Question

From a sample of 25 graduate​ students, the mean number of months of work experience prior to entering an MBA program was 33.59. The national standard deviation is known to be 19 months. What is a 90​% confidence interval for the population​ mean?

Answer 1

The 90​% confidence interval for the population​ mean is between 27.34 months and 39.84 months.

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 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 = 1.645*(19)/(√(25)) = 6.25`

The lower end of the interval is the sample mean subtracted by M. So it is 33.59 - 6.25 = 27.34 months

The upper end of the interval is the sample mean added to M. So it is 33.59 + 6.25 = 39.84 months

The 90​% confidence interval for the population​ mean is between 27.34 months and 39.84 months.