We are evaluating the sheet metal scrap rate in a contractor proposal. Based on a sample of 24 parts you calculate a mean rate of 6.50% (treat as 6.50) and a standard deviation of 1.20. Calculate a 80% confidence interval to be used to support negotiations. (Carry intermediate calculations to three decimal places.)
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Standard error of the mean will be
1.20/sqrt(23) = 0.2502
Using a t-distribution table, look up 23 degrees of freedom.
The number of standard errors associated with a "tail" of 0.10 or "two tails" of 0.20 is 1.319.
1.319*0.2502 = 0.3300
Hence, the 80% confidence interval is
from 6.17 to 6.83 (percent scrap rate)
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