document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998759>Question 998759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8.32 In a survey of 2,395 adults, 1,916 reported that<BR>\n" );
document.write( "e-mails are easy to misinterpret, but only 1,269 reported that<BR>\n" );
document.write( "telephone conversations are easy to misinterpret. (Data<BR>\n" );
document.write( "extracted from “Open to Misinterpretation,” USA Today,<BR>\n" );
document.write( "July 17, 2007, p. 1D.)<BR>\n" );
document.write( "a. Construct a 95% confidence interval estimate for the<BR>\n" );
document.write( "population proportion of adults who report that e-mails<BR>\n" );
document.write( "are easy to misinterpret.<BR>\n" );
document.write( "b. Construct a 95% confidence interval estimate for the<BR>\n" );
document.write( "population proportion of adults who report that telephone<BR>\n" );
document.write( "conversations are easy to misinterpret.<BR>\n" );
document.write( "c. Compare the results of (a) and (b).\r<BR>\n" );
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document.write( "8.40 If a quality control manager wants to estimate, with<BR>\n" );
document.write( "95% confidence, the mean life of light bulbs to within +- 20 hours and also assumes that the population standard<BR>\n" );
document.write( "deviation is 100 hours, how many light bulbs need to be<BR>\n" );
document.write( "selected? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616507 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=616507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The proportion in the sample was 0.8<BR>\n" );
document.write( "The SE is sqrt ((0.8)(0.2/2395}=0.00817<BR>\n" );
document.write( "a 95% CI is 1.96*SE for the interval half width.<BR>\n" );
document.write( "It equals 0.016<BR>\n" );
document.write( "The CI is (0.784,0.816)<BR>\n" );
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document.write( "Telephone<BR>\n" );
document.write( "0.5298 is point estimate proportion<BR>\n" );
document.write( "SE={0.5298*0.4702/2395}^(1/2)=0.0102<BR>\n" );
document.write( "1.96*SE=0.02<BR>\n" );
document.write( "The CI is (0.51,0.53).  More decimal places may be added if desired.  The CI is wider, because the proportion is closer to 0.5<BR>\n" );
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document.write( "sample size unknown<BR>\n" );
document.write( "we know that 1.96 * SE is the interval, and the interval must be +/- 20 hours<BR>\n" );
document.write( "The SE is the SD/sqrt(n)<BR>\n" );
document.write( "1.96*SD/sqrt(n)=20<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "3.84*10000/n =400<BR>\n" );
document.write( "n=38416/400=96.04 round to 97<BR>\n" );
document.write( "Check this<BR>\n" );
document.write( "mean +/-  s/sqrt(n)<BR>\n" );
document.write( "that is 100/sqrt(97)=10.153<BR>\n" );
document.write( "That *1.96=19.90, slightly below 20 because need to round the 96.04 up to next higher.<BR>\n" );
document.write( "97 light bulbs.<BR>\n" );
document.write( " </SPAN>\n" );
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