Question

Suppose we have a collection of the heights of all students at your college. Each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college. Which of the following statements about the confidence intervals is most accurate?

A. About 95% of the heights of all students at the college will be contained in these interval
B. About 95% of the time, a student’s sample mean height will be contained in his or her interval.
C. About 95% of the intervals will contain the population mean height.
D. About 95% of the intervals will be identical.

Answer 1

Correct option: (C)

Explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

Or, if n such (1 - α)% confidence intervals are constructed then (1 - α)% of these interval will consist of the true parameter value.

It is provided that each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college.

So there sill be n = 250, 95% confidence intervals for mean height of all students at the college.

Then 95% of these 250 confidence intervals for mean will consist of the true mean height of the college students.

Thus, the correct option is (C).