document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269246>Question 269246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A machine produces 3-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:<BR>\n" );
document.write( "2.97  2.86  2.82  2.86  2.95  2.80  2.81  2.98  2.88  2.83  2.95  2.95<BR>\n" );
document.write( "Assuming that  = 0.01, test the hypothesis that the population mean is equal to 3.<BR>\n" );
document.write( "·         State the null and alternate hypotheses<BR>\n" );
document.write( "·         Calculate the mean and standard deviation<BR>\n" );
document.write( "·         Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "·         Determine the critical value(s).<BR>\n" );
document.write( "·         State your decision: Should the null hypothesis be rejected?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197376 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=197376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A machine produces 3-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:<BR>\n" );
document.write( "2.97  2.86  2.82  2.86  2.95  2.80  2.81  2.98  2.88  2.83  2.95  2.95<BR>\n" );
document.write( "Assuming that  = 0.01, test the hypothesis that the population mean is equal to 3.<BR>\n" );
document.write( "·         State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: u = 3<BR>\n" );
document.write( "H1: u is not equal to 3<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "·         Calculate the mean and standard deviation<BR>\n" );
document.write( "sample mean = 2.89 ; s = 0.067<BR>\n" );
document.write( "·         Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "ts = t(2.89) = (2.89-3)/[0.067/sqrt(12)] = -5.687<BR>\n" );
document.write( "----<BR>\n" );
document.write( "·         Determine the critical value(s).<BR>\n" );
document.write( "cv = +/-invT(0.005,11) = +/-3.106<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Conclusion: Since ts is in the reject interval, Reject Ho.<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "·         State your decision: Should the null hypothesis be rejected?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );