document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=264516>Question 264516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new car is designed to run a mean of at least 50 000 kilometres before its first tune-up. Tests with 30 cars show a sample mean of 49 500 kilometres and a sample standard deviation of 1000 kilometres.   <BR>\n" );
document.write( "a.<BR>\n" );
document.write( "Develop the null and alternative hypotheses most appropriate for testing the claim that the new car can run at least 50 000 kilometres before its first tune-up.  <BR>\n" );
document.write( "b.<BR>\n" );
document.write( "Using a .05 level of significance, test whether or not there is sufficient evidence to reject the claim of a mean of at least 50 000 kilometres.  <BR>\n" );
document.write( "c.<BR>\n" );
document.write( "What is the p-value.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194752 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=194752\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A new car is designed to run a mean of at least 50 000 kilometres before its first tune-up. Tests with 30 cars show a sample mean of 49 500 kilometres and a sample standard deviation of 1000 kilometres. <BR>\n" );
document.write( "a.<BR>\n" );
document.write( "Develop the null and alternative hypotheses most appropriate for testing the claim that the new car can run at least 50 000 kilometres before its first tune-up.<BR>\n" );
document.write( "Ho: u >= 50.000<BR>\n" );
document.write( "Ha: u < 50,000 <BR>\n" );
document.write( "b.<BR>\n" );
document.write( "Using a .05 level of significance, test whether or not there is sufficient evidence to reject the claim of a mean of at least 50 000 kilometres.<BR>\n" );
document.write( "test statistic: t(49,5000) = (49500-50,000)/[1000/Sqrt(30)] = -2.7386...<BR>\n" );
document.write( "critical value: invT(0.05,df=29) = -1.6991..<BR>\n" );
document.write( "Conclusion: Since the ts is to the left of the cv, reject Ho.<BR>\n" );
document.write( "--------------------------- <BR>\n" );
document.write( "c.<BR>\n" );
document.write( "What is the p-value.<BR>\n" );
document.write( "p-value = P(t<-1.6991 when df = 29) = tcdf(-100,-2.7386,df=29) = 0.00522<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );