document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170645>Question 170645</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780072966930/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. (a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why? (b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. (c) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hypothesis that the true mean is 520 ml?<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 #125976 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=125976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. <BR>\n" );
document.write( "(a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?<BR>\n" );
document.write( "Mean of the sample means: 520 ml<BR>\n" );
document.write( "St. Dev. of the sample means: 4/sqrt(10) <BR>\n" );
document.write( "Both are prescribed by the Central Limit Theorem<BR>\n" );
document.write( "----------------------------------------------------------- <BR>\n" );
document.write( "(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. <BR>\n" );
document.write( "Ho: mean = 520<BR>\n" );
document.write( "Ha: mean is not 520<BR>\n" );
document.write( "Reject Ho if z(mean of the sample) is > 1.96 or <-1.96<BR>\n" );
document.write( "------------------------------------------------------------<BR>\n" );
document.write( "(c) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hypothesis that the true mean is 520 ml?<BR>\n" );
document.write( "z(515) = (515-520)/[4/sqrt(10)]= -3.9528...<BR>\n" );
document.write( "Yes, it is evidence the mean is not 520.<BR>\n" );
document.write( "============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );