document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157324>Question 1157324</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 35 bacteria reveals a sample mean of ¯x(x-bar)=74 hours with a standard deviation of s=6 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.7 hours at a 95% level of confidence.\r<BR>\n" );
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document.write( "What sample size should you gather to achieve a 0.7 hour margin of error? Round your answer up to the nearest whole number.\r<BR>\n" );
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document.write( "n = _______ bacteria </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780248 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=780248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 0.7=t*s/sqrt(n)<BR>\n" );
document.write( "problem is that t is dependent on the sample size which isn't known. So start with z<BR>\n" );
document.write( "0.7=1.96*6/sqrt(n)<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "0.49=3.8416*36/n<BR>\n" );
document.write( "282.24 or 283<BR>\n" );
document.write( "t (df=282)=1.968\r<BR>\n" );
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document.write( "recalculate using that and n=284.5 round to 285\r<BR>\n" );
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document.write( "This sample size will give exactly 0.7 margin of error<BR>\n" );
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