document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142670>Question 1142670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are testing the claim that the proportion of men who own cats is larger than the proportion of women who own cats.\r<BR>\n" );
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document.write( "You sample 90 men, and 85% own cats.\r<BR>\n" );
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document.write( "You sample 50 women, and 40% own cats.\r<BR>\n" );
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document.write( "Find the pooled value of p, as a decimal, rounded to two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763438 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the proportion of men who own cats is 85%.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "p = .85<BR>\n" );
document.write( "q = .15<BR>\n" );
document.write( "s = sqrt(.85 * .15 * 90) = 3.87476937.\r<BR>\n" );
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document.write( "the proportion of women who own cats is 40%.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "p = .4<BR>\n" );
document.write( "q = .6<BR>\n" );
document.write( "s = sqrt(.4 * .6 * 50) = .0692820323.\r<BR>\n" );
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document.write( "in solving your problem, this reference comes in handy.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://stattrek.com/hypothesis-test/difference-in-proportions.aspx\" target =\"_blank\">https://stattrek.com/hypothesis-test/difference-in-proportions.aspx</a>\r<BR>\n" );
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document.write( "the pooled value of p is equal to (p1 * n1 + p2 * n2) / (n1 + n2).\r<BR>\n" );
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document.write( "this becomes (.85 * 90 + .40 * 50) / (90 + 50) = .6893 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "the pooled value of p is used to provide the standard error of the test.\r<BR>\n" );
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document.write( "the standard error of the test is equal to sqrt(p * q * (1/n1 + 1/n2)).\r<BR>\n" );
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document.write( "p is the pooled proportion.<BR>\n" );
document.write( "q is equal to 1 - p<BR>\n" );
document.write( "n1 is the sample size of the first sample.<BR>\n" );
document.write( "n2 is the sample size of the second sample.<BR>\n" );
document.write( "SE = standard error.\r<BR>\n" );
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document.write( "in this problem, you get SE = sqrt(.6893 * .3107 * (1/90 + 1/50)) = .0816 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "your test statistic is z = (p1 - p2) / SE\r<BR>\n" );
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document.write( "in this problem, that becomes z = (.85 - .40) / .0816 = 5.51 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "at a .05 one tailed alpha on the right, your critical z-score would be 1.65.\r<BR>\n" );
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document.write( "a z-score of 5.51 is well beyond this critical z-score.\r<BR>\n" );
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document.write( "you can therefore conclude that the proportion of men who own cats is larger than the proportion of women who own cats.\r<BR>\n" );
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document.write( "the results of the test are statistically significant.<BR>\n" );
document.write( "this means that the test z-score is greater then the critical z-score.\r<BR>\n" );
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document.write( "you were not, however, asked to do all this.\r<BR>\n" );
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document.write( "your solution, based on what you were asked, is that the pooled p is equal to .69 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "there is a z-score calculator that does all the dirty work for you.\r<BR>\n" );
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document.write( "this calculator can be found at <a  rel=nofollow HREF= \"https://www.socscistatistics.com/tests/ztest/default2.aspx\" target = \"_blank\">https://www.socscistatistics.com/tests/ztest/default2.aspx</a>\r<BR>\n" );
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document.write( "this calculator doesn't tell you how to calculate the pooled p.<BR>\n" );
document.write( "it does, however, use the pooled value of p to find the standard error.<BR>\n" );
document.write( "this, in turn, contributes to the z-score of the test.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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