Question

Here are measurements (in millime- ters) of a critical dimension on an SRS of 16 of the more than 200 auto engine crankshafts produced in one day: 224.120 224.001 224.017 223.982 223.989 223.961 223.960 224.089 223.987 223.976 223.902 223.980 224.098 224.057 223.913 223.999 (a) Construct and interpret a 95% confidence interval for the process mean at the time these crankshafts were produced.

Answer 1

(23.97, 24.03)

Explanation:

Given the data:

224.120 224.001 224.017 223.982 223.989 223.961 223.960 224.089 223.987 223.976 223.902 223.980 224.098 224.057 223.913 223.999

Confidence interval = m ± Zcritical(s/√n)

n = sample size = 16

Zcritical at 95% = 1.96

Using calculator :

Sample mean, m = 224.0019

Standard deviation, s = 0.0618

Lower bound : 24.0019 - 1.96(0.0618/√16) = 23.971618

Upper bound : 24.0019 + 1.96(0.0618/√16) = 24.032182

(23.97, 24.03)