document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314594>Question 314594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> As a part of contract negotiations, management claims that the mean annual salary for clerical workers is $30,000. The union would like to show the mean is lower. A random sample of 17 annual clerical salaries is collected and yields a sample mean of $28,157 and standard deviation of $3500. Is this sufficient evidence to support the Union's position? Use a significance level of a = 0.05. You may assume the mean annual salaries are normally distributed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225104 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=225104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As a part of contract negotiations, management claims that the mean annual salary for clerical workers is $30,000. <BR>\n" );
document.write( "The union would like to show the mean is lower.<BR>\n" );
document.write( "Ho: u = 30,000<BR>\n" );
document.write( "Ha: u < 30,000<BR>\n" );
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document.write( "A random sample of 17 annual clerical salaries is collected and yields a sample mean of $28,157 and standard deviation of $3500. Is this sufficient evidence to support the Union's position? Use a significance level of a = 0.05. You may assume the mean annual salaries are normally distributed.<BR>\n" );
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document.write( "t(28157) = (28157-30000)/[3500/sqrt(17)] = -2.1711<BR>\n" );
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document.write( "p-value: P(t<-2.1711 with df = 16) = 0.0227<BR>\n" );
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document.write( "Conclusion:  Since the p-value is less than 5%, reject<BR>\n" );
document.write( "Ho.  The test results do not support mgmt's opinion.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "stan H. </SPAN>\n" );
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