document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=180477>Question 180477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The manufacturer of Winston Tire Company claims its new tires last for an average 40,000 miles.  An independent testing agency road-tested 20 tires to substantiate the claim made by the Winston Tire Company.  The sample mean was 39,000 miles with a sample standard deviation of 5,000 miles.  Using the .05 level of significance and the five-step hypothesis testing procedure, determine if there is reason to reject the claim made by Winston Tire Company and conclude that tires last for less than 40,000 miles.\r<BR>\n" );
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document.write( "My question: Am I on the right track and/or if not, what are the steps and formulas to use to solve for this?\r<BR>\n" );
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document.write( "I came up with: \r<BR>\n" );
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document.write( "H0: (Mu) = 40,000<BR>\n" );
document.write( "H1: (Mu) not equal to 40,000\r<BR>\n" );
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document.write( "Z = 39,000 – 40,000/5,000/ sqrt 20 = - 4\r<BR>\n" );
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document.write( "I would say: \r<BR>\n" );
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document.write( "Reject the null in favor of the alternative, since – 4 falls in the rejection region. \r<BR>\n" );
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document.write( "Thank you\r<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 #135248 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=135248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The manufacturer of Winston Tire Company claims its new tires last for an average 40,000 miles. An independent testing agency road-tested 20 tires to substantiate the claim made by the Winston Tire Company. The sample mean was 39,000 miles with a sample standard deviation of 5,000 miles. Using the .05 level of significance and the five-step hypothesis testing procedure, determine if there is reason to reject the claim made by Winston Tire Company and conclude that tires last for less than 40,000 miles. \r<BR>\n" );
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document.write( "My question: Am I on the right track and/or if not, what are the steps and formulas to use to solve for this? <BR>\n" );
document.write( "I came up with: <BR>\n" );
document.write( "H0: (Mu) = 40,000<BR>\n" );
document.write( "H1: (Mu) <  40,000 <BR>\n" );
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document.write( "Note: I changed to a left-tail test because of the words \"..conclude that<BR>\n" );
document.write( "tires last for LESS than 40,000 miles\".<BR>\n" );
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document.write( "Critical Value for a left-tail test with alpha=5% is -1.645<BR>\n" );
document.write( "Rule: Reject Ho if test statistic is < -1.645<BR>\n" );
document.write( "Z = (39,000 – 40,000)/[5,000/ sqrt 20] = -0.8944.<BR>\n" );
document.write( "p-value: P(z < -0.8944) = 0.186 = 18.6%<BR>\n" );
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document.write( "Note: I changed your test statistic result.<BR>\n" );
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document.write( "I would say: <BR>\n" );
document.write( "Reject the null in favor of the alternative, since – 4 falls in the rejection region. <BR>\n" );
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document.write( "Coclusion should be: Since the test statistic is not in the rejection interval,<BR>\n" );
document.write( "Fail to reject Ho.<BR>\n" );
document.write( "You could also say: Since p-value is greater than 5% Fail to reject Ho.<BR>\n" );
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document.write( "Interpretatation of the p-value: 18.6% of test result could have provided <BR>\n" );
document.write( "stronger evidence for rejecting Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "P.S.  Please let me know if this answer is any help to you. I see quite<BR>\n" );
document.write( "a few Stat questions but get little feedback from the questioners.<BR>\n" );
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