document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044004>Question 1044004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey of 628 males ages&#8203; 18-64, 393 say they have gone to the dentist in the past year.<BR>\n" );
document.write( "Construct&#8203; 90% and&#8203; 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If&#8203; convenient, use technology to construct the confidence intervals.\r<BR>\n" );
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document.write( "The&#8203; 90% confidence interval for the population proportion p is? Round to three decimal places as&#8203; needed.)\r<BR>\n" );
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document.write( "The&#8203; 95% confidence interval for the population proportion p is? Round to three decimal places as&#8203; needed.)\r<BR>\n" );
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document.write( "Interpret your results of both confidence intervals.<BR>\n" );
document.write( "A.With the given&#8203; confidence, it can be said that the sample proportion of males ages&#8203; 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.<BR>\n" );
document.write( "B.With the given&#8203; confidence, it can be said that the population proportion of males ages&#8203; 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval.<BR>\n" );
document.write( "C.With the given&#8203; confidence, it can be said that the population proportion of males ages&#8203; 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval.\r<BR>\n" );
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document.write( "Which interval is&#8203; wider?\r<BR>\n" );
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document.write( "a)The&#8203; 90% confidence interval\r<BR>\n" );
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document.write( "b)The&#8203; 95% 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 #659232 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> proportion(p) = 393 / 628 = 0.6258<BR>\n" );
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document.write( "standard error(se) = square root( 0.6258 * (1-0.6258) / 628 ) = 0.0193<BR>\n" );
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document.write( "90% confidence interval(CI)<BR>\n" );
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document.write( "alpha(a) = 1 - (90/100) = 0.10<BR>\n" );
document.write( "critical probability(p*) = 1 - (0.10/2) = 0.95<BR>\n" );
document.write( "degrees of freedom(df) = 628 -1 = 627<BR>\n" );
document.write( "critical value(use t statistic calculator) = 1.647<BR>\n" );
document.write( "margin of error(me) = 1.647 * 0.0193 = 0.0318<BR>\n" );
document.write( "90% ci is 0.626 + or - 0.032, that is, (0.594, 0.658)<BR>\n" );
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document.write( "95% ci<BR>\n" );
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document.write( "a = 1 - (95/100) = 0.05<BR>\n" );
document.write( "p* = 1 - (0.05/2) = 0.975<BR>\n" );
document.write( "df = 627<BR>\n" );
document.write( "cv = 1.964<BR>\n" );
document.write( "me = 1.964 * 0.0193 = 0.0379<BR>\n" );
document.write( "95% ci is 0.626 + or - 0.038, that is, (0.588, 0.664)<BR>\n" );
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document.write( "90% ci is (0.594, 0.658)<BR>\n" );
document.write( "95% ci is (0.588, 0.664)<BR>\n" );
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document.write( "We are trying to estimate the population proportion, answer is B<BR>\n" );
document.write( "95% ci is wider, answer is b<BR>\n" );
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