document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047800>Question 1047800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5.7   Suppose that the population standard deviation (sigma) for a normally distributed standardized test of achievement is known to be 7.20.  You can use these to estimate the standard error of the mean for a randomly drawn sample size of 16.  \r<BR>\n" );
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document.write( "  6  5    6  12   5  10  11  13<BR>\n" );
document.write( "12  10  9  20  23 28  20  18\r<BR>\n" );
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document.write( "But now suppose that we do not feel comfortable assuming that s = 7.20. Use the scores above to<BR>\n" );
document.write( "a.	estimate the standard error of the sample mean ()\r<BR>\n" );
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document.write( "b.	find the 95% confidence interval for the mean.<BR>\n" );
document.write( "      <BR>\n" );
document.write( "c. find the 99% confidence interval for the mean<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 #663365 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=663365\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample mean = 13<BR>\n" );
document.write( "sample SD = 6.9 (Generally rounded to one more decimal point than  Data values have)<BR>\n" );
document.write( "Recommend following to check work on sample means and 'corrected' standard deviations.<BR>\n" );
document.write( "www.numberempire.com/statisticscalculator.php<BR>\n" );
document.write( "95% confidence interval <BR>\n" );
document.write( "Small Sample - We are using the T distribution because <BR>\n" );
document.write( "a)  population standard deviation is not being used<BR>\n" );
document.write( "b) n = 16 < 30<BR>\n" );
document.write( "use t-value = 2.13<BR>\n" );
document.write( "SE = (2.13)(6.9/sqrt(16)) = (2.13)1.725<BR>\n" );
document.write( "Round the confidence interval limits to the same number of decimal places as the sample standard deviation<BR>\n" );
document.write( "CI = 13 ± SE\r<BR>\n" );
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document.write( "99% confidence interval <BR>\n" );
document.write( "Small Sample<BR>\n" );
document.write( "use t-value = 2.95<BR>\n" );
document.write( "SE = (2.95)(6.9/sqrt(16)) = (2.95)1.725 = 5.1<BR>\n" );
document.write( "Round the confidence interval limits to the same number of decimal places as the sample standard deviation<BR>\n" );
document.write( "CI = 13 ± 5.1 </SPAN>\n" );
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