document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137977>Question 1137977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99 % confidence assuming s equals 19.2 based on earlier​ studies? Suppose the doctor would be content with 90 % confidence. How does the decrease in confidence affect the sample size​ required?\r<BR>\n" );
document.write( "\n" );
document.write( "A​ 99% confidence level requires....BLANK....subjects? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755857 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=755857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 99%CI is tdf=?, 0.995*s/sqrt(n); 2=t*19.2/sqrt(n)<BR>\n" );
document.write( "square both sides and move the sqrt(n) over<BR>\n" );
document.write( "4n=t^2*19.2^2<BR>\n" );
document.write( "n=t^2(368.64/4)=t^2*92.16<BR>\n" );
document.write( "Since the t-value will be at least 2 and probably larger, the sample size will be a minimum of 370.  At that size, z can be used\r<BR>\n" );
document.write( "\n" );
document.write( "half-interval of 2=1.96*19.2/sqrt(n)<BR>\n" );
document.write( "4n=1.96^2*19.2^2<BR>\n" );
document.write( "n=354.04 or 355.\r<BR>\n" );
document.write( "\n" );
document.write( "The decrease in the confidence interval t 90% changes the t/z value to 1.645, and that is about 5/8 as much as the 99% confidence<BR>\n" );
document.write( "Because we are dealing with squares here, that will be about 25/64 or just under 40% of the prior sample size.  Lower confidence allows smaller samples, all else remaining constant.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );