document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=420668>Question 420668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey of 4,581 U.S. households that owned a mobile phone found that 58 percent are satisfied with the coverage of their cellular phone provider. (a) Assuming that this was a random sample, construct a 90 percent confidence interval for the true proportion of satisfied U.S. mobile phone owners. (b) Why is the confidence interval so narrow?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293860 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=293860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A survey of 4,581 U.S. households that owned a mobile phone found that 58 percent are satisfied with the coverage of their cellular phone provider. <BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "(a) Assuming that this was a random sample, construct a 90 percent confidence interval for the true proportion of satisfied U.S. mobile phone owners. <BR>\n" );
document.write( "---<BR>\n" );
document.write( "p-hat = 0.58<BR>\n" );
document.write( "ME = 1.645*sqrt[0.58*0.42/4581] = 0.0987<BR>\n" );
document.write( "---<BR>\n" );
document.write( "90%CI: 0.58-0.0987< p < 0.58+0.0987<BR>\n" );
document.write( "---<BR>\n" );
document.write( "90%CI: 0.4813 < p < 0.6787<BR>\n" );
document.write( "-------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "(b) Why is the confidence interval so narrow?<BR>\n" );
document.write( "Its width is 2ME and ME is small because the sample size is large.<BR>\n" );
document.write( "======================================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============= <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );