document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233490>Question 233490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9.68- A process is supposed to produce aluminum castings with a mean weight of 1.223 kg. The weights follow a normal distribution with known standard deviation 0.084 kg. (a) Set up hypothesesand a two-tailed decision rule to detect quality control violations using the .05 level of significance. (b) From the following sample of 12 castings, what conclusion can you draw?\r<BR>\n" );
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document.write( "1.067 1.204 1.047 1.167 1.368 1.251<BR>\n" );
document.write( "1.274 1.185 1.261 1.345 1.077 1.335<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 #172325 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=172325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A process is supposed to produce aluminum castings with a mean weight of 1.223 kg. The weights follow a normal distribution with known standard deviation 0.084 kg.<BR>\n" );
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document.write( "(a) Set up hypotheses and a two-tailed decision rule to detect quality control violations using the .05 level of significance.<BR>\n" );
document.write( "Ho: u = 1.223<BR>\n" );
document.write( "Ha: u is not equal to 1.223 <BR>\n" );
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document.write( "(b) From the following sample of 12 castings, what conclusion can you draw? <BR>\n" );
document.write( "1.067 1.204 1.047 1.167 1.368 1.251<BR>\n" );
document.write( "1.274 1.185 1.261 1.345 1.077 1.335<BR>\n" );
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document.write( "The mean of the sample is 1.2151<BR>\n" );
document.write( "The std of the sample is 0.11041<BR>\n" );
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document.write( "test statistic: t(1.2151) = (1.2151-1.223)/[0.11041/sqrt(12)] = -0.24786..<BR>\n" );
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document.write( "p-value = 2P(t < -0.2486 with df = 11) = 2*0.40440 = 0.8088<BR>\n" );
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document.write( "Since the p-value is greater than 5%, fail to reject Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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