Question

Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 100 clamps, the mean time to complete this step was 54.6 seconds. Assume that the population standard deviation is = 11 seconds. Construct a 98% confidence interval for the mean time needed to complete this step. Round the critical value to no less than three decimal places.

Answer 1

The 98% confidence interval for the mean time needed to complete this step is between 52.0403 seconds and 57.1597 seconds

Explanation:

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

`\alpha = (1-0.98)/(2) = 0.01`

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
`1-0.01 = 0.99`, so
`z = 2.327`

Now, find the margin of error M as such

`M = z*(\sigma)/(√(n))`

In which
`\sigma` is the standard deviation of the population and n is the size of the sample.

`M = 2.327(11)/(√(100)) = 2.5597`

The lower end of the interval is the sample mean subtracted by M. So it is 54.6 - 2.5597 = 52.0403 seconds

The upper end of the interval is the sample mean added to M. So it is 54.6 + 2.5597 = 57.1597 seconds

The 98% confidence interval for the mean time needed to complete this step is between 52.0403 seconds and 57.1597 seconds