document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035368>Question 1035368</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The manufacturer of a particular all-season tire claims that the tires last for 22,000 miles.  After purchasing the tires you discover that yours did not last the full 22,000 miles.  Suppose that a sample of 100 tires made by that manufacturer lasted on average 21,819 miles with a sample standard deviation of 1,295 miles.  Is there sufficient evidence to refute the manufacturer’s claim that the tires last 22,000 miles?  Let a = 0.05.  Assume that the population standard deviation is s = 1300.<BR>\n" );
document.write( "a.      Define the null and alternative hypotheses.<BR>\n" );
document.write( "b.      Find the appropriate rejection region.<BR>\n" );
document.write( "c.      Compute the test statistic.<BR>\n" );
document.write( "d.      What is your conclusion?  Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650035 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=650035\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The manufacturer of a particular all-season tire claims that the tires last for 22,000 miles. After purchasing the tires you discover that yours did not last the full 22,000 miles. Suppose that a sample of 100 tires made by that manufacturer lasted on average 21,819 miles with a sample standard deviation of 1,295 miles. Is there sufficient evidence to refute the manufacturer’s claim that the tires last 22,000 miles? Let a = 0.05. Assume that the population standard deviation is s = 1300.<BR>\n" );
document.write( "a. Define the null and alternative hypotheses.<BR>\n" );
document.write( "Ho: u >= 22000 (claim)<BR>\n" );
document.write( "Ha: u < 22000<BR>\n" );
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document.write( "b. Find the appropriate rejection region.<BR>\n" );
document.write( "z < -1.645<BR>\n" );
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document.write( "c. Compute the test statistic.<BR>\n" );
document.write( "z(21819-22000)/(1300/sqrt(100) = -1.3923<BR>\n" );
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document.write( "d. What is your conclusion? Explain.<BR>\n" );
document.write( "Since the test stat is not in the reject interval,<BR>\n" );
document.write( "fail to reject Ho. The test results support the claim.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "---------  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );