document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182495>Question 1182495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Santos and Casey began arguing about who did better on their tests, but they couldn't decide who did better given they took different tests.<BR>\n" );
document.write( "Santos took a test in Art History and earned a 77.3, and Casey took a test in Math and earned a 69.<BR>\n" );
document.write( "Use the fact that all student's test grades in the Art History class had a mean of 61.4 and a standard deviation of 9.5 to answer the following questions.\r<BR>\n" );
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document.write( "a. Z-score for Santo's test grade <BR>\n" );
document.write( "   z = _______\r<BR>\n" );
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document.write( "b. X-score for Casey's test grade.<BR>\n" );
document.write( "   z=  _______\r<BR>\n" );
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document.write( "c. Which person did relatively better?<BR>\n" );
document.write( "   Santos<BR>\n" );
document.write( "   Casey<BR>\n" );
document.write( "   They did equally well </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812555 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "For the entire art history class, we have<BR>\n" );
document.write( "mu = population mean score = 61.4<BR>\n" );
document.write( "sigma = population standard deviation of the scores = 9.5<BR>\n" );
document.write( "The population being just this art class only.\r<BR>\n" );
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document.write( "Santos got a 77.3 on the test, so this is the raw score x.\r<BR>\n" );
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document.write( "Convert to a z score<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (77.3-61.4)/9.5<BR>\n" );
document.write( "z = 1.67368421052631<BR>\n" );
document.write( "z = 1.67<BR>\n" );
document.write( "This is the approximate z score for Santos\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "We run into a problem because Casey took a math test, and not an art history test. \r<BR>\n" );
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document.write( "Let's assume that both classes had the same population parameters (mu and sigma)\r<BR>\n" );
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document.write( "If so, then,<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (69-61.4)/9.5<BR>\n" );
document.write( "z = 0.8<BR>\n" );
document.write( "this represents Casey's z score but again only if the assumption above holds true. If Casey's math class had different mu and/or sigma values, then we won't get the same z score. It seems strange how your teacher didn't mention this. \r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "Again, we have to rely everything on the assumption made at the top of part (b). That assumption being mu and sigma are the same for art history and math.\r<BR>\n" );
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document.write( "If that assumption is true, then we see that Santos did better compared to Casey because his z score is higher (ie z = 1.67 is larger than z = 0.80).\r<BR>\n" );
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document.write( "If the assumption is false, then we cannot answer part (b) nor (c) because we simply don't have enough information. I would ask your teacher for clarification on this. <BR>\n" );
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