document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257773>Question 257773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question:\r<BR>\n" );
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document.write( "3.A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is cheating its customers. The agency select 20 of these bottles, measures their contents, and obtains a sample mean of 11.7 ounces with a standard deviation of 0.70 ounce. Assume the distribution is normally distributed. Test the agency’s claim that the brewery is cheating its customers\r<BR>\n" );
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document.write( "a. Use the critical value t0 method from the normal distribution to test for the population mean &#61549;-symbol is a mean. Test the agency’s claim at the level of significance &#61537;-symbol is significance of alpha = 0.05. \r<BR>\n" );
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document.write( "1.	H0 : <BR>\n" );
document.write( "Ha : <BR>\n" );
document.write( "2.	&#61537; = significance of alpha symbol<BR>\n" );
document.write( "3.	Test statistics:    <BR>\n" );
document.write( "4.	P-value or critical z0 or t0.    \r<BR>\n" );
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document.write( "5.	Rejection Region: <BR>\n" );
document.write( "6.	Decision:        <BR>\n" );
document.write( "                    <BR>\n" );
document.write( "7.	Interpretation: \r<BR>\n" );
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document.write( "b. Use the critical value t0 method from the normal distribution to test for the population mean &#61549;-symbol is a mean. Test the agency’s claim at the level of significance &#61537;-symbol is signficance of alpha = 0.01\r<BR>\n" );
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document.write( "1.	H0 : <BR>\n" );
document.write( "Ha : <BR>\n" );
document.write( "2.	&#61537;-symbol is a significance of alpha = 0<BR>\n" );
document.write( "3.	Test statistics: <BR>\n" );
document.write( "4.	P-value or critical z0 or t0.  <BR>\n" );
document.write( "5.	Rejection Region:   <BR>\n" );
document.write( "6.	Decision:  <BR>\n" );
document.write( "7.	Interpretation:  \r<BR>\n" );
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document.write( "I have tried to understand this chapter but no luck.\r<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 #191619 by </B><A HREF=/tutors/aboutme.mpl?userid=onlinetutor365.com><B>onlinetutor365.com(14)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onlinetutor365.com><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/cgi-bin/show-face.mpl?user=onlinetutor365.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=191619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is cheating its customers. The agency select 20 of these bottles, measures their contents, and obtains a sample mean of 11.7 ounces with a standard deviation of 0.70 ounce. Assume the distribution is normally distributed. Test the agency’s claim that the brewery is cheating its customers<BR>\n" );
document.write( "  <BR>\n" );
document.write( "a. Use the critical value t0 method from the normal distribution to test for the population mean&#61549;. Test the agency’s claim at the level of significance &#61537; = 0.05. \r<BR>\n" );
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document.write( "1.	H0 : µ=12<BR>\n" );
document.write( "Ha : µ < 12 (because the problem claims there is cheating which is less than 12)<BR>\n" );
document.write( "2.	&#61537; =0.05 <BR>\n" );
document.write( "3.	Test statistics: <BR>\n" );
document.write( "t= (11.7-12)/[0.7/square root(20) = -1.92 <BR>\n" );
document.write( "   <BR>\n" );
document.write( "4.	P-value or critical z0 or t0.  <BR>\n" );
document.write( "The critical value of to=-1.729  \r<BR>\n" );
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document.write( "5.	Rejection Region: \r<BR>\n" );
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document.write( " 	 	 	12	 	 <BR>\n" );
document.write( "	-1.729				t-score\r<BR>\n" );
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document.write( "6.	Decision: <BR>\n" );
document.write( "Since test statistic of t=-1.92 <-1.729, we reject the null hypothesis.       <BR>\n" );
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document.write( "7.	Interpretation: \r<BR>\n" );
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document.write( "We conclude that there is significant evidence of the manufacturer's claim and provides strong evidence that the brewery is cheating\r<BR>\n" );
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document.write( "b. Use the critical value t0 method from the normal distribution to test for the population mean&#61549;. Test the agency’s claim at the level of significance &#61537; = 0.01<BR>\n" );
document.write( "(References: example 1 though 5 pages 397 - 401, end of section exercises 23 – 28   pages 404 - 405)   (5 points)\r<BR>\n" );
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document.write( "1.	H0 : µ=12<BR>\n" );
document.write( "Ha : µ < 12 (because the problem claims there is cheating which is less than 12)<BR>\n" );
document.write( "2.	&#61537; =0.05 <BR>\n" );
document.write( "3.	Test statistics: <BR>\n" );
document.write( "t= (11.7-12)/[0.7/square root(20) = -1.92 <BR>\n" );
document.write( "   <BR>\n" );
document.write( "4.	P-value or critical z0 or t0.  <BR>\n" );
document.write( "The critical value of to=-1.729  \r<BR>\n" );
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document.write( "5.	Rejection Region: \r<BR>\n" );
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document.write( " 	 	 	12	 	 <BR>\n" );
document.write( "	-2.539				t-score\r<BR>\n" );
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document.write( "6.	Decision: <BR>\n" );
document.write( "Since test statistic of t=-1.92 >-2.539, we fail to reject the null hypothesis.       <BR>\n" );
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document.write( "7.	Interpretation: \r<BR>\n" );
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document.write( "We conclude that there is no significant evidence of the manufacturer's claim and provides strong evidence that the brewery is cheating\r<BR>\n" );
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