Question

Suppose a regional computer center wants to evaluate the performance of its memory system. One measure of performance is the average time between failures of its disk drive. To estimate the value, the center recorded the time between failures for a random sample of 45 drive failures. The sample mean has been computed to be 1,762 hours and the sample standard deviation is 215. Estimate the true mean time between failures with a 90% confidence interval? Interpret the confidence interval.

Answer 1

The 90% confidence interval is (1408.325 hours, 2115.675 hours).

Explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1-0.9)/(2) = 0.05`

Now, we have to find z in the Ztable as such z has a pvalue of
`1-\alpha`.

So it is z with a pvalue of
`1-0.05 = 0.95`, so
`z = 1.645`

Now, find M as such

`M = z*s`

In which s is the standard deviation of the sample. So

`M = 1.645*215 = 353.675`

The lower end of the interval is the mean subtracted by M. So it is 1762 - 353.675 = 1408.325 hours.

The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 2115.675 hours.

The 90% confidence interval is (1408.325 hours, 2115.675 hours).