document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130980>Question 130980</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At Ajax Spring Water, a 1/2 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?<BR>\n" );
document.write( "(B) Set up hypotheses and a twotailed decision rult 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 that contradict the hypothesis that the true mean is 520ml? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95703 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=95703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At Ajax Spring Water, a 1/2 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" );
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document.write( "(A) which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?<BR>\n" );
document.write( "The t-distribution which is suitable for small-sample testing.<BR>\n" );
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document.write( "(B) Set up hypotheses and a twotailed decision rule for the correct mean using the 5 percent level of significance.<BR>\n" );
document.write( "Ho: mu = 520<BR>\n" );
document.write( "Ha: mu is not equal to 520<BR>\n" );
document.write( "Critical values for alpha = 5% and 9 degrees of freedom : t = +-1.833<BR>\n" );
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document.write( "(C) If a sample of 16 bottles shows a mean fill of 515 ml, does that contradict the hypothesis that the true mean is 520ml?<BR>\n" );
document.write( "Critical values for alpha=5% and 15 degrees of freedom : t= +-1.753<BR>\n" );
document.write( "Test statistic: t(515)=(515-520)/[4/sqrt(16)]=-5*4/4 = -5<BR>\n" );
document.write( "Conclusion: Since -5 < -1.753, reject Ho; this contradicts the hypothesis<BR>\n" );
document.write( "that the true mean is 520 ml.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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