document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030262>Question 1030262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In this problem, how do they get the 2.682?\r<BR>\n" );
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document.write( "Forty-nine items are randomly selected from a population of 500 items. The sample mean is 40 and the sample standard deviation 9.<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 #645147 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=645147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what is the problem asking for?<BR>\n" );
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document.write( "student states that a 99% confidence interval is needed<BR>\n" );
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document.write( "Margin of Error(M.E.) = critical value * standard deviation of statistic<BR>\n" );
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document.write( "Confidence interval(C.I.) = critical value + or - M.E.<BR>\n" );
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document.write( "the sample mean is 40 and sample standard deviation is 9<BR>\n" );
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document.write( "since sample size is > 30, we can assume normal distribution<BR>\n" );
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document.write( "M.E. = 9 / sqrt(49) = 1<BR>\n" );
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document.write( "critical value(CV) is calculated using these steps<BR>\n" );
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document.write( "1) alpha = 1 - (99/100) = 0.01<BR>\n" );
document.write( "critical probability = 1 - (0.01/2) = 0.995<BR>\n" );
document.write( "consult the z-tables for the associated z-value<BR>\n" );
document.write( "z-value = 2.576<BR>\n" );
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document.write( "Normal Distribution<BR>\n" );
document.write( "C.I. = 2.576 + or - 1<BR>\n" );
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document.write( "Now use the student t-distribution to calculate the critical value<BR>\n" );
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document.write( "the degrees of freedom(D.F.) = sample size - 1<BR>\n" );
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document.write( "D.F. = 49 - 1 = 48<BR>\n" );
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document.write( "the C.V. is the t-score having 48 degrees of freedom and a cumulative probability equal to 0.995<BR>\n" );
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document.write( "consult the table of t-scores<BR>\n" );
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document.write( "t-score = 2.682<BR>\n" );
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document.write( "Student t-distribution<BR>\n" );
document.write( "C.I. = 2.682 + or - 1<BR>\n" );
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