Question

The National Center for Educational Statistics surveyed 5400 college graduates about the lengths of time required to earn their bachelors degrees. The mean is 5.4 years and the standard deviation is 1.9 years. Based on this sample, construct a 90% confidence interval for the mean time required by all college graduates

Answer 1

The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.

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*(1.9)/(√(4500)) = 0.04`

The lower end of the interval is the sample mean subtracted by M. So it is 5.4 - 0.04 = 5.36 years.

The upper end of the interval is the sample mean added to M. So it is 5.4 + 0.04 = 5.44 years.

The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.