Question

What is the formula for the confidence interval? Then, define what each variable represents.

Answer 1

The confidence interval for a (1−α)% confidence level is given by

(θ0−Zα/2 σ/√n, θ0+Zα/2 σ/√n)

θ0 is the measured statistic, Zα/2 is the cutoff/critical value, and σ/√n is the standard error. σ is the population standard deviation (if known) or can be estimated by a sample standard deviation. n is the sample size. The cutoff value depends on the test you wish to use, and θ0 depends on the statistic you wish to estimate.