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Preventing production of defective items. It costs more to
Chapter 6, Problem 78E(choose chapter or problem)
Preventing production of defective items. It costs more to produce defective items—because they must be scrapped or reworked—than it does to produce nondefective items. This simple fact suggests that manufacturers should ensure the quality of their products by perfecting their production processes rather than through inspection of finished products (Out of the Crisis, Deming, 1986). 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 .1 millimeter (mm) with 90% 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 90% confidence interval for \(\mu\) is constructed using n = 100, will it be wider or narrower than would have been obtained using the sample size determined in part a? Explain.
c. If management requires that \(\mu\) be estimated to within .1 mm and that a sample size of no more than 100 be used, what is (approximately) the maximum confidence level that could be attained for a confidence interval that meets management’s specifications?
Questions & Answers
QUESTION:
Preventing production of defective items. It costs more to produce defective items—because they must be scrapped or reworked—than it does to produce nondefective items. This simple fact suggests that manufacturers should ensure the quality of their products by perfecting their production processes rather than through inspection of finished products (Out of the Crisis, Deming, 1986). 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 .1 millimeter (mm) with 90% 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 90% confidence interval for \(\mu\) is constructed using n = 100, will it be wider or narrower than would have been obtained using the sample size determined in part a? Explain.
c. If management requires that \(\mu\) be estimated to within .1 mm and that a sample size of no more than 100 be used, what is (approximately) the maximum confidence level that could be attained for a confidence interval that meets management’s specifications?
ANSWER:Step1 of 4
From the given problem we have a manufacturer wishes to estimate the mean length of items produced by the process during the past 24 hours. Also we have \(\sigma=2 \text { and } \mathrm{ME}=0.1\).
Here our goal is:
a). We need to find How many parts should be sampled in order to estimate the population mean to within 0.1mm with 90% confidence. the standard deviation of lengths produced by the stamping operation is about 2 mm.
b). Suppose time permits the use of a sample size no larger than 100. If a 90% confidence interval for ? is constructed using n = 100. Then we need to check whether it be wider or narrower than would have been obtained using the sample size determined in part (a).
c). Suppose management requires that ? be estimated to within 0.1 mm and that a sample size of no more than 100 be used. Then we need to find the maximum confidence level that could