document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=359889>Question 359889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An engineering firm is evaluating their back charges.  They originally believed their average back charge was $1800. They are concerned that the true average is higher, which could hurt their quarterly earnings. They randomly select 40 customers, and calculate the corresponding sample mean back charge to be $1950.  If the standard deviation of back charges is $500, and alpha = 0.01, should the engineering firm be concerned?  Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #256805 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=256805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An engineering firm is evaluating their back charges. They originally believed their average back charge was $1800. They are concerned that the true average is higher, which could hurt their quarterly earnings. They randomly select 40 customers, and calculate the corresponding sample mean back charge to be $1950. If the standard deviation of back charges is $500, and alpha = 0.01, should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results<BR>\n" );
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document.write( "Ho: u = 1800<BR>\n" );
document.write( "Ha: u > 1800<BR>\n" );
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document.write( "t(1950) = (1950-1800)/[500/sqrt(40)] = 1.8974<BR>\n" );
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document.write( "p-value = p(t >1.8974 when df=39) = 0.3260<BR>\n" );
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document.write( "Since the p-value is greater than 1%, fail to reject Ho.<BR>\n" );
document.write( "The test results support Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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