document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205357>Question 1205357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey of 300 students at York University revealed that 112 favour an NDP candidate for M.P.  Construct a 98% confidence interval for the percentage of all York University students who favour an NDP candidate.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842101 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=842101\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = 112/300<BR>\n" );
document.write( "q = 1 - p = 1 - 112/300 = 300 /300 - 112/300 = (300 - 112)/300 = 188/300.<BR>\n" );
document.write( "standard error = sqrt(112/300 * 188/300 / 300) = .027926.<BR>\n" );
document.write( "98% two tail confidence interval requires a z-score of plus or minus 2.326.<BR>\n" );
document.write( "z = (x-m)/s<BR>\n" );
document.write( "z = plus or minus 2.326.<BR>\n" );
document.write( "x = x<BR>\n" );
document.write( "m = p = 112/300 = .373333<BR>\n" );
document.write( "s = .027963.<BR>\n" );
document.write( "on the low end of the confidence interval, -2.326 = (x-.373333)/.027963.<BR>\n" );
document.write( "solve for x to get x = -2.326 * .027963 + .373333 = .30829.<BR>\n" );
document.write( "on the high end of the confidence interval, 2.326 = (x - .373333)/.027963.<BR>\n" );
document.write( "solve for x to get x = 3.236 * .027963 + .373333 = .43837.<BR>\n" );
document.write( "your 98% confidence interval is from .30829 to .43837.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is what it looks like using z-scores.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/121221.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is what it looks like using raw scores.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/121222.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the z-score formula:<BR>\n" );
document.write( "z = the z-score<BR>\n" );
document.write( "x = the sample proportion<BR>\n" );
document.write( "m = the mean proportion which is equal to p<BR>\n" );
document.write( "s = the standard error.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p is equal to the proportion of the sample size that favor an NDP candidate.<BR>\n" );
document.write( "q = 1-p is equal to the proportion of the sample size that do not favor an NDP candidate.<BR>\n" );
document.write( "the mean proportion is equal to p which is equal to m in the z-score formula.\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( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );