document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161977>Question 1161977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a random sample of 80 workers from a factory in City A, it was found that 5% were unable to read, while in a random sample of 50 workers in city B, 8% were unable to read.  Can it be concluded that there is a difference in the proportions of nonreaders in the two cities?  Use alpha = .10.  Find the 90% confidence interval for the difference of the two proportions.  Does the confidence interval support your original conclusion? \r<BR>\n" );
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document.write( "a. State the hypotheses and identify the claim.<BR>\n" );
document.write( "b. Find the critical value(s).<BR>\n" );
document.write( "c. Compute the test value.<BR>\n" );
document.write( "d. Make the decision.<BR>\n" );
document.write( "e. Summarize the results. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785730 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=785730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference between two proportions test is<BR>\n" );
document.write( "z=(p1-p2)/sqrt(p1(1-pi)/n1+p2(1-p2)/n2))\r<BR>\n" );
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document.write( "The half-interval of the CI is the z*SE, where z(0.95) =1.645 for a 90% CI<BR>\n" );
document.write( "That is added to and subtracted from the difference of the means, which is -0.03 if we make it p(A)-p(B)\r<BR>\n" );
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document.write( "Ho:p(A)-p(B)=0<BR>\n" );
document.write( "Ha: p(A)-p(B) does not equal 0 <BR>\n" );
document.write( "alpha=0.10 p{reject Ho|Ho true}<BR>\n" );
document.write( "SE=sqrt (.05*.95/80+.08*.92/50)<BR>\n" );
document.write( "=0.04545<BR>\n" );
document.write( "the z value is -0.66, p-value=0.49 so Ho is not rejected\r<BR>\n" );
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document.write( "The half-interval is z*SE=1.645*0.0454=0.075<BR>\n" );
document.write( "the interval is (-0.105, +0,.045). Because 0 is in the confidence interval, we are 90% confident that the true parameter of the difference is in the interval, and because 0 is in the interval, that is another way of saying the two proportions could be part of the same population and therefore not different,\r<BR>\n" );
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document.write( " </SPAN>\n" );
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