document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181555>Question 1181555</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 30 bacteria reveals a sample mean of  x = 74 hours with a standard deviation of  s = 5 hours.  You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 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 0.45 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 #811818 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=811818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the half-interval or 0.45=t(0.975,df=unknown)*s/sqrt(n); t=2.045<BR>\n" );
document.write( "start using z and 1.96 to estimate: 0.45=1.96*5/sqrt(n)<BR>\n" );
document.write( "sqrtIn)=9.8/0.45=21.78<BR>\n" );
document.write( "n=474.27 or 475<BR>\n" );
document.write( "The t-value for this is very close to 1.96 but maybe a percentage poignant away, or a sample size of 5-9<BR>\n" );
document.write( "At 475, the error is 0.451; at 480, 0.448<BR>\n" );
document.write( "It is exactly 0.45 at n=477. </SPAN>\n" );
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