document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=459100>Question 459100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The US Department of Agriculture claims that the mean consumption of coffee by a person in the US is 24.2 gallons. A random sample of 120 people shows that the mean consumption is 23.5 gallons per year with a standard deviation of 3.2 gallons. At significance level 0.05 can you reject the claim?\r<BR>\n" );
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document.write( "I set Ho: u=24.2, Ha: u=23.5, found the z-score to be -2.4. I used that to find the p-value, which I got .0164, but I'm not sure if that's right.<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 #314870 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=314870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ha should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu%3C%3E24.2 ALIGN=MIDDLE  ALT=\"mu%3C%3E24.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because we do NOT know the population standard deviation, we CANNOT use the z test statistic. We must use the t test statistic (note: the sample size of 120 is large enough to get away with using a normal distribution, since the T distribution approaches a normal distribution for large n, but it's better to stick with T if you don't know the population standard deviation)\r<BR>\n" );
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document.write( "That test statistic is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} = \frac{23.5-24.2}{\frac{3.2}{\sqrt{120}}} = -2.396286\"> which rounds to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2.4 ALIGN=MIDDLE  ALT=\"t=-2.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So you have the correct value, just the wrong distribution.\r<BR>\n" );
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document.write( "Now use a calculator, or a table, to find the area under the curve T distribution curve from negative infinity to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2.4 ALIGN=MIDDLE  ALT=\"t=-2.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: the degrees of freedom are equal to 120 - 1 = 119). This area is equal to 0.0089728\r<BR>\n" );
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document.write( "Double this area (this is a two tailed test) to get 2* 0.0089728 = 0.0179456\r<BR>\n" );
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document.write( "So the p-value is roughly 0.018 (rounded to three places)(so you're close)\r<BR>\n" );
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document.write( "Since the p-value is less than alpha at 0.05, this means that we reject the null hypothesis.\r<BR>\n" );
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document.write( "Remember the claim was \"the mean consumption of coffee by a person in the US is 24.2 gallons.\", so the claim was Ho: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=24.2 ALIGN=MIDDLE  ALT=\"mu=24.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Because we rejected Ho (the null hypothesis), this means that we reject the claim that \"the mean consumption of coffee by a person in the US is 24.2 gallons.\" </SPAN>\n" );
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