document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110626>Question 1110626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.<BR>\n" );
document.write( "1306	1215	1299	1215	1268	1316	1275	1317	1275\r<BR>\n" );
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document.write( "(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)<BR>\n" );
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document.write( "s =	 <BR>\n" );
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document.write( "(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)<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 #725707 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) x = 1276 and standard deviation is 39<BR>\n" );
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document.write( "(b) 90% confidence interval<BR>\n" );
document.write( "alpha(a) = 1 - (90/100) = 0.10<BR>\n" );
document.write( "critical probability(p*) = 1 - (a/2) = 0.95<BR>\n" );
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document.write( "since the sample size is small(sample size < 30) and the population is normally distributed, we use the student t-tables<BR>\n" );
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document.write( "degrees of freedom(df) = 9 - 1 = 8<BR>\n" );
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document.write( "from the student t-tables, we see that a df=8 and p*=0.95 has a critical value(t-statistic) of 1.86<BR>\n" );
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document.write( "we do not have the population standard deviation, so we use the standard error<BR>\n" );
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document.write( "standard error(se) = sample standard deviation/square root(sample size)<BR>\n" );
document.write( "se = 39/square root(9) = 13<BR>\n" );
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document.write( "margin of error(me) is cv * se<BR>\n" );
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document.write( "me = 1.86 * 13 = 24.18 is approximately 24<BR>\n" );
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document.write( "90% confidence interval is 1276 + or - 24<BR>\n" );
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document.write( "lower limit is 1252<BR>\n" );
document.write( "upper limit is 1300<BR>\n" );
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