document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085998>Question 1085998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid<BR>\n" );
document.write( "diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds<BR>\n" );
document.write( "with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation<BR>\n" );
document.write( "of 14 pounds.\r<BR>\n" );
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document.write( "a. H0: _______\r<BR>\n" );
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document.write( "b. Ha: _______\r<BR>\n" );
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document.write( "c. In words, CLEARLY state what your random variable Xor P&#8242; represents.\r<BR>\n" );
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document.write( "d. State the distribution to use for the test.\r<BR>\n" );
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document.write( "e. What is the test statistic?\r<BR>\n" );
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document.write( "f. What is the p-value? In one or two complete sentences, explain what the p-value means for this problem.\r<BR>\n" );
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document.write( "g. Use the previous information to sketch a picture of this situation. CLEARLY, label and scale the horizontal axis and<BR>\n" );
document.write( "shade the region(s) corresponding to the p-value\r<BR>\n" );
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document.write( "H. Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate<BR>\n" );
document.write( "conclusion, using complete sentences.<BR>\n" );
document.write( "i. Alpha: _______<BR>\n" );
document.write( "ii. Decision: _______<BR>\n" );
document.write( "iii. Reason for decision: _______<BR>\n" );
document.write( "iv. Conclusion: _______\r<BR>\n" );
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document.write( "I. Construct a 95% confidence interval for the true mean or proportion. Include a sketch of the graph of the situation.<BR>\n" );
document.write( "Label the point estimate and the lower and upper bounds of the confidence interval.<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 #700285 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=700285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: mean 1<= mean 2, meaning liquid diet causes less or the same weight loss as powder.<BR>\n" );
document.write( "Ha:mean 1>mean 2<BR>\n" );
document.write( "alpha=0.05 P{reject Ho|ho true}<BR>\n" );
document.write( "2 sample t test where (x1 bar-x2 bar)/SE will give a t-statistic with df=83, 0.95, 1 df lost from each group.<BR>\n" );
document.write( "Test statistic for 1 way test is t>1.644.  Reject if t >1.644, otherwise fail to reject.<BR>\n" );
document.write( "t=(45-42)/SE<BR>\n" );
document.write( "SE is sqrt (s1^2/n1 + (s2^2/n2))=sqrt (196/36 + 144/49=sqrt(8.38)=2.895<BR>\n" );
document.write( "t=3/2.895=1.036<BR>\n" );
document.write( "p-value=0.15.  That means if the Ho is true, we would have a 15% chance of finding a result this great or more.  Since we require a 5% chance or less, we fail to reject Ho.<BR>\n" );
document.write( "CI=1.644*2.895=4.76<BR>\n" );
document.write( "One way confidence interval is 4.76 should be < the difference in the means.  It is not.  If a two way confidence interval is desired, there has to be a two way test, and here the question implies a one way test.  A two way test would have the question: \"is there a difference between the powder and the liquid?\" </SPAN>\n" );
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