document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=986136>Question 986136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The quality-control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours.  The population standard deviation is 100 hours.  A random sample of 64 light bulbs indicates a sample mean life of 350 hours.<BR>\n" );
document.write( "a) at the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?<BR>\n" );
document.write( "b)compute the p-value and interpret its meaning.<BR>\n" );
document.write( "c) construct a 95% confidence interval estimate of the population mean life of the light bulbs<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 #606870 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=606870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho=mean is 375<BR>\n" );
document.write( "Ha=mean is not 375<BR>\n" );
document.write( "alpha=0.05<BR>\n" );
document.write( "Test statistic is z=(xbar-mean)/100/(sqrt(64))<BR>\n" );
document.write( "critical value is |z|>1.96<BR>\n" );
document.write( "calculation is z=25*8/100=+2<BR>\n" );
document.write( "Reject Ho.  There is a significant difference in the mean life of the population of light bulbs.<BR>\n" );
document.write( "CI is 1.96*12.5=24.5 on each side, so it is (350.5,399.5).  The value of the sample mean is not in the confidence interval.<BR>\n" );
document.write( "the p-value is 0.0456.  This means that if the true mean were 375, in a sample of 64, we would expect to get this result about 4.56% of the time, below the 5% cut-off we established at the outset.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );