document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135555>Question 135555</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780072966930/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A 20 minute consumer survey mailed to 500 adults aged 25-34 included a $5 Starbucks gift certificate.The same survey was mailed to 500 adults aged 25-34 without the gift certificate. There were 65 responses from the first group and 45 from the second group.(a)Perform a two tailed test comparing the response rates(proportions)at &#8733; = .05. (b) Form a confidence interval for the difference of proportions, without pooling the samples. Does it include zero?<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 #99321 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A 20 minute consumer survey mailed to 500 adults aged 25-34 included a $5 Starbucks gift certificate.The same survey was mailed to 500 adults aged 25-34 without the gift certificate. There were 65 responses from the first group and 45 from the second group.<BR>\n" );
document.write( "(a)Perform a two tailed test comparing the response rates(proportions)at &#8733; = .05. <BR>\n" );
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document.write( "p-hat with certificate = 65/500 = 0.13<BR>\n" );
document.write( "p-hat no certificate = 45/500 = 0.09<BR>\n" );
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document.write( "Ho: p-hats difference = 0<BR>\n" );
document.write( "Ha: p-hats no difference<BR>\n" );
document.write( "Pooled: p-bar = (65+45)/1000 = 110/1000 = 0.11<BR>\n" );
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document.write( "Crit value: z = +/- 1.96<BR>\n" );
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document.write( "Test Stat: z(0.13-0.09) = (0.04-0)/sqrt[(0.11)(0.89)/500 + (0.11)(0.89)/500]<BR>\n" );
document.write( "= 0.04/0.019789 = 2.02<BR>\n" );
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document.write( "Conclusion: Test stat is greater than crit value so Reject Ho.<BR>\n" );
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document.write( "(b) Form a confidence interval for the difference of proportions, without pooling the samples. p-hat(diff)=(0.13-0.09)<BR>\n" );
document.write( "E = 1.96sqrt[(0.13)(0.87)/500 + (0.09)(0.91)/500] = 1.96*0.019748=0.03871<BR>\n" );
document.write( "CI: 0.04-0.03871 < p < 0.04+0.03871<BR>\n" );
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document.write( "Does it include zero? No<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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