document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975169>Question 975169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The percentages of adults 25 years of age and older who have completed 4 or more years of college are 23.6% for females and 27.8% for males. A random sample of women and men who were 25 years old or older was surveyed with these results. Estimate the true difference in proportions with 95% con&#64257;dence, and compare your interval with the Almanac statistics. The sample size is 350 for women and 400 for men with 100 women and 115 men completed 4 or more years respectively. <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 #596971 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=596971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a two sample proportion test.\r<BR>\n" );
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document.write( "The z value +/- the standard error will give the answer.\r<BR>\n" );
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document.write( "z= (phatw-phatm)/sqrt {[ (pw)(1-pw)/nw] + (pm)(1-pm)/pm]}\r<BR>\n" );
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document.write( "can do this by hand, but calculators are fine, so long as one knows what is going on.<BR>\n" );
document.write( "We expect the difference to be 4.2%, and the confidence interval will contain that value should there be no statistical significance at the 5% level.  Any result in the CI is considered equal to any other result.\r<BR>\n" );
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document.write( "It's worth looking at the point estimates:  For women, it is 0.286 and men 0.288.\r<BR>\n" );
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document.write( "This is a difference of -0.002.\r<BR>\n" );
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document.write( "z=-0.053 p=0.478\r<BR>\n" );
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document.write( "standard error is (.286)(.714)/350=0.0005834<BR>\n" );
document.write( "and (.288)(.712)/400 = 0.0005126<BR>\n" );
document.write( "sum is 000110; sqrt(sum) is 0.0331=SE<BR>\n" );
document.write( "multiply by z-value of 1.96, and we get 0.0649\r<BR>\n" );
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document.write( "CI (-0.0651,+0.0647)<BR>\n" );
document.write( "The CI contains the difference of 0 for the estimation of the true difference in proportions; therefore, the null hypothesis of no difference cannot be rejected.  Given the sample size, a percentage as large as shown in the Almanac could be found in a sample if there were no true difference in the parameters.\r<BR>\n" );
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