Question

A college admissions director wants to estimate the mean age of all students enrolled

at her school. In a random sample of 30 students at the school, the mean age is 23.1
years. From past studies, it is known that the population standard deviation is 1.7
years.
(a) Construct a 90% confidence interval for the mean age.

Answer 1

To construct a 90% confidence interval for the mean age of students, we first need to calculate the margin of error. We can do this using the formula:

margin of error = (critical value) * (standard deviation / square root of sample size)

The critical value for a 90% confidence interval is 1.645, and the standard deviation is 1.7 years. The sample size is 30, so the square root of the sample size is 5.477. Plugging these values into the formula, we get:

margin of error = 1.645 * (1.7 / 5.477) = 0.517

The 90% confidence interval is then calculated as:

mean age ± margin of error

Plugging in the mean age of 23.1 years, we get:

23.1 ± 0.517

So, the 90% confidence interval for the mean age of students is (22.583, 23.617). This means that we can be 90% confident that the true mean age of all students at the school is between 22.583 years and 23.617 years.