Statistical Inference: A Short Course

12.6 Confidence Intervals for and

To determine how precisely and have been estimated from the sample data, let us find 100(1 − α)% confidence intervals for these parameters. To this end:

a. a 100(1 − α)% confidence interval for is

(12.21)

b. a 100(1 − α)% confidence interval for is

(12.22)

where − and are, respectively, the lower and upper percentage points of the t distribution and 1 − α is the confidence coefficient. Hence Equation (12.21) informs us that we may be 100(1 − α)% confident ...