document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139079>Question 1139079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey of 2383 U.S. adults, 1073 think that there should be more government<BR>\n" );
document.write( "regulation of oil companies.<BR>\n" );
document.write( "(a) Construct a 95% confidence interval for the population proportion p of U.S.<BR>\n" );
document.write( "adults who think that there should be more government regulation of oil<BR>\n" );
document.write( "companies. (Be sure to verify that the assumptions are met for the procedure<BR>\n" );
document.write( "you use.)<BR>\n" );
document.write( "(b) Find the minimum sample size needed to estimate p that ensures with 99%<BR>\n" );
document.write( "confidence that the estimate is accurate within 3% (E = 0.03) of the population<BR>\n" );
document.write( "proportion. Use p hat = q hat = 0.5 in your calculation.\r<BR>\n" );
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document.write( "I have been working on this problem all day and I do not know what to do.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756861 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=756861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assume random sample, and numbers and probability are sufficiently large to use normal approximation.<BR>\n" );
document.write( "The point estimate is 1073/2383=0.450<BR>\n" );
document.write( "the half-interval is z*sqrt(p*1-p)/n)=1.96*sqrt(0.45*0.55/2383)<BR>\n" );
document.write( "0.45+/-1.96(1.01), the half-interval is 0.02<BR>\n" );
document.write( "the whole interval is (0.43, 0.47)\r<BR>\n" );
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document.write( "The half-interval is z0.995*sqrt (p*(1-p)/n)<BR>\n" );
document.write( "z is 2.576<BR>\n" );
document.write( "p and 1-p are 0.5<BR>\n" );
document.write( "the half-interval equals the error of 0.03<BR>\n" );
document.write( "square both sides and z^2*p(1-p)/n=0.0009<BR>\n" );
document.write( "so 6.64*0.25=0.0009n<BR>\n" );
document.write( "n=1844.44 or 1845<BR>\n" );
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