document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169837>Question 1169837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> En una investigación sobre el proceso de venta de un determinado producto fabricado<BR>\n" );
document.write( "en varios establecimientos, se requiere el tamaño de la muestra con una confianza del<BR>\n" );
document.write( "95%. Se realiza una investigación preliminar, obteniendo los siguientes resultados:<BR>\n" );
document.write( "media = $4.800 unidad; desviación típica $225. Con los anteriores datos, calcule el<BR>\n" );
document.write( "tamaño muestral, si se considera un error del 1% y E=% (X)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794685 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In an investigation into the sales process of a certain manufactured product<BR>\n" );
document.write( "at various establishments, the sample size is required with a confidence of the<BR>\n" );
document.write( "95%. A preliminary investigation is carried out, obtaining the following results:<BR>\n" );
document.write( "mean = $ 4,800 unit; standard deviation $ 225. With the above data, calculate the<BR>\n" );
document.write( "sample size, if an error of 1% is considered and E =% (X)\r<BR>\n" );
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document.write( "confidence interval of 95% leads to a critical z-score of plus or minus 1.96.\r<BR>\n" );
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document.write( "mean = 4800<BR>\n" );
document.write( "standard deviation = 220\r<BR>\n" );
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document.write( "if you want the error to be 1%, then the limits need to be 4752 to 4848.\r<BR>\n" );
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document.write( "standard error = standard deviation divided by square root of sample size.\r<BR>\n" );
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document.write( "for the low end of the confidence interval, do the following:\r<BR>\n" );
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document.write( "z-score formula is z = (x - m) / s\r<BR>\n" );
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document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "at the low end, the formula becomes -1.96 = (4752 - 4800) / s<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "-1.96 = -48 / s<BR>\n" );
document.write( "solve for s to get:<BR>\n" );
document.write( "s = -48/-1.96 = 24.48979592.\r<BR>\n" );
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document.write( "s = standard deviation divided by sqrt(sample size)<BR>\n" );
document.write( "standard deviation = 220.<BR>\n" );
document.write( "s = 24.48979592<BR>\n" );
document.write( "formula becomes:<BR>\n" );
document.write( "24.48979592 = 220 / sqrt(sample size)<BR>\n" );
document.write( "solve for sqrt(sample size) to get:<BR>\n" );
document.write( "sqrt(sample size) = 220 / 24.48979593<BR>\n" );
document.write( "solve for sample size to get:<BR>\n" );
document.write( "sample size = (220 / 24.48979593) ^ 2 = 80.7002777.\r<BR>\n" );
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document.write( "that should be your answer.<BR>\n" );
document.write( "you can round to the next highest integer to get sample size = 81.\r<BR>\n" );
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document.write( "with a sample size of 80.7002777, you get:<BR>\n" );
document.write( "s = 220 / sqrt(80.7002777) = 24.48979593.\r<BR>\n" );
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document.write( "your z-score formula becomes:<BR>\n" );
document.write( "z = (-48)/24.48979593 = -1.96\r<BR>\n" );
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document.write( "on the high side, your z-score formula becomes:<BR>\n" );
document.write( "z = 48/24.48979593 = 1.96\r<BR>\n" );
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document.write( "you have established the 95% two tailed confidence interval and your error will be plus or minus 1%.\r<BR>\n" );
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document.write( "to see this visually, use the z-score calculator at <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "here's the visuals.\r<BR>\n" );
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document.write( "just in case you don't understand english, here it is in spanish.\r<BR>\n" );
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document.write( "En una investigación sobre el proceso de venta de un determinado producto manufacturado<BR>\n" );
document.write( "En varios establecimientos, el tamaño de la muestra se requiere con la confianza de<BR>\n" );
document.write( "95%. Se realiza una investigación preliminar, obteniendo los siguientes resultados:<BR>\n" );
document.write( "media = $ 4,800 unidad; desviación estándar $ 225. Con los datos anteriores, calcule la<BR>\n" );
document.write( "tamaño de la muestra, si se considera un error del 1% y E =% (X)\r<BR>\n" );
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document.write( "El intervalo de confianza del 95% conduce a una puntuación z crítica de más o menos 1,96.\r<BR>\n" );
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document.write( "media = 4800<BR>\n" );
document.write( "desviación estándar = 220\r<BR>\n" );
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document.write( "Si desea que el error sea del 1%, los límites deben ser de 4752 a 4848.\r<BR>\n" );
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document.write( "error estándar = desviación estándar dividida por la raíz cuadrada del tamaño de la muestra.\r<BR>\n" );
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document.write( "para el extremo inferior del intervalo de confianza, haga lo siguiente:\r<BR>\n" );
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document.write( "La fórmula del puntaje z es z = (x - m) / s\r<BR>\n" );
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document.write( "x es la puntuación bruta<BR>\n" );
document.write( "m es la media<BR>\n" );
document.write( "s es el error estándar.\r<BR>\n" );
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document.write( "en el extremo inferior, la fórmula se convierte en -1,96 = (4752 - 4800) / s<BR>\n" );
document.write( "simplificar para obtener:<BR>\n" );
document.write( "-1,96 = -48 / s<BR>\n" );
document.write( "resolver para que s obtenga:<BR>\n" );
document.write( "s = -48 / -1,96 = 24,48979592.\r<BR>\n" );
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document.write( "s = desviación estándar dividida por sqrt (tamaño de la muestra)<BR>\n" );
document.write( "desviación estándar = 220.<BR>\n" );
document.write( "s = 24,48979592<BR>\n" );
document.write( "fórmula se convierte en:<BR>\n" );
document.write( "24.48979592 = 220 / sqrt (tamaño de muestra)<BR>\n" );
document.write( "resuelva para sqrt (tamaño de muestra) para obtener:<BR>\n" );
document.write( "sqrt (tamaño de muestra) = 220 / 24.48979593<BR>\n" );
document.write( "resolver el tamaño de la muestra para obtener:<BR>\n" );
document.write( "tamaño de muestra = (220 / 24.48979593) ^ 2 = 80.7002777.\r<BR>\n" );
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document.write( "esa debería ser tu respuesta.<BR>\n" );
document.write( "puede redondear al siguiente entero más alto para obtener un tamaño de muestra = 81.\r<BR>\n" );
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document.write( "con un tamaño de muestra de 80.7002777, obtiene:<BR>\n" );
document.write( "s = 220 / sqrt (80.7002777) = 24.48979593.\r<BR>\n" );
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document.write( "su fórmula de puntuación z se convierte en:<BR>\n" );
document.write( "z = (-48) /24.48979593 = -1.96\r<BR>\n" );
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document.write( "en el lado alto, su fórmula de puntuación z se convierte en:<BR>\n" );
document.write( "z = 48 / 24,48979593 = 1,96\r<BR>\n" );
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document.write( "ha establecido el intervalo de confianza de dos colas del 95% y su error será más o menos 1%.\r<BR>\n" );
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document.write( "para ver esto visualmente, use la calculadora de puntuación z en <a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\"> http://davidmlane.com/hyperstat/z_table.html </a>\r<BR>\n" );
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document.write( "aquí están las imágenes.\r<BR>\n" );
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