document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285032>Question 285032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A machine produces 5-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows: <BR>\n" );
document.write( "5.01  5.00  4.93  4.95  4.98  5.05  5.01  5.05  4.97  5.08  5.03  4.91<BR>\n" );
document.write( "Assuming that  = 0.05, test the hypothesis that the population mean is equal to 5.<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?\r<BR>\n" );
document.write( "\n" );
document.write( "I TRIED LOOKING FOR THE NULL AND ALTERNATE HYPOTHESIS<BR>\n" );
document.write( "HO: U < 5<BR>\n" );
document.write( "Ha: U > 5<BR>\n" );
document.write( "N = 12\r<BR>\n" );
document.write( "\n" );
document.write( "WHEN I CALCULATE THE MEAN AND WITH THE STANDARD DEVIATION SHOUL I GO THROUGH THE VARIENCE THEN GO TO THE FORMULA FOR THE STANDARD DEVIATION. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206706 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=206706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A machine produces 5-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows: <BR>\n" );
document.write( "5.01 5.00 4.93 4.95 4.98 5.05 5.01 5.05 4.97 5.08 5.03 4.91<BR>\n" );
document.write( "Assuming that = 0.05, test the hypothesis that the population mean is equal to 5.<BR>\n" );
document.write( "· State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: u = 5<BR>\n" );
document.write( "Ha: u is not equal to 5<BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "· Calculate the mean and standard deviation<BR>\n" );
document.write( "x-bar = (sum of the lengths)/12 = 4.9975<BR>\n" );
document.write( "s = 0.0515<BR>\n" );
document.write( "--------------------  <BR>\n" );
document.write( "· Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "test stat = t(4.9975) = (4.9975-5)/(0.0515/sqrt(12) = -0.0140\r<BR>\n" );
document.write( "\n" );
document.write( "----------------------<BR>\n" );
document.write( "· Determine the critical value(s): t = +-invT(0.975)= +-2.2010<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "· State your decision: Should the null hypothesis be rejected?<BR>\n" );
document.write( "Since the test statistic is not in the reject interval, fail<BR>\n" );
document.write( "to reject Ho.<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "I TRIED LOOKING FOR THE NULL AND ALTERNATE HYPOTHESIS<BR>\n" );
document.write( "HO: U < 5<BR>\n" );
document.write( "Ha: U > 5<BR>\n" );
document.write( "N = 12 <BR>\n" );
document.write( "WHEN I CALCULATE THE MEAN AND WITH THE STANDARD DEVIATION SHOULD I GO THROUGH THE VARIENCE THEN GO TO THE FORMULA FOR THE STANDARD DEVIATION.<BR>\n" );
document.write( "Note: I used a TI-84 calculator to find the mean and the standard deviation.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );