Question

An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of 8. A psychologist gave the self-esteem test to a random sample of 70 individuals, and their mean score was 62. Construct a 95% confidence interval for the true mean of all test scores. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

What is the lower limit of the 95% confidence interval?

What is the upper limit of the 95% confidence interval?

Answer 1

Given that the sample mean is = 62 and sample sie = 70 and the population standard deviation given is = 8.

The confidence interval is calculated as:

where Zc is the critical value which is at 95% is calculated using excel formula for normal distribution, the formula is =NORM.S.INV(0.975), the Zc is computed as 1.96.

Now the confidence interval is calculated as:

So, the lower limit is 60.126 and the Upper limit is 63.876.

Note: Please do tell if the standard deviation is not of the population but of the sample, then I will update the confidence interval accordingly.