A sample of 25 pieces of laminate used in the manufacture of circuit boards was

Question

A sample of 25 pieces of laminate used in the manufacture of circuit boards was selected, and the amount of warpage (in.) under particular conditions was determined for each piece, resulting in a sample mean warpage of 0.0632 and a sample standard deviation of 0.0065. (a) Calculate a prediction for the amount of warpage of a single piece of laminate in a way that provides information about precision and reliability. (Use a 95% prediction interval. Round your answers to three decimal places.) provides information redcion Interval, Round your answers to three decimal placsnti iri b) Calculate an interval or which you can have a high degree o confidence that at least 95% of al pieces the two limits of the interval. (Use a 99% tolerance interval. Round your answers to three decimal places. amina e result in amounts or war age at are between iri You may need to use the appropriate table in the Appendix of Tables to answer this question

Explanation / Answer

99% CI for the standard deviation

CI for 99%

n = 22

std. dev. (s) = 5.388

qchisq(0.005,21) = 8.03365

qchisq(0.995,21) = 41.40106

Then the CI for standard deviation is

sqrt [(21*5.388/41.401,21*5.388/8.034)]

99% CI ( 3.8374 , 8.7113 )

This interval is valid when the distribution is approximately normal. In other words, the observations must pass the normality test.

mean = 0.1 , s= 0.7

z value at 95% cI= 1.96

z = ( x - mean) / s

1.96 = ( x - 0.1) / 0.7

x = 1.472 = 2 books

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