document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155919>Question 1155919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A machine is set to fill a small bottle with 9.0 grams of medicine. A sample of eight bottles revealed an average of 8.8 grams and a standard deviation of 0.23 grams.<BR>\n" );
document.write( "(a) Compute the 95% confidence interval for the population mean µ.<BR>\n" );
document.write( "(b) At 1% significance level, should we conclude that the mean weight is below 9.0 grams?<BR>\n" );
document.write( " Specify your H0 and H1, the test you use, and your conclusions. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778591 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=778591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: Weight is 9.0 gm  or above<BR>\n" );
document.write( "Ha: Weight is below 9.0 gm <BR>\n" );
document.write( "alpha=0.01 P{reject Ho|Ho true}<BR>\n" );
document.write( "test statistic is a t df=7 0.995<BR>\n" );
document.write( "critical value t<3.499<BR>\n" );
document.write( "calculation t=(8.8-9)/0.23/sqrt(8)<BR>\n" );
document.write( "=-0.2*sqrt(8)/0.23=-2.45. Fail to reject Ho.<BR>\n" );
document.write( "Conclude that at the 1% level that there is insufficient evidence to say that the filling is not 9.0 gm. (p-value=0.022) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );