document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256273>Question 256273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with this problem?\r<BR>\n" );
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document.write( "The average weight of a package of rolled oats is supposed to be at least 18 ounces.  A sample of 18 packages shows a mean of 17.78 with a standard deviation of 0.41 ounces.       <BR>\n" );
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document.write( "a) What is the appropriate null and alternate hypothesis to determine if the packages <BR>\n" );
document.write( "are under filled?   <BR>\n" );
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document.write( "b) What is the p-value for the hypothesis test? <BR>\n" );
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document.write( "c) Using &#945; = 0.01, draw a conclusion for the hypothesis test.  Make sure you state <BR>\n" );
document.write( "your conclusion in the context of the problem. <BR>\n" );
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document.write( "d) Using &#945; = 0.05, draw a conclusion for the hypothesis test.  Make sure you state <BR>\n" );
document.write( "your conclusion in the context of the problem.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188516 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=188516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 with a standard deviation of 0.41 ounces. \r<BR>\n" );
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document.write( "a) What is the appropriate null and alternate hypothesis to determine if the packages are under filled?<BR>\n" );
document.write( "Ho: u >= 18<BR>\n" );
document.write( "H1: u < 18<BR>\n" );
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document.write( "b) What is the p-value for the hypothesis test?<BR>\n" );
document.write( "The test statistic is t = (17.78-18)/[0.41/sqrt(18)] = -0.22/0.09664<BR>\n" );
document.write( "= -2.2765<BR>\n" );
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document.write( "So the p-value is <BR>\n" );
document.write( "P(t<-2.2765 when df = 17) = tcdf(-100,-2.2765,17) = 0.01802..<BR>\n" );
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document.write( "c) Using &#945; = 0.01, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.<BR>\n" );
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document.write( "Since the p-value is greater than 1%, we fail to reject Ho.<BR>\n" );
document.write( "Based on this test we do not believe the rolled oats packages are under filled.<BR>\n" );
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document.write( "d) Using &#945; = 0.05, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.<BR>\n" );
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document.write( "Since the p-value is less than 5% we reject Ho.<BR>\n" );
document.write( "Based on this test we conclude the rolled oats packs do not contain at least<BR>\n" );
document.write( "18 ounces.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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