document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178386>Question 1178386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) A poll of 2,295 likely voters was conducted on the president’s performance. Approximately what margin of error would the approval rating estimate have if the confidence level is 95%? (Round your answer to 4 decimal places.)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Margin of error            <BR>\n" );
document.write( ".0172\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "(b) The poll showed that 46 percent approved the president’s performance. Construct a 90 percent confidence interval for the true proportion. (Round your answers to 4 decimal places.)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "The 90% confidence interval is from <BR>\n" );
document.write( "  to   \r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "(c) Would you agree that the percentage of all voters opposed is likely to be 50 percent?<BR>\n" );
document.write( "  <BR>\n" );
document.write( "multiple choice 2<BR>\n" );
document.write( "Yes, the confidence interval contains .50.<BR>\n" );
document.write( "No, the confidence interval does not contain .50. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807849 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=807849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Std error is sqrt(0.5*0.5/2295), with no other data being given, this is the most conservative result.<BR>\n" );
document.write( "it is 0.0104<BR>\n" );
document.write( "the margin of error for a 95%CI is z(0.95)*SE=0.020; the 0.0172 would work for using 50% probability and a 90% CI<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Now given that it was 46%, one can recompute the SE as 0.01780 for a 90% Ci.<BR>\n" );
document.write( "90%CI is (0.4422, 0.4778)<BR>\n" );
document.write( "I would agree that the percentage of voters opposed is likely to be 50%, because the 90% CI for approval does not contain 50%, so therefore the 90% CI for opposition WILL contain 50%.\r<BR>\n" );
document.write( "\n" );
document.write( "Two comments: the first part does not give a point estimate, so one has to use 50%.  If it did give a point estimate, then the value would change for the CI.<BR>\n" );
document.write( "Second, the value algebraically and on the calculator will be different, because the algebraic proportion can have a fraction in the numerator (half of 2295 is 1147.5.)  But the calculator will require an integer, and to four decimal places, the result will be different.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );