document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206941>Question 1206941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the 95% margin of error in estimating a population mean 𝜇 for the following values. (Round your answer to three decimal places.)<BR>\n" );
document.write( "n = 7,000, s2 = 64 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844735 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe you want to find the margin of error associated with a 95% confidence interval.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given tht n = 7000 and s^2 = 64.<BR>\n" );
document.write( "n is the sample size.<BR>\n" );
document.write( "s^2 is the variance.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the standard deviation is equal to the square root of the variance = sqrt(64) = 8.<BR>\n" );
document.write( "the standard error is equal to the standard deviation divided by the square root of the sample size = 8 / sqrt(7000) = .0956182887.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z-score for 95% confidence interval is z = plus or minus 1.96.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the margin of error is equal to (x-m) where x is the critical raw score and m is the mean).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the high side of the confidence interval, the formula becomes 1.96 = (x-m)/s.<BR>\n" );
document.write( "solve for (x-m) to get (x-m) = 1.96 * .0956182887 = .1874118459.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the low side of the confidence interval, the formula becomes -1.96 = (x-m)/s.<BR>\n" );
document.write( "solve for (x-m) to get (x-m) = -1.96 * .0956182887 = -.1874118459.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the margin of error is the same.<BR>\n" );
document.write( "it is added to the mean to get the high side of the confidence interval critical raw score (x).<BR>\n" );
document.write( "it is subtract from the mean to get the low side of the confidence interval critical raw score(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the mean is in the middle to the confidence interval.<BR>\n" );
document.write( "in this type of problem, it can be anything as long as the same standard error is used.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for example, if the mean is .5 (randomly chosen), then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the high side of the confidence interval will be 1.96 = (x - .5) / s which becomes 1.96 = (x - .5) / .0956182887.<BR>\n" );
document.write( "solve for x to get b = 1.96 * .095.... + .5 = .6874118459<BR>\n" );
document.write( "your margin of error is .6874118459 minus .5 = .1874118459 which is your desired margin of error.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "same thing happens on the low side of the confidence interval where the z-score is -1.96.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the standard error of .0956182887 is what we had calculated earlier in this analysis.\r<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" );