If the engineer wants to be 95% confident that the error in estimating the mean life is less than 15 hours, with confidence interval of +/- 5%, and standard deviation of 0.5, The sample size should be 385 samples.
Accordingly, the Necessary Sample Size is calculated as follows:
Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²
For example, given a 95% confidence level, 0.5 standard deviation, and a margin of error (confidence interval) of +/- 5%. Necessary Sample Size =
((1.96)² x 0.5(0.5)) / (0.05)²
(3.8416 x 0.25) / .0025
0.9604 / 0.0025
384.16
So in order to get 95% confidence level, with confidence interval of +/- 5%, and standard deviation of 0.5, The sample size should be 385 samples.
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