document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196386>Question 1196386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You measure 21 backpacks' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 8.3 ounces. Based on this, what is the maximal margin of error associated with a 99% confidence interval for the true population mean backpack weight.\r<BR>\n" );
document.write( "\n" );
document.write( "Give your answer as a decimal, to two places\r<BR>\n" );
document.write( "\n" );
document.write( "±<BR>\n" );
document.write( "  <BR>\n" );
document.write( " ounces </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #829221 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=829221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size = 21<BR>\n" );
document.write( "sample mean = 45<BR>\n" );
document.write( "population standard deviation = 8.3<BR>\n" );
document.write( "sample standard error = 8.3 / sqrt(21) = 1.811208489.<BR>\n" );
document.write( "confidence level = .99<BR>\n" );
document.write( "critical alpha = .01 / 2 = .005.<BR>\n" );
document.write( "critical z-score = plus or minus 2.575829303.<BR>\n" );
document.write( "z-score formula = z = (x - m) / s<BR>\n" );
document.write( "z is the critical z-score.<BR>\n" );
document.write( "x is the critical raw score<BR>\n" );
document.write( "m is the sample mean<BR>\n" );
document.write( "s is the standard error.<BR>\n" );
document.write( "solving for x, you get:<BR>\n" );
document.write( "x1 = z1 * se + 45 = -2.57582903 * 1.811208489 + 45 = 40.3346361.<BR>\n" );
document.write( "x2 = z2 * se + 45 = 2.57582903 * 1.811208489 + 45 = 49.6653639.<BR>\n" );
document.write( "maximum margin of error = (x2 - x1) / 2 = 4.6653639.<BR>\n" );
document.write( "your solution is 4.67 rounded to two decimal places.<BR>\n" );
document.write( "confirmation that the confidence level = 99% is shown below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/091502.jpg\"><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );