document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171865>Question 1171865</A>: <I><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( " <BR>\n" );
document.write( "Use the sample data and confidence level given below to complete parts​ (a) through​ (d).<BR>\n" );
document.write( "A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll,<BR>\n" );
document.write( "n=943 and x=579 who said​ \"yes.\" Use a 99% confidence level.\r<BR>\n" );
document.write( "\n" );
document.write( "a) Find the best point estimate of the population proportion p.<BR>\n" );
document.write( "b)Identify the value of the margin of error E.<BR>\n" );
document.write( "c) Construct the 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 #796786 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)<BR>\n" );
document.write( "The best estimate for the population proportion p is the sample proportion phat (read as \"p-hat\")\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In this case, <BR>\n" );
document.write( "phat = (number of yes responses)/(number total)<BR>\n" );
document.write( "phat = x/n<BR>\n" );
document.write( "phat = 579/943<BR>\n" );
document.write( "phat = 0.61399787910922<BR>\n" );
document.write( "phat = 0.614<BR>\n" );
document.write( "Which is approximate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "====================================================<BR>\n" );
document.write( "Part (b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "At 99% confidence, the z critical value is roughly z = 2.576\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The margin of error is<BR>\n" );
document.write( "E = z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "E = 2.576*sqrt(0.61399787910922*(1-0.61399787910922)/943)<BR>\n" );
document.write( "E = 0.040838360004<BR>\n" );
document.write( "E = 0.04<BR>\n" );
document.write( "This is approximate. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "====================================================<BR>\n" );
document.write( "Part (c)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We'll use the results of parts (a) and (b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The lower boundary L of the confidence interval is <BR>\n" );
document.write( "L = (center) - (margin of error)<BR>\n" );
document.write( "L = (phat) - (E)<BR>\n" );
document.write( "L = 0.61399787910922 - 0.040838360004<BR>\n" );
document.write( "L = 0.57315951910522<BR>\n" );
document.write( "L = 0.5732\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And the upper boundary U is<BR>\n" );
document.write( "L = (center) + (margin of error)<BR>\n" );
document.write( "L = (phat) + (E)<BR>\n" );
document.write( "L = 0.61399787910922 + 0.040838360004<BR>\n" );
document.write( "L = 0.65483623911322<BR>\n" );
document.write( "L = 0.6548\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The 99% confidence interval in the form L < p < U is roughly 0.5732 < p < 0.6548\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can write this as (0.5732, 0.6548)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We are 99% confident that the population proportion p is between 0.5732 and 0.6548<BR>\n" );
document.write( "</font><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );