SECTION 6.2 SUMMARY

• • A test of significance is intended to assess the evidence provided by data against a null hypothesis H₀ in favor of an alternative hypothesis H_a.

• • The hypotheses are stated in terms of population parameters. Usually, H₀ is a statement that no effect or no difference is present, and H_a says that there is an effect or difference in a specific direction (one-sided alternative) or in either direction (two-sided alternative).

• • The test is based on a test statistic. The P-value is the probability, computed assuming that H₀ is true, that the test statistic will take a value at least as extreme as that actually observed. Small P-values indicate strong evidence against H₀. Calculating P-values requires knowledge of the sampling distribution of the test statistic when H₀ is true.

• • If the P-value is as small or smaller than a specified value α, the data are statistically significant at significance level α.

• • Significance tests for the hypothesis H₀: μ = μ₀ concerning the unknown mean μ of a population are based on the z statistic:

  The z test assumes an SRS of size n, known population standard deviation σ, and either a Normal population or a large sample. P-values are computed from the Normal distribution (Table A). Fixed α tests use the table of standard Normal critical values (Table D).