Question 436818: Hi!
I was hoping I could get some help with this problem.
Thanks!
It costs more to produce defective items–-since they must be scrapped or reworked–-than it does to produce non-defective items. This simple fact suggest that manufacturers should ensure the quality of their products by perfecting their production processes rather than through inspection of finished products. In order to better understand a particular metal stamping process, a manufacturer wishes to estimate the mean length of items produced by the process during the past 24 hours.
A. How many parts should be sampled in order to estimate the population mean to within 0.3 mm with 95% confidence. Previous studies of this machine have indicated that the standard deviation of lengths produced by the stamping operation is about 2 mm.
B. Time permits the use of a sample size no larger than 100. If a 95% confidence interval for ì is constructed using n = 100, will it be wider or narrower than would have been obtained using the sample size from part a?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In order to better understand a particular metal stamping process, a manufacturer wishes to estimate the mean length of items produced by the process during the past 24 hours.
A. How many parts should be sampled in order to estimate the population mean to within 0.3 mm with 95% confidence. Previous studies of this machine have indicated that the standard deviation of lengths produced by the stamping operation is about 2 mm.
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Since ME = zs/sqrt(n)
sqrt(n) = zs/ME
n = [zs/ME]^2
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n = [1.96*2/0.3] = 171 when rounded up
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B. Time permits the use of a sample size no larger than 100. If a 95% confidence interval for ì is constructed using n = 100, will it be wider or narrower than would have been obtained using the sample size from part a?
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Since n and ME and indirectly related, ME will be larger when n is smaller.
But the CI is alway 2*ME, so the CI will be larger when n is smaller.
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Note: Please let me know if you do not understand these answers.
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Cheers,
Stan H.
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