Chapter 8, Problem R8.5RE

a.

To determine

To find: The 95% confidence interval for the mean length of the component

Answer to Problem R8.5RE

The confidence interval is (223.971, 224.033)

Explanation of Solution

Given:

The data set:

224.12
224.001
224.017
223.982
223.989
223.961
223.96
224.089
223.987
223.976
223.902
223.98
224.098
224.057
223.913
223.999

Formula used:

The formula to compute the t - confidence interval for population mean is:

  $CI=\overline{x}\pm t_{\alpha /2,df}\times \frac{s}{\sqrt{n}}$

Calculation:

Here, t -confidence interval is to be used because population standard deviation is unknown.

The obtained excel output is:

  

Thus, the required confidence interval is (223.971, 224.033)

b.

To determine

To explain: Whether the mean has drifted from 224mm.

Answer to Problem R8.5RE

No, it has not drifted from 24 mm.

Explanation of Solution

From the above, it is known that the confidence interval is (223.971, 224.033). Since, the upper limit is 224.033 which is above 224. Thus, it cannot be said that the mean has drifted from 224 mm.