Question 233490
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.
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(a) Set up hypotheses and a two-tailed decision rule to detect quality control violations using the .05 level of significance.
Ho: u = 1.223
Ha: u is not equal to 1.223 
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(b) From the following sample of 12 castings, what conclusion can you draw? 
1.067 1.204 1.047 1.167 1.368 1.251
1.274 1.185 1.261 1.345 1.077 1.335
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The mean of the sample is 1.2151
The std of the sample is 0.11041
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test statistic: t(1.2151) = (1.2151-1.223)/[0.11041/sqrt(12)] = -0.24786..
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p-value = 2P(t < -0.2486 with df = 11) = 2*0.40440 = 0.8088
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Since the p-value is greater than 5%, fail to reject Ho.
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Cheers,
Stan H.