document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198410>Question 198410</A>: <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. <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( " (b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent<BR>\n" );
document.write( "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 hypothesis that the true mean is 520 ml?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148949 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=148949\">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( "The \"t\" distribution because the samples are small.<BR>\n" );
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document.write( "(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance.\r<BR>\n" );
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document.write( "Ho: u = 520<BR>\n" );
document.write( "Ha: u is not equal to 520<BR>\n" );
document.write( "Reject Ho is the test statistic is less than -2.262 or greater than +2.262\r<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 hypothesis that the true mean is 520 ml?<BR>\n" );
document.write( "Note: You have changed the sample size.<BR>\n" );
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document.write( "t(515) = (515-520)/[4/Sqrt(16)] = -5<BR>\n" );
document.write( "The p-value for a 2-tail test with t = -5 and df=15 = 2[P(t<-5)]=0.000158<BR>\n" );
document.write( "Since the p-value is less than 5%, reject Ho.<BR>\n" );
document.write( "The test does not support the claim that the mean amount is 520 mL.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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