document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026006>Question 1026006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two different varieties of mushroom were grown on 6 and 7 plots of the same size. At the end of the crop run, the following quantities of yield were observed for the two varieties: Variety I 16 12 11 13 15 17 Variety II 11 11 10 15 14 16 10 Using the Mann-Whitney U test, verify at 0.05 level of significance whether the two varieties of mushroom produce the same yield. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641407 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The array of the 13 values are as follows:\r<BR>\n" );
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document.write( "10, 10, 11, 11, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2811%29 ALIGN=MIDDLE  ALT=\"highlight%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2812%29 ALIGN=MIDDLE  ALT=\"highlight%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2813%29 ALIGN=MIDDLE  ALT=\"highlight%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 14, 15, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2815%29 ALIGN=MIDDLE  ALT=\"highlight%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2816%29 ALIGN=MIDDLE  ALT=\"highlight%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 16, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2817%29 ALIGN=MIDDLE  ALT=\"highlight%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Their corresponding ranks are <BR>\n" );
document.write( "1.5, 1.5, 4, 4, 4, 6, 7, 8, 9.5, 9.5, 11.5, 11.5, 13\r<BR>\n" );
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document.write( "(The highlighted boxed numbers are the values from Variety 1.)\r<BR>\n" );
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document.write( "The sum of corresponding ranks of the highlighted numbers is T = 4+ 6+7+9.5+11.5 + 13 = 51\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U+=+n%5B1%5D%2An%5B2%5D+%2B+%28n%5B1%5D%2A%28n%5B1%5D%2B1%29%29%2F2+-+T+=+6%2A7+%2B%286%2A7%29%2F2+-+51+=+12 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looking at the critical values table of the Mann-Whitney U with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%5D+=+6 ALIGN=MIDDLE  ALT=\"n%5B1%5D+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B2%5D=++7 ALIGN=MIDDLE  ALT=\"n%5B2%5D=++7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+=+0.05 ALIGN=MIDDLE  ALT=\"alpha+=+0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the critical value would be 6.\r<BR>\n" );
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document.write( "Since U = 12 > 6, we conclude that there is significant difference between the two yields, and the two varieties of mushrooms do NOT produce the same yield. </SPAN>\n" );
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