document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203080>Question 1203080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a trucking firm suspects that the mean lifetime of a certain tire it uses is less than 34,000 miles. To check the claim, the firm randomly selects and tests 54 of these tires and gets a mean lifetime of 33,390 miles with a standard deviation of 1200 miles. At α = 0.05<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 #838340 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838340\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population mean = 34000 = m<BR>\n" );
document.write( "sample size = 54 = n<BR>\n" );
document.write( "sample mean = 33390 = x<BR>\n" );
document.write( "sample standard deviation = 1200 = d<BR>\n" );
document.write( "one tailed confidence interval is .95 with .05 tail on the left end of it.<BR>\n" );
document.write( "it's a one tail confidence interval because the test is to determine if the mean lifetime of the sample is less than the population mean.<BR>\n" );
document.write( "since the standad deviation is taken from the sample, the t-test is used.<BR>\n" );
document.write( "the standard error of the test is equal to the standard deviation of the sample divided by the square root of the sample size = d / sqrt(n) = 1200 / sqrt(54) = 163.2993162.<BR>\n" );
document.write( "the t-score formula is t = (x-m)/s which is equal to (33390 - 34000) / 163.2993162 = -3.73547.<BR>\n" );
document.write( "the area to the left of that t-score, with 53 degrees of freedom, is equal to .00029828.<BR>\n" );
document.write( "this is considerably less than the critical p-value of .05.<BR>\n" );
document.write( "also, the critical t-score at 95% left side one tailed confidence interval is equal to t = -1.674116.<BR>\n" );
document.write( "the test t-score of -3.73547 is greater than this, supporting the conclusion that the results of the test are significant.<BR>\n" );
document.write( "this means that the mean lifetime of those certain tires can be assumed to actually be less than the 34000 originally stated.<BR>\n" );
document.write( "this is what the t-test results look like on a graph.\r<BR>\n" );
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