIHGGUuJbufrn6/+lT1uOp3qv9enVz9vYZ3tGO7adGzzbToGW0uAf+s6pXVJxoW8muqBzUE/Dc3XJNnu2nRs8206BltLgFf9a5df37b5gN2aNEDjDCXa/AA7E2LntEEPEvhvejZZt6LntEEPEtxYOoBAJZEwLMU50w9AExIi57RBDxL8fypB4AJadEzmoBnKbToAUYQ8ADzp0XPaAKepdCiZ5tp0TOagGcpDkw9AMCSCHiWQouebaZFz2gCnqXQomebadEzmoBnKbToAUaY0z82s03O3Hxw7G5R3WnqIRbmiuqTUw/BCfET1VOnHoJlEfDTeHE93D99OsqV1e3ePfUUy3FN9Yc/Uz1h6kk4Ie6XgGckAT+Nm9ULp56BVbu0utupU08BTMc1eID506JnNAEPMH9a9Iwm4AFghQQ8wPx5L3pGE/AA8+e96BlNix7Yb7/9bfWIqYdYkvdUd6qDU8+xFJ+q3lD/qvqpqWeZkoAH9tvtXzn1BKzapdXd/PsVTtEDwBoJeABYIQEPACsk4AFghQQ8AKyQgAeAFRLwALBCAh4AVkjAA8AKCXgAWCEBDwArJOABYIUEPACskIAHgBUS8ACwQgIeAFZIwAPACgl4AFghAQ8AKyTgAWCFBDwArJCAB4AVEvAAsEICHgBWSMADwAoJeABYIQEPACsk4AFghQQ8AKyQgAeAFRLwALBCAh4AVkjAA8AKCXgAWKE5BvxJ1a2b52wAsAhzCdFbVk+q3lF9urqmuq56Z/WU6rTpRgOA5ZlLwD+zund1SXVudWp1dvWY6u6b7QDAMTpl6gE2HlJ9dfXBXfd9pHp99ebqsuqxE8wFAIs0lyP4y6oH7rHtAdXl+zgLACzeXI7gL6leXD2hurS6tjq9urA6s3rwdKMBwPLMJeDfWF1QXVSdV51VXVU9t3ptdf1kkwHAAs0l4L+lelP1quPcz3dVj99j21dUbz/O/QPAIswl4P+4+svqh6rXHcd+fm/zcSTPqL70OPYNAIsxl5Jd1Q9W31/9dnXXiWcBgEWbyxF81V9V/7C6Z/Xs6rPVb1av2GwDAI7RnI7gd/xJwzX5pzS06P+4+sCkEwHAwswx4KsONrTnf6T68uo7px0HAJZlLqfo/0XDy+KO5GD1F/s4y364dT1x6hlYtStreC8JYEvNJeCfPvUA++z0etrUM7B+t5x6AGA6cwn4bfOZ+rapZ2DVPl79yXVTTwFMR8BP4yP1yqlnYNUure529dRTANOZa8kOADgOAh4AVkjAA8AKuQYP7LdbvGjqCVi1y4f/nDbtFNMT8MB+O/MRU0/ANrjN1ANMTcAD++36O009Aat2XfX++tzUc0xNwAP77UPvrq+eegjW69LqbvWRqeeYmpIdAKyQgAeAFRLwALBCAh4AVkjAA8AKCXgAWCEBDwArJOABYIUEPACskIAHgBUS8ACwQgIeAFZIwAPACgl4AFghAQ8AKyTgAWCFBDwArJCAB4AVEvAAsEICHgBWSMADwAoJeABYoVOmHmBLnVxPnHqGhbms+vKph1iQK6sOTj0FMB0BP41H19POnHqIhXlO9QNTD7Ewl009ADAdAT+N90w9wAJ9tHrT1EMALIVr8CzFg6ceAGBJBDxL8empBwBYEgHPUjxs6gEAlkTAsxQ/PPUAAEsi4AFghQQ8S/HZqQcAWBIBz1Jo0QOMIOBZCi16gBEEPEuhRQ8wgoBnKbToAUYQ8ACwQgKepdCiBxhBwLMUWvQAIwh4lkKLHmAEAc9SaNEDjCDgWQoteoARBDwArJCAZym06AFGEPAshRY9wAgCnqXQogcYQcCzFFr0ACMIeJZCix5gBAEPACs0x4A/qbp185yN6WjRA4wwlxC9ZfWk6h0NZaprquuqd1ZPqU6bbjRmQoseYIS5BPwzq3tXl1TnVqdWZ1ePqe6+2c5206IHGOGUqQfYeEj11dUHd933ker11Zury6rHTjAX8/Gw6iVTDwGwFHM5gr+seuAe2x5QXb6PszBPWvQAI8zlCP6S6sXVE6pLq2ur06sLqzNz/RUARplLwL+xuqC6qDqvOqu6qnpu9drq+mPcz9nVXffYdofjG5GJadEDjDCXgK8hxF+16/btGn6oH2u41xDid99j2+2rj9200ZgBZ3EARphLwH9l9ezq8Q1H7i+svr66oXpD9X3V+49hP3+6+TiSc6ovPe5JmYoWPcAIcynZ/Wr159Xbq5+t3tRwDf6M6i8awp/t5r3oAUaYS8BfWD2t+kx1t+rnGo7YPlP9ZPWt043GTGjRA4wwl4B/ffW9DW9T+5rqvru23b/hHe0AgGM0l2vwj61e3vByuXdU/7X67obAv3MKVmjRA4wyl4D/YHWPzceFDUf0n6zeV72y4VQ9280veetx0numnoBVO5ZG9jaYS8BXHezGW/BsNy369fjD8+tDUw/B6h2YeoCpzSng4cZ4L/r1+KmpB1gg65/R5lKyg6PRomebWf+MJuABYIUEPEuhRc82s/4ZTcCzFFr0bDPrn9EEPEuhRc82s/4ZTcCzFN6Lnm1m/TOagGcptIjZZtY/owl4AFghAc9SaBGzzax/RhPwLIUWMdvM+mc0Ac9SaBGzzax/RhPwLIUWMdvM+mc0Ac9SaBGzzax/RhPwALBCAp6l0CJmm1n/jCbgWQotYraZ9c9oAp6l0CJmm1n/jCbgWQotYraZ9c9oAp6l0CJmm1n/jCbgAWCFBDxLoUXMNrP+GU3AsxRaxGwz65/RBDxLoUXMNrP+GU3AsxRaxGwz65/RBDxLoUXMNrP+GU3AA8AKCXiWQouYbWb9M5qAZym0iNlm1j+jCXiWQouYbWb9M5qAZym0iNlm1j+jCXiWQouYbWb9M5qAB4AVEvAshRYx28z6ZzQBz1JoEbPNrH9GE/AshRYx28z6ZzQBz1JoEbPNrH9GE/AshRYx28z6ZzQBDwArJOBZCi1itpn1z2gCnqXQImabWf+MJuBZCi1itpn1z2gCnqXQImabWf+MJuBZCi1itpn1z2gCHgBWSMCzFFrEbDPrn9EEPEuhRcw2s/4ZTcCzFFrEbDPrn9EEPEuhRcw2s/4ZTcCzFFrEbDPrn9EEPACskIBnKbSI2WbWP6MJeJZCi5htZv0zmoBnKbSI2WbWP6MJeJZCi5htZv0zmoBnKbSI2WbWP6MJeABYoTkG/EnVrZvnbExHi5htZv0z2lxC9JbVk6p3NJRJrqmuq95ZPaU6bbrRmAktYraZ9c9ocwn4Z1b3ri6pzq1Orc6uHlPdfbOd7aZFzDaz/lmsqxuC/UjOqD58Ah7jGdULTsB+mIYWMdvM+l+u51XnT/HAczmCv6x64B7bHlBdvo+zME9axGwz65/RTpl6gI1LqhdXT6gura6tTq8urM7M9ScAGGUuAf/G6oLqouq86qzqquq51Wur649xPxdXj9xj2z2rDxzPkFvgK6sfm3qIPVxQPWfqIY7g+urHq49PPQjHzfofz/qfsZOmHuBG3K7hpSFXj/iaMzZfdyQPqk6u/tNxzrVmp1VfNvUQezit+szUQ+zhsurg1ENw3Kz/m8b6v3HPq55avXvqQabyiobWfA3/g72h+lzDS+X+qPrSE/AYj6gedwL2AwDHautLdvevbrH5889U72l4s5vTqzdX/2WiuQBgkeZyDX63r6++o/rE5vZTq3dNNw4ALM9cjuBreB38KdVbG4p2Oy6s/maKgQBgqeZyBP+6hjehuX31qeoO1R9U31q9rKGlCQAco7kE/EWb/57aEO47TfhPNbTfXz/FUACwVHMJ+B3XNVxv37nm/qcTzgIAizWna/AAwAki4AFghQQ8AKyQgAeAFRLwALBCc/7HZk60+1c/X31s6kG4SS6sbph6CJjIDdXbpx6Cm+Q21b2qD009CMzVa6YeACZk/TOaU/QAsEICHgBWSMADwAoJeABYIQEPACsk4FmKz0w9AEzI+gdW64umHgAmZP0DAAAAAAAAAAAAAAAAAAAAALBvnlw9J29+AwCr8UXVfaceAmCsO1evr55QfaC6rLrPru0Prd5eXVO9pLrdfg8I++SU6lnVVdWHG47ad7y3Om//RwK46e5cfbx6YnXL6mnV/9hs+/Lq6urbqy+pfrl6wQQzwn54ePW2hiD/2urT1fmbbe9NwAMLc+eGo/NTNrfv0vBDrupHql/Z9bm3q66rTt6v4WAfPbx6d/UN1UnVWdWpm23vTcBzDPxzsczNFdX1mz9fv+v+cxp+sO24siHgnaZnjX6n+qnqudUHqx/ML7OMJOCZm4N73H9Fdcddt29XndZwfRLW5k7Vq6uvqb6xelD12EknYnEEPEvx8oaS3X2rM6unVy/t84/yYS0eXP1WdXbDkftp1acmnQjgONy5Q9fcj3T7YQ0t+o81hPvt92802FenN6zxj1cfaWjU33yz7b25Bg8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACwL/4fZPb6sIppDGEAAAAASUVORK5CYII=" alt="plot of chunk unnamed-chunk-13"/> </p>
<pre><code class="r">wilcox.test(peso ~ carfisi, data = datos, paired = F)
</code></pre>
<pre><code>#>
#> Wilcoxon rank sum test with continuity correction
#>
#> data: peso by carfisi
#> W = 978.5, p-value = 0.6458
#> alternative hypothesis: true location shift is not equal to 0
</code></pre>
<ul>
<li>Comenta cuáles son las hipótesis nula y alternativa del contraste.<br/></li>
<li>¿Qué información nos proporciona el estadístico de contraste?</li>
<li>¿Qué nos indica el p-valor?</li>
<li>¿Qué podemos concluir en el contexto del problema?</li>
</ul>
<p><br />
<br /></p>
<h2>6. Ejercicios</h2>
<p>En la base de datos <strong>estres.csv</strong> se incluye información sobre los niveles de estrés de un grupo de trabajadores, así
como otras variables de interés.</p>
<p>Realiza las siguientes actividades en R:</p>
<ul>
<li><strong>A</strong>. Lee la base de datos <em>estres</em>, examina la estructura de los datos (<em>str</em>) y utiliza la función <em>attach</em>
para hacerla accesible y trabajar más cómodamente con sus variables. ¿Qué variables son <em>factor</em>? ¿Y qué variables son <em>integer</em>?</li>
<li><strong>B</strong>. Describe la variable sueldo. ¿Parece una distribución normal?. Determina un intervalo de confianza del 90% para la media
poblacional del sueldo de los trabajadores.</li>
<li><strong>C</strong>. Hace unos años se publicó un informe donde se indicaba que el colectivo de estos trabajadores presentaba una media del nivel de
estrés de 5 puntos, aunque tenemos nuestras dudas…. Plantea un contraste de hipótesis sobre la media poblacional del nivel de estrés
y considerando la información de nuestra muestra, resuelve el contraste en R. ¿Qué conclusiones obtenemos?</li>
<li><strong>D</strong>. ¿Hay diferencias de sueldo por género? Primero explora gráfica y numéricamente qué nos dice nuestra muestra respecto esta
relación del sueldo y género. A continuación plantea el contraste correspondiente, resuélvelo con R y comenta los resultados obtenidos</li>
<li><strong>E</strong>. La variable <em>carga física</em> NO se distribuye como una variable normal. Nos gustaría confirmar si hay diferencias entre la
exposición de <em>carga física</em> entre hombres y mujeres. ¿Qué procedimiento estadístico podríamos utilizar? Indica cuál es la hipótesis
nula y la alternativa. Resuélve el contrate utilizando R y comenta los resultados obtenidos.
<br />
<br /></li>
</ul>
<h2>7. Bibliografía y enlaces interesantes:</h2>
<ul>
<li><p><a href="http://www.antonibosch.com/system/downloads/487/original/EC-MOORE2_Contenido.pdf?1358332517">David S. Moore. Estadística aplicada básica. Editorial Antoni Bosch.</a> Manual de Estadística Básica.</p></li>
<li><p><a href="http://www.statmethods.net/">Quick-R</a> Web con recursos para trabajar con R.</p></li>
<li><p><a href="http://www.r-tutor.com/">r-tutor</a> An R Introduction to Statistics.</p></li>
</ul>
<hr/>
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