document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360460>Question 360460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.<BR>\n" );
document.write( "                      Number of Crimes by Area<BR>\n" );
document.write( "           A   B   C   D   E   F   G   H<BR>\n" );
document.write( "before    14   7   4   5  17  12   8   9<BR>\n" );
document.write( "after      2   7   3   6   8  13   3   5\r<BR>\n" );
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document.write( "Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the p-value.<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 #257341 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=257341\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The following are the values for the before-minus-after values:<BR>\n" );
document.write( "d = 12,   0,   1,   -1,   9 ,  -1,   5  , 4\r<BR>\n" );
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document.write( "The average m of these values are 29/8 = 3.625.<BR>\n" );
document.write( "Now the following corresponding values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-m%29%5E2 ALIGN=MIDDLE  ALT=\"%28d-m%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <BR>\n" );
document.write( "70.14,13.14,6.89,21.39,28.89,21.39,1.89,0.14.<BR>\n" );
document.write( "Their sum is 163.87.<BR>\n" );
document.write( "The standard deviation of the differences would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+sqrt%28163.87%2F7%29+=+4.8384 ALIGN=MIDDLE  ALT=\"s+=+sqrt%28163.87%2F7%29+=+4.8384\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the standard error is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SE=s%2Fsqrt%288%29+=+4.8384%2Fsqrt%288%29+=+1.71 ALIGN=MIDDLE  ALT=\"SE=s%2Fsqrt%288%29+=+4.8384%2Fsqrt%288%29+=+1.71\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Now we use a one-tailed matched-pairs t-test.\r<BR>\n" );
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document.write( "Null hypothesis: D = 0<BR>\n" );
document.write( "Alternative hypothesis: D > 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28m+-+D%29%2F+SE+=+%283.625+-0%29%2F1.71 ALIGN=MIDDLE  ALT=\"t+=+%28m+-+D%29%2F+SE+=+%283.625+-0%29%2F1.71\"   DISABLED_style= \"max-width:90%; height:auto;\" >, under assumption of the null hypothesis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2.12 ALIGN=MIDDLE  ALT=\"t+=+2.12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28T+%3C+2.12%29+=+0.9641 ALIGN=MIDDLE  ALT=\"P%28T+%3C+2.12%29+=+0.9641\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the p-value is 0.0359.  Since 0.0359>0.01, we don't reject the null hypothesis.  Hence the differences in the sample aren't significant to say that there is a drop in the number of crimes.<BR>\n" );
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