Statistical Inference: A Short Course

10.7 Hypothesis Tests for μ (σ Known)

Example 10.1

A sample of size n = 25 is taken from a population that is N(μ,6) (μ is unknown but σ is known) and it is determined that = 43.75. Test H₀: μ = μ_o = 40 versus H₁: μ > 40 at the α = 0.05 level of significance. Following part (a) above,

Since (Fig. 10.4), . With = 3.125 > 1.645, we are within R so that we reject H₀ at the 0.05 level of significance. Here = 43.75 exceeds = 40 by 3.75 units—that is greater than , the lower limit for “too much.”

Figure 10.4 Right-tail test with α = 0.05.

Example 10.2

A sample of size n = 25 is extracted from ...