document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203742>Question 1203742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the year 2010, in a sample of 200 workers, 18% of Canadians indicate that they have<BR>\n" );
document.write( "taken time off work due to personal mental health issues. In the year 1990, a similar<BR>\n" );
document.write( "study was conducted and found that in a sample of 200 workers, 7% of Canadians<BR>\n" );
document.write( "indicated that they have taken time off work due to personal mental health conditions.<BR>\n" );
document.write( "a) Are the proportions of Canadians who take time off work due to personal mental<BR>\n" );
document.write( "health issue in 2010 is different than the proportion in 1990? Use α = 0.1. Use the<BR>\n" );
document.write( "critical value approach.<BR>\n" );
document.write( "b) Construct a 98% confidence interval for the difference in proportions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839555 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=839555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i used the two sample z-score proportion calculator at <a  rel=nofollow HREF= \"https://www.socscistatistics.com/tests/ztest/default2.aspx\" target = \"_blank\">https://www.socscistatistics.com/tests/ztest/default2.aspx</a> to solve this.<BR>\n" );
document.write( "the results are shown below:\r<BR>\n" );
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document.write( "calcuator says test alpha = .00086 which is significantly less than the critical alpha of .10.<BR>\n" );
document.write( "this indicates the results are significant, meaning that the sample difference is more then likely real and not just a result of random differences in sample proportions.<BR>\n" );
document.write( "the conclusion is that the proportions between 1990 and 2010 have changed, meaning that the different sample proportions are not due to random variations in sample proportions.\r<BR>\n" );
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document.write( "i checked the results manually and they agree with the calculator results that indicates the results are significant by a wide margin.\r<BR>\n" );
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document.write( "the method used is in the following reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://sixsigmastudyguide.com/two-sample-test-of-proportions/\" target = \"_blank\">https://sixsigmastudyguide.com/two-sample-test-of-proportions/</a>\r<BR>\n" );
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document.write( "the pooled version was used.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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