document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157904>Question 1157904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are a researcher studying the lifespan of a certain species of bacteria.  A preliminary sample of 40 bacteria reveals a sample mean of ¯x=72 hours with a standard deviation of s= 5.2 hours.  You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.55 hours at a 99% level of confidence.\r<BR>\n" );
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document.write( "What sample size should you gather to achieve a 0.55 hour margin of error? Round your answer up to the nearest whole number.\r<BR>\n" );
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document.write( "n =_______bacteria\r<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 #780850 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780850\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> half-interval is t (df=unknown, 0.995)*s/sqrt(n).  Use z first<BR>\n" );
document.write( "=2.576*5.2/sqrt(n)=0.55 units hours<BR>\n" );
document.write( "13.3952/sqrt(n)=.55<BR>\n" );
document.write( "so 13.3952/0.55=sqrt(n)<BR>\n" );
document.write( "n=593.16 round to 594\r<BR>\n" );
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document.write( "t df=594 should be close to z<BR>\n" );
document.write( "divide t 0.995/z 0.995 and multiply by 594<BR>\n" );
document.write( "that gives 596 rounded upward.<BR>\n" );
document.write( "can check <BR>\n" );
document.write( "t=2.584<BR>\n" );
document.write( "t*s/sqrt(586)=.55\r<BR>\n" );
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document.write( "596 is the sample size needed.\r<BR>\n" );
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