Question

You are in an Intro Psych class of 137 students. You ask 25 of your classmates their age and calculate a mean of 18.2 and a sample standard deviation of 1.5. Calculate the standard error and report the 80% and 99% confidence intervals for the estimated average age of the class.

Answer 1

Solution:

The standard error is given as follows:

Where, SE is standard error, s is sample standard deviation and n is sample size.

We have, s = 1.5 and n = 25

The standard error is 0.3.

The 80% confidence interval estimate of population mean is given as follows:

Where, x̄ is sample mean, s is sample standard deviation, n is sample size and t_{(0.20/2, n-1)} is critical t-value to construct 80% confidence interval.

We have, x̄ = 18.2, s = 1.5 and n = 25

Using t-table we get, t_{(0.20/2, 25-1)} = 1.318

Hence, 80% confidence intervals for the estimated average age of the class is,

The 80% confidence interval for the estimated average age of the class is (17.8046, 18.5954).

The 99% confidence interval estimate of population mean is given as follows:

Where, x̄ is sample mean, s is sample standard deviation, n is sample size and t_{(0.01/2, n-1)} is critical t-value to construct 99% confidence interval.

We have, x̄ = 18.2, s = 1.5 and n = 25

Using t-table we get, t_{(0.01/2, 25-1)} = 2.797

Hence, 99% confidence intervals for the estimated average age of the class is,

The 99% confidence interval for the estimated average age of the class is (17.3609, 19.0391).

Please rate the answer. Thank you.