document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136378>Question 1136378</A>: <I><SPAN STYLE=\"word-break: break-all;\">  survey of 3161 ​adults, 1410 say they have started paying bills online in the last year.<BR>\n" );
document.write( "Construct a​ 99% confidence interval for the population proportion. Interpret the results.<BR>\n" );
document.write( "A​ 99% confidence interval for the population proportion is ___<BR>\n" );
document.write( "​(Round to three decimal places as​ needed.)<BR>\n" );
document.write( "Interpret your results. Choose the correct answer below.<BR>\n" );
document.write( "A.<BR>\n" );
document.write( "The endpoints of the given confidence interval show that adults pay bills online​ 99% of the time.<BR>\n" );
document.write( "B.<BR>\n" );
document.write( "With​ 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.<BR>\n" );
document.write( "C.<BR>\n" );
document.write( "With​ 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754186 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=754186\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A 99% CI interval is mean +/- z(0.995)sqrt (p*(1-p)/n); z=2.576<BR>\n" );
document.write( "p=1410/3161=0.4461<BR>\n" );
document.write( "the half-interval is 2.576*sqrt (.4461*0.5539/3161)=0.0228<BR>\n" );
document.write( "the interval is (0.4233, 0.4689)\r<BR>\n" );
document.write( "\n" );
document.write( "We don't know the true proportion but we are extremely confident it lies in this interval.This is C.  CIs are about populations, not samples when they are interpreted.  That is why they are constructed. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );