Chapter 8, Problem 8CRE

a.

To determine

To find: The confidence interval for the process mean for the time at which these crankshafts were produced.

Answer to Problem 8CRE

The sample size is 35.

Explanation of Solution

Given:

The data set is:

224.12
224.001
22.017
223.982
223.982
223.989
223.961
223.96
224.089
223.987
229.976
223.902
223.902
223.98
224.098
224.057
223.913
223.999

Formula used:

The formula to compute the confidence interval is:

  $\overline{x}-t_{\frac{\alpha }{2}}\times \frac{s}{\sqrt{n}}<\mu <\overline{x}+t_{\frac{\alpha }{2}}\times \frac{s}{\sqrt{n}}$

Calculation:

The confidence interval using Ti-83 calculator could be computed as:

  

Thus, the confidence interval is (223.97, 224.03)

Interpretation:

There is 95% probability that the population mean is between 223.97 and 224.03.

b.

To determine

To find: Whether the process mean has drifted or not.

Answer to Problem 8CRE

Yes.

Explanation of Solution

From the above part, it is known that the population mean process is between 223.97 and 224.03. Since, the interval is containing 224 it could be said that the process mean has drifted.