document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135377>Question 135377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A vending machine company that dispenses coffee into cups must fill the cups with 7.8oz of liquid. Before selling the vending machine to a college or business, the company tests the machine to be sure it is dispensing an average amount of 7.8oz of coffee. A sample of 6 amounts is shown below. The amount of coffee is assumed to be normally distributed with a standard deviation of 0.10 oz. At the .10 level of significance, does the machine dispense as expected? <BR>\n" );
document.write( "Treat as a small sample. \r<BR>\n" );
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document.write( "7.81  7.77  7.89  7.83  7.75  7.79 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99187 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=99187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A vending machine company that dispenses coffee into cups must fill the cups with 7.8oz of liquid. Before selling the vending machine to a college or business, the company tests the machine to be sure it is dispensing an average amount of 7.8oz of coffee. A sample of 6 amounts is shown below. The amount of coffee is assumed to be normally distributed with a standard deviation of 0.10 oz. At the .10 level of significance, does the machine dispense as expected? <BR>\n" );
document.write( "Treat as a small sample. <BR>\n" );
document.write( "7.81 7.77 7.89 7.83 7.75 7.79<BR>\n" );
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document.write( "Ho: u = 7.8<BR>\n" );
document.write( "Ha; u is not 7.8<BR>\n" );
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document.write( "x-bar = 7.8067 ; s=0.04967<BR>\n" );
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document.write( "Critical value for 2-tail t-test for alpha=10% and df=5: t =1.476<BR>\n" );
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document.write( "Test statistic: t(7.8067) = (7.8067-7.8)/[0.04967/sqrt(6)] = 0.3304<BR>\n" );
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document.write( "Conclusion: Since test stat is not in the reject interval, Fail to <BR>\n" );
document.write( "reject Ho. The test provides statistical evidence that the machine<BR>\n" );
document.write( "dispenses as expected.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );