document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039782>Question 1039782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A food snack manufacturer samples 9 bags of pretzels off the assembly line and weighed their contents. If the sample mean is 10.4 and the sample standard deviation is 0.15, find the 95% confidence interval of the true mean.<BR>\n" );
document.write( "	A.	<BR>\n" );
document.write( "(10.30, 10.50)<BR>\n" );
document.write( "	B.	<BR>\n" );
document.write( "(10.05, 10.75)<BR>\n" );
document.write( "	C.	<BR>\n" );
document.write( "(10.35, 10.45)<BR>\n" );
document.write( "	D.	<BR>\n" );
document.write( "(10.28, 10.52)<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 #654950 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=654950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3>Use a table like <a  rel=nofollow HREF=\"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">this one</a> to find the t critical value is t = 2.306\r<BR>\n" );
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document.write( "How to find this value? Look at the row that has df = 8 and look at the column that corresponds to 95% confidence. The value 2.306 is found at this row and column intersection\r<BR>\n" );
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document.write( "Note: degrees of freedom = df = n-1 = 9-1 = 8\r<BR>\n" );
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document.write( "We have the following information\r<BR>\n" );
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document.write( "xbar = 10.4 is the sample mean<BR>\n" );
document.write( "s = 0.15 is the standard deviation<BR>\n" );
document.write( "n = 9 is the sample size<BR>\n" );
document.write( "t = 2.306 is the t critical value (found above)\r<BR>\n" );
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document.write( "Let's compute the lower and upper boundaries<BR>\n" );
document.write( "L = lower boundary<BR>\n" );
document.write( "U = upper boundary\r<BR>\n" );
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document.write( "L = xbar - t*s/sqrt(n)<BR>\n" );
document.write( "L = 10.4 - 2.306*0.15/sqrt(9)<BR>\n" );
document.write( "L = 10.2847<BR>\n" );
document.write( "L = 10.28\r<BR>\n" );
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document.write( "U = xbar + t*s/sqrt(n)<BR>\n" );
document.write( "U = 10.4 + 2.306*0.15/sqrt(9)<BR>\n" );
document.write( "U = 10.5153<BR>\n" );
document.write( "U = 10.52\r<BR>\n" );
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document.write( "The 95% confidence interval, for the population mean mu, is therefore (L,U) = <font color=red>(10.28, 10.52)</font> which is <font color=red>choice D</font><BR>\n" );
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