document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=852037>Question 852037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to the federal government, 24% of workers covered by their company's health care plan were not required to contribute to the premium (Statistical Abstract of the United States: 2006). A recent study found that 81 out of 400 workers sampled were not required to contribute to their company's health care plan.\r<BR>\n" );
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document.write( "a. Develop hypotheses that can be used to test whether the percent of workers not required to contribute to their company's health care plan has declined.<BR>\n" );
document.write( "H0: p _________________<BR>\n" );
document.write( "Ha: p _________________\r<BR>\n" );
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document.write( "b. What is a point estimate of the proportion receiving free company sponsored health care insurance?\r<BR>\n" );
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document.write( "c. Has a statistically significant decline occurred in the proportion of workers receiving free company sponsored health care insurance? Use alpha= 0.05 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #513155 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=513155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> pp = population proportion<BR>\n" );
document.write( "sp = sample proportion<BR>\n" );
document.write( "n = sample size<BR>\n" );
document.write( "pq = 1 - pp<BR>\n" );
document.write( "se = standard error = sqrt((pp*pq)/n)\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "pp = .24<BR>\n" );
document.write( "pq = 1 - .24 = .76<BR>\n" );
document.write( "sp = 81/400 = .2025<BR>\n" );
document.write( "n = 400<BR>\n" );
document.write( "se = sqrt ((.24*.76)/400) = .021354\r<BR>\n" );
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document.write( "z = z-score = (sp - pp) / se\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "z = (.2025 - .24) / .021354 which is equal to -1.756111\r<BR>\n" );
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document.write( "since you are looking for whether the ratio has declined, this is a one tailed test at .05 alpha.\r<BR>\n" );
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document.write( "you are looking for the proportion of the normal distribution curve that has a z-score less than -1.75611.\r<BR>\n" );
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document.write( "the z-score table tells you that this ratio is .039535.\r<BR>\n" );
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document.write( "since this is less than than than the stated alpha of .05, the results are statistically significant.\r<BR>\n" );
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document.write( "the answers to your questions are:\r<BR>\n" );
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document.write( "a. Develop hypotheses that can be used to test whether the percent of workers not required to contribute to their company's health care plan has declined.<BR>\n" );
document.write( "H0: p ____= .24_____________<BR>\n" );
document.write( "Ha: p ____< .24_____________<BR>\n" );
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document.write( "b. What is a point estimate of the proportion receiving free company sponsored health care insurance?<BR>\n" );
document.write( "sp = sample proportion = .2025<BR>\n" );
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document.write( "c. Has a statistically significant decline occurred in the proportion of workers receiving free company sponsored health care insurance? Use alpha= 0.05<BR>\n" );
document.write( "yes (.039535 is smaller than .05, therefore the results are significant).\r<BR>\n" );
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document.write( "a good reference on how to do a hypothesis on a proportion can be found at the following link:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://banach.millersville.edu/~BobBuchanan/math130/HTProportion/main.pdf\" target = \"_blank\">http://banach.millersville.edu/~BobBuchanan/math130/HTProportion/main.pdf</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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