document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184081>Question 1184081</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The average dividend yield of a random sample of 25 JSE-listed companies this year was found <BR>\n" );
document.write( "to be 14.5%, with a sample standard deviation of 3.4%. Assume that dividend yields are <BR>\n" );
document.write( "normally distributed.  <BR>\n" );
document.write( "3.1.1 Calculate, with 90% confidence, the actual mean dividend yield of all JSE-listed <BR>\n" );
document.write( "companies this year. Interpret the finding.<BR>\n" );
document.write( "3.1.2 Calculate, with 95% confidence, the actual mean dividend yield of all JSE-listed <BR>\n" );
document.write( "companies this year. Compare the interval with the one calculated in 3.1.1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814619 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=814619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> since the standard deviation is taken from the sample, rather than from the population, use the t-score rather than the z-score.\r<BR>\n" );
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document.write( "sample size = 25<BR>\n" );
document.write( "sample mean = 14.5%<BR>\n" );
document.write( "sample standard deviation = 3.4%\r<BR>\n" );
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document.write( "standard error = sample standard deviation divided by square root of sample size = 3.4/sqrt(25) = 3.4/5 = .68\r<BR>\n" );
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document.write( "critical t-score with 24 degrees of freedom at 90% two-tailed confidence level = plus or minus 1.711.\r<BR>\n" );
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document.write( "critical t-score with 24 degrees of freedom at 95% two-tailed confidence level = plus or minus 2.064.\r<BR>\n" );
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document.write( "these were taken from the following table:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.math.odu.edu/stat130/t-tables.pdf\" target = \"_blank\">http://www.math.odu.edu/stat130/t-tables.pdf</a>\r<BR>\n" );
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document.write( "they were also verified through use of the ti-84 plus scientific calculator.\r<BR>\n" );
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document.write( "with a critical t-score of plus or minus 1.711, the critical raw score is calculated as shown below:\r<BR>\n" );
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document.write( "-1.711 = (x - 14.5) / .68<BR>\n" );
document.write( "solve for x to get x = -1.711 * .68 + 14.5 = 13.33652%\r<BR>\n" );
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document.write( "1.711 = (x - 14.5) / .68<BR>\n" );
document.write( "solve for x to get x = 1.711 * .68 + 14.5 = 15.66345%\r<BR>\n" );
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document.write( "with a critical t-score of plus or minus 2.064, the critical raw score is calculated as shown below:\r<BR>\n" );
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document.write( "-2.064 = (x - 14.5) / .68<BR>\n" );
document.write( "solve for x to get x = -2.064 * .68 + 14.5 = 13.09648%\r<BR>\n" );
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document.write( "2.064 = (x - 14.5) / .68<BR>\n" );
document.write( "solve for x to get x = 2.064 * .68 + 14.5 = 15.90352%\r<BR>\n" );
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document.write( "at 90% confidence level, the range is from 13.33652% to 15.66345%<BR>\n" );
document.write( "at 95% confidence level, the range is from 13.09648% to 15.90352%\r<BR>\n" );
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document.write( "the range is larger at 95% confidence level than at 90% confidence level.\r<BR>\n" );
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document.write( "this is to be expected because there needs to be less change of error at 95% confidence level than at 90% confidence level.\r<BR>\n" );
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document.write( "at 90% confidence level, 90% of the sample means, each with a sample size of 25, are expected to be within the range specified.\r<BR>\n" );
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document.write( "at 95% confidence level, 95% of the sample means, each with a sample size of 25, are expected to be within the range specified.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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