To become an actuary it is necessary to pass a series of 10

To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program.

A- the critical value used in constructing a 90% confidence interval is:

B- what is the lower and Upper boundaries of a 90% confidence interval for the mean score?

Solution

For the given sample the degree of freedom = n-1 = 8-1 = 7

Now the sample mean (m) = 6 and the standard deviation (s) = 2

The confidence interval for t-test is given by [m ± (t critical * s/?n)]

t critical at 90% confidence level is 1.895

Therefore confidence interval is [(6- 2.68), (6+2.68)]

or confidence interval = (3.32, 8.68)