document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197695>Question 1197695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A consumer group claims that the average annual consumption of high fructose corn syrup by a person in the U.S. is 48.8 pounds. You believe it is higher. You take a simple random sample of 34 people in the U.S. and find an average of 53.8 pounds with a standard deviation of 6 pounds. Test at 10% significance<BR>\n" );
document.write( "We can work this problem because:\r<BR>\n" );
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document.write( "Select an answer\r<BR>\n" );
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document.write( "Test Statistic: \r<BR>\n" );
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document.write( "P-value: \r<BR>\n" );
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document.write( "Did something significant happen? <BR>\n" );
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document.write( "Select the Decision Rule: <BR>\n" );
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document.write( "There <BR>\n" );
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document.write( " enough evidence to conclude  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831090 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "n = 34 = sample size<BR>\n" );
document.write( "xbar = 53.8 = sample mean<BR>\n" );
document.write( "s = 6 = sample standard deviation\r<BR>\n" );
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document.write( "mu = population mean<BR>\n" );
document.write( "sigma = population standard deviation<BR>\n" );
document.write( "Sigma is unknown, which is a common occurrence in stats. <BR>\n" );
document.write( "Despite sigma being unknown, we can use the Z distribution because n > 30. <BR>\n" );
document.write( "The T distribution is approximately fairly close to the standard Z distribution for these large values of n.\r<BR>\n" );
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document.write( "If sigma were unknown and n < 30, then we'd have to use the T distribution.\r<BR>\n" );
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document.write( "Hypothesis:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5B0%5D ALIGN=MIDDLE  ALT=\"H%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >: mu = 48.8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5BA%5D ALIGN=MIDDLE  ALT=\"H%5BA%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >: mu > 48.8<BR>\n" );
document.write( "The claim is in the alternative hypothesis.<BR>\n" );
document.write( "This gives us a right tailed test.\r<BR>\n" );
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document.write( "Computing the test statistic:<BR>\n" );
document.write( "z = (xbar - mu)/(s/sqrt(n))<BR>\n" );
document.write( "z = (53.8 - 48.8)/(6/sqrt(34))<BR>\n" );
document.write( "z = 4.85912657903776<BR>\n" );
document.write( "z = 4.86\r<BR>\n" );
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document.write( "Use a Z calculator to find that <BR>\n" );
document.write( "P(Z > 4.86) = 0.000000587<BR>\n" );
document.write( "which is the approximate p-value.<BR>\n" );
document.write( "I don't know how the tutor @ewatrrr got P(z ≤ 4.859) = .000014 as that is not correct.\r<BR>\n" );
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document.write( "This p-value 0.000000587 is very small. <BR>\n" );
document.write( "Depending how you round this, the p-value is effectively 0.\r<BR>\n" );
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document.write( "Whenever the p-value is smaller than alpha, we reject the null.<BR>\n" );
document.write( "We conclude that mu > 48.8 appears to be the case.\r<BR>\n" );
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document.write( "If you wanted to go the critical value route, then at 10% significance, the critical value is roughly z = 1.28 since P(Z > 1.28) = 0.10 approximately\r<BR>\n" );
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document.write( "The test statistic (z = 4.86) is to the right of the critical value (z = 1.28), which places the test statistic in the rejection region.<BR>\n" );
document.write( "This is another way to see why we reject the null in favor of the alternative hypothesis.<BR>\n" );
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