On the basis of extensive tests, the yield point of a particular type of mild st

Question

On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with sigma = 100. The composition of bars has been slightly modified, but the modification is not believed to have affected either the normality or the value of sigma = 100. Assuming this to be the case, if a sample of 25 modified bars resulted in a sample average yield point of 8139 lb, compute a 90% CI for the true average yield point of the modified bar. How would you modify the interval in the first part to obtain a confidence level of 92%?

Explanation / Answer

The formula used for determining the confidence interval is
Sample mean +/- Critical value (or z-score corresponding to 90% confidence) * Standard
error of mean
8139 +/- 1.645 * 100/sqrt 25
8139 +/- 1.645 * 20
8139 +/- 32.9

LCL = 810.61

UCL = 8171.9

b) The only difference in this case is finding the critical value i.e., z-score corresponding to 92% confidence which is 1.75 approximately
Then the confidence interval is
8139 +/- 1.75 * 100/sqrt 25
8139 +/- 1.75 * 20
8139 +/- 35
Lower limit is 8139 - 35 = 8104
The upper limit is 8139 + 35 = 8174

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