document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=557083>Question 557083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain<BR>\n" );
document.write( "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<BR>\n" );
document.write( "to be weighed?  Why?<BR>\n" );
document.write( "B) Set up hypotheses and a two-tailed decision rule for the correct mean using<BR>\n" );
document.write( "the 5 percent level of significance.<BR>\n" );
document.write( "C) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hyposthesis that the true mean is 520? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362499 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=362499\">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<BR>\n" );
document.write( "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<BR>\n" );
document.write( "to be weighed?::: the t-distribution <BR>\n" );
document.write( "Why?::: small sample<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "B) Set up hypotheses and a two-tailed decision rule for the correct mean using<BR>\n" );
document.write( "the 5 percent level of significance.<BR>\n" );
document.write( "Ho: u = 520 ml (claim)<BR>\n" );
document.write( "Ha: u # 520 ml<BR>\n" );
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document.write( "Reject Ho is t < -2.26 or if t > 2.26<BR>\n" );
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document.write( "C) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hyposthesis that the true mean is 520?<BR>\n" );
document.write( "t(515) = (515-520)/[4/sqrt(16)] = -5/1 = -5<BR>\n" );
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document.write( "Since t = -5 is in the reject interval, reject Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );