document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178848>Question 1178848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Agra-Tech Industries has recently introduced feed supplements for both cattle and hogs<BR>\n" );
document.write( "(pigs) that will increase the rate at which the animals gain weight. Three years of feedlot<BR>\n" );
document.write( "tests indicate that steers fed the supplement will weigh an average of 125 pounds more<BR>\n" );
document.write( "than those not fed the supplement. However, not every steer on the supplement has the<BR>\n" );
document.write( "same weight gain; results vary. The standard deviation in weight-gain advantage for the<BR>\n" );
document.write( "steers in the three-year study has been 10 pounds.<BR>\n" );
document.write( "Similar tests with hogs indicate those fed the supplement average 40 additional pounds<BR>\n" );
document.write( "compared with hogs not given the supplement. The standard deviation for the hogs was<BR>\n" );
document.write( "also 10 pounds. Even though the standard deviation is the same for both cattle and hogs,<BR>\n" );
document.write( "the mean weight gains differ.\r<BR>\n" );
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document.write( "i) Identify two main variables discussed in this scenario.<BR>\n" );
document.write( "ii) Compute the coefficient of variation for each variable.<BR>\n" );
document.write( "iii) Based on the answers to part ii, which population has data values that are more variable relative to the size of the population mean? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850288 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem:\r<BR>\n" );
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document.write( "**i) Identify Two Main Variables:**\r<BR>\n" );
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document.write( "The two main variables discussed in this scenario are:\r<BR>\n" );
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document.write( "1.  **Weight Gain Advantage for Steers (Cattle)**<BR>\n" );
document.write( "2.  **Weight Gain Advantage for Hogs (Pigs)**\r<BR>\n" );
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document.write( "**ii) Compute the Coefficient of Variation for Each Variable:**\r<BR>\n" );
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document.write( "The coefficient of variation (CV) is a measure of relative variability. It is calculated as:\r<BR>\n" );
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document.write( "CV = (Standard Deviation / Mean) * 100%\r<BR>\n" );
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document.write( "* **Steers (Cattle):**<BR>\n" );
document.write( "    * Mean (μ_steers) = 125 pounds<BR>\n" );
document.write( "    * Standard Deviation (σ_steers) = 10 pounds<BR>\n" );
document.write( "    * CV_steers = (10 / 125) * 100% = 0.08 * 100% = 8%\r<BR>\n" );
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document.write( "* **Hogs (Pigs):**<BR>\n" );
document.write( "    * Mean (μ_hogs) = 40 pounds<BR>\n" );
document.write( "    * Standard Deviation (σ_hogs) = 10 pounds<BR>\n" );
document.write( "    * CV_hogs = (10 / 40) * 100% = 0.25 * 100% = 25%\r<BR>\n" );
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document.write( "**iii) Based on the Answers to Part ii, Which Population Has Data Values That Are More Variable Relative to the Size of the Population Mean?**\r<BR>\n" );
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document.write( "* **Hogs (Pigs) have a higher coefficient of variation (25%)** compared to Steers (8%).\r<BR>\n" );
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document.write( "This means that the weight gain advantage for hogs is **more variable relative to its mean** than the weight gain advantage for steers. Even though both have the same standard deviation, the mean weight gain for hogs is much smaller, making the relative variability larger.<BR>\n" );
document.write( " </SPAN>\n" );
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