document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192862>Question 1192862</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.03 margin of error at a 99% level of confidence. <BR>\n" );
document.write( "a) With no prior research, what sample size should you gather in order to obtain a 0.03 margin of error? Round your answer up to the nearest whole number.<BR>\n" );
document.write( "b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of hat p =0.19 . Using this new information what sample size should you gather in order to obtain a 0.03 margin of error? Round your answer up to the nearest whole number </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825425 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=825425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> error for conservative 0.5 estimate=z(0.995)*sqrt(0.5*0.5/n)<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "0.0009=6.636*0.25/n<BR>\n" );
document.write( "n=6.636*0.25/0.0009=1843.27 or 1944.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "second one 0.03=2.576*.sqrt(0.0969/n)<BR>\n" );
document.write( "0.0009=6.635*0.0969/n<BR>\n" );
document.write( "n=713.29 or 714.\r<BR>\n" );
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document.write( "Really want to make a difference, use less confidence and allow the error to get a little larger... </SPAN>\n" );
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