A manufacturer produces piston rings for an automobile engine. It is known that

Question

A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with ? = 0.001 millimeters. A random sample of 15 rings has a mean diameter of x = 74.160. Construct a 99% two-sided confidence interval on the true mean piston diameter and a 95% lower confidence bound on the true mean piston diameter. Round your answers to 3 decimal places. (a) Calculate the 99% two-sided confidence interval on the true mean piston diameter. (b) Calculate the 95% one-sided lower confidence interval on the true mean piston diameter.

Explanation / Answer

a)

CI for 99%

n = 15

mean = 74.16

t-value of 99% CI = 2.9768

std. dev. = 0.0010

SE = std.dev./sqrt(n)

= 0.001/sqrt(15)

= 0.00026

ME = t*SE

= 2.9768*0.00026

= 0.00077

Lower Limit = Mean - ME = 74.16 - 0.00077 = 74.15923

Upper Limit = Mean + ME = 74.16 + 0.00077 = 74.16077

99% CI (74.159 , 74.161)

b)

CI for 90%

n = 15

mean = 74.16

t-value of 95% CI = 1.7613

std. dev. = 0.0010

SE = std.dev./sqrt(n)

= 0.001/sqrt(15)

= 0.00026

ME = t*SE = 1.7613*0.00026 = 0.00045

Lower Limit = Mean - ME = 74.16 - 0.00045 = 74.15923

95% CI (74.16, infinte )

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