Question

You want to estimate the average of a population, for these a sample of size 21 was taken, and the average and variance of the sample were calculated. These are 10.52 and 3.25 respectively.
a. Build a confidence interval for the average, if 90 percent confidence is desired. (15 pts)
b. Calculate the sample size if you want the relative error to be 10 percent with a reliability of 95 percent. (15 pts)

Answer 1

a) df = 21 - 1 = 20

At 90% confidence level, the critical value is t^* = 1.725

The 90% confidence interval is

b) At 95% confidence level, the critical value is t^* = 2.086

Margin of error = 0.1