Power of the One-Sample z-Test

The one-sample z-test applies when sampling is normal and the variance is known. Its power function describes the probability of rejecting $H_0: \mu = \mu_0$ at a specific alternative $\mu = \mu_1$.

This note matters mainly as the clean benchmark for later power and sample-size formulas.

R

power.t.test(delta = 0.15, sd = sigma, n = n,
             sig.level = 0.05,
             type = "one.sample",
             alternative = "two.sided")

In STA305, this built-in function is also used to automate practical power calculations.

Related

• STA305
• Power of a Statistical Test
• Sample Size Determination