document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186795>Question 1186795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t. \r<BR>\n" );
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document.write( "Test the claim that the mean lifetime of a particular car engine is greater than 220,000 miles. Sample data are summarized as n = 23, x-bar = 226,450  and  s=11,500.  Use a significance level of  5%.   Find the test statistic t.\r<BR>\n" );
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document.write( "2.69\r<BR>\n" );
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document.write( "-2.69\r<BR>\n" );
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document.write( "2.24\r<BR>\n" );
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document.write( "-2.24\r<BR>\n" );
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document.write( "12.9\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 #849371 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849371\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the test statistic t:\r<BR>\n" );
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document.write( "1. **Identify the given values:**\r<BR>\n" );
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document.write( "*   n (sample size) = 23<BR>\n" );
document.write( "*   x̄ (sample mean) = 226,450 miles<BR>\n" );
document.write( "*   s (sample standard deviation) = 11,500 miles<BR>\n" );
document.write( "*   μ (population mean under the null hypothesis) = 220,000 miles\r<BR>\n" );
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document.write( "2. **Use the formula for the t-statistic:**\r<BR>\n" );
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document.write( "t = (x̄ - μ) / (s / √n)\r<BR>\n" );
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document.write( "3. **Plug in the values:**\r<BR>\n" );
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document.write( "t = (226,450 - 220,000) / (11,500 / √23)<BR>\n" );
document.write( "t = 6,450 / (11,500 / 4.7958)<BR>\n" );
document.write( "t = 6,450 / 2400.05<BR>\n" );
document.write( "t ≈ 2.687\r<BR>\n" );
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document.write( "Rounding to two decimal places, the test statistic *t* is approximately 2.69.<BR>\n" );
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