document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120540>Question 1120540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car dealer states that a new brand of car gets 35 miles per gallon on  average. Suppose a consumer group claims that these cars get less than 35 miles per gallon. A sample of 40 cars is selected, and the sample mean for the 40 cars is 33 miles per gallon while the standard deviation is 3.8.\r<BR>\n" );
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document.write( "1) State the null and alternative hypotheses for this test.<BR>\n" );
document.write( "2) Calculate the test statistic for this test. Explain what this test statistic represents.<BR>\n" );
document.write( "3) Use technology to calculate the p-value for this test. Explain what this p-value represents.<BR>\n" );
document.write( "4) State the conclusion for this test at the 0.05 level of significance. Do you think the car dealer is telling the truth? Why or why not?<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 #736206 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=736206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: mean is >=35<BR>\n" );
document.write( "Ha: mean is not<BR>\n" );
document.write( "alpha=0.05<BR>\n" );
document.write( "test stat is a t 0.95, df=39<BR>\n" );
document.write( "critical value t < -1.69. If the test statistic is less than -1.69, it will be considered to be outside the possibility of a chance random effect.  One way test<BR>\n" );
document.write( "test statistic t=(33-35)/3.8/sqrt (40)  (mbar-mean)/s/sqrt(n)<BR>\n" );
document.write( "t=-2*sqrt(40)/3.8=-3.33. This is the number of sd s in the t-distribution for data with a mean of 35 and s of 3.8 with df=39.<BR>\n" );
document.write( "p value=0.001.  If the null hypothesis were true, the probability of getting a result of this magnitude or less is one in a thousand.<BR>\n" );
document.write( "Reject Ho and conclude that the mean is less than 35 mpg.  \r<BR>\n" );
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document.write( "There are many such reasons for this including the dealer is not telling the truth; that is not a statistical conclusion given what is given.\r<BR>\n" );
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