document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131776>Question 1131776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a study of cell phone use and brain hemispheric&#8203; dominance, an Internet survey was&#8203; e-mailed to 2640 subjects randomly selected from an online group involved with ears. 1038 surveys were returned. Construct a 90&#8203;% confidence interval for the proportion of returned surveys.\r<BR>\n" );
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document.write( "&#8203;a) Find the best point estimate of the population proportion p.<BR>\n" );
document.write( "= ____<BR>\n" );
document.write( "&#8203;(Round to three decimal places as&#8203; needed.)\r<BR>\n" );
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document.write( "&#8203;b) Identify the value of the margin of error E.<BR>\n" );
document.write( "E = _____\r<BR>\n" );
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document.write( "&#8203;(Round to three decimal places as&#8203; needed.)\r<BR>\n" );
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document.write( "&#8203;c) Construct the confidence interval.<BR>\n" );
document.write( "= ____ < p < ____\r<BR>\n" );
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document.write( "&#8203;(Round to three decimal places as&#8203; needed.)\r<BR>\n" );
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document.write( "&#8203;d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.<BR>\n" );
document.write( "A.<BR>\n" );
document.write( "There is a 90&#8203;% chance that the true value of the population proportion will fall between the lower bound and the upper bound.<BR>\n" );
document.write( "B.<BR>\n" );
document.write( "One has 90&#8203;% confidence that the sample proportion is equal to the population proportion.<BR>\n" );
document.write( "C.<BR>\n" );
document.write( "One has 90&#8203;% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.<BR>\n" );
document.write( "D.<BR>\n" );
document.write( "90&#8203;% of sample proportions will fall between the lower bound and the upper bound. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748470 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=748470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The point estimate is the best guess and that is 1038/2640 or 0.393<BR>\n" );
document.write( "the half-interval is z(0.95), for two sided confidence interval, * sqrt (p*(1-p)/n); the sqrt term is the standard error of the mean.<BR>\n" );
document.write( "=1.645*sqrt(0.393*0.607/2640)<BR>\n" );
document.write( "=0.0156\r<BR>\n" );
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document.write( "The CI is the point estimate+/- z*SE or 0.393+/-0.0156<BR>\n" );
document.write( "(0.3774, 0.4086) \r<BR>\n" );
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document.write( "This means that one is 90% confident that the true value, unknown and unknowable is in this interval.  That is C.  <BR>\n" );
document.write( "A is not true because the population proportion either does or doesn't fall in the interval, it isn't moving around.<BR>\n" );
document.write( "B is not usually true ever except in small populations.<BR>\n" );
document.write( "D refers to doing many sample proportions, and 90% of them will contain the population parameter.  We don't know which 90 those are, however. </SPAN>\n" );
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