document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1160297>Question 1160297</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A chemist compare the sugar contents of two brands of beverages with the same bottle sizes. Ten bottles of Brand X had an average sugar content of 3.1 grams with a standard deviation of 0.5 grams, while eight bottles of Brand Y had an average sugar of 2.7 grams with a standard deviation of 0.7 grams. We know that two sets of data are independent random samples from normal populations, and they have equal variances. Construct a 95% confidence interval for the difference (X-Y) between the mean sugar contents of the two brands of beverages. Decide which brand has a higher sugar ratio. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #783636 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=783636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the 95% CI (t) is (-0.2382, 1.0382) gms sugar.<BR>\n" );
document.write( "Because 0 is in the interval, one cannot conclude that one brand has more sugar than the other.\r<BR>\n" );
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document.write( "This can also be done with a two sample t-test with Ho: mu x=mu Y and Ha: mu X ne mu Y<BR>\n" );
document.write( "Done with a 2-sample t-test, df=12.3, the test statistic is t=1.36  and the p-value 0.20.  This fails to reject the Ho so there is insufficient evidence with these samples to show a difference in sugar ratio.   </SPAN>\n" );
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