SOLUTION: 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

Question 233490: 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?
1.067 1.204 1.047 1.167 1.368 1.251
1.274 1.185 1.261 1.345 1.077 1.335

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
---------------
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.

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