document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179000>Question 1179000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A medical researcher wants to determine whether a drug changes the body's temperature.  Seven test subjects are randomly selected, and the body temperature (in degrees Fahrenheit) of each is measured.  The subjects are then given the drug and after 20 minutes, the body temperature of each is measured again.  The results are listed below.  At α=0.05, is there enough evidence to conclude that the drug reduces the body's temperature? \r<BR>\n" );
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document.write( "Subject <BR>\n" );
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document.write( "1 <BR>\n" );
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document.write( "2 <BR>\n" );
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document.write( "3 <BR>\n" );
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document.write( "4 <BR>\n" );
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document.write( "5 <BR>\n" );
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document.write( "6 <BR>\n" );
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document.write( "7 \r<BR>\n" );
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document.write( "Initial Temperature <BR>\n" );
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document.write( "103.4 <BR>\n" );
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document.write( "102.5 <BR>\n" );
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document.write( "101.1 <BR>\n" );
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document.write( "103.4 <BR>\n" );
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document.write( "102.9 <BR>\n" );
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document.write( "100.2 <BR>\n" );
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document.write( "100.9 \r<BR>\n" );
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document.write( "Second temperature <BR>\n" );
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document.write( "99.2 <BR>\n" );
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document.write( "98.4 <BR>\n" );
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document.write( "98.2 <BR>\n" );
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document.write( "99 <BR>\n" );
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document.write( "98.6 <BR>\n" );
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document.write( "99.7 <BR>\n" );
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document.write( "97.8 \r<BR>\n" );
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document.write( " Conditions:                                                     \r<BR>\n" );
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document.write( " Significance Level:\r<BR>\n" );
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document.write( "Hypothesis:                                                      \r<BR>\n" );
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document.write( "Conclusion: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813642 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=813642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The following are the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bi%5D ALIGN=MIDDLE  ALT=\"d%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = temp after - temp before:\r<BR>\n" );
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document.write( "-4.2, -4.1, -2.9, -4.4, -4.3, -0.5, -3.1.\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bm%5D+=+-23.5%2F7+=+-3.357 ALIGN=MIDDLE  ALT=\"d%5Bm%5D+=+-23.5%2F7+=+-3.357\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+sqrt%28%281%2F%28n-1%29%29%2Asum%28%28d%5Bi%5D+-+d%5Bm%5D%29%5E2%2C+i=1%2C7%29%29+=+sqrt%28%281%2F6%29%2Asum%28%28d%5Bi%5D+%2B3.357%29%5E2%2C+i=1%2C7%29%29+=+1.395 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > to 3 d.p.\r<BR>\n" );
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document.write( "Now \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B0%5D%3A++d+=+0 ALIGN=MIDDLE  ALT=\"H%5B0%5D%3A++d+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5Ba%5D%3A+d%3C+0 ALIGN=MIDDLE  ALT=\"H%5Ba%5D%3A+d%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with 5% significance level.\r<BR>\n" );
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document.write( "Using the test statistic  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=%28d%5Bm%5D-d%29%2F%28s%2Fsqrt%28n%29%29=+%28d%5Bm%5D-0%29%2F%28s%2Fsqrt%28n%29%29+=+%28sqrt%28n%29%2Ad%5Bm%5D%29%2Fs ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, one obtains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28sqrt%287%29%2A-3.357%29%2F1.395+=+-6.367 ALIGN=MIDDLE  ALT=\"t+=+%28sqrt%287%29%2A-3.357%29%2F1.395+=+-6.367\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The critical t-value is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B0.025%5D+=+-2.447 ALIGN=MIDDLE  ALT=\"t%5B0.025%5D+=+-2.447\"   DISABLED_style= \"max-width:90%; height:auto;\" > using https://stattrek.com/online-calculator/t-distribution.aspx.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-6.367+%3C+-2.447+=+t%5B0.025%5D ALIGN=MIDDLE  ALT=\"t+=+-6.367+%3C+-2.447+=+t%5B0.025%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we reject the null hypothesis and conclude that the drug reduces the body'stemperature. </SPAN>\n" );
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