A test of significance assesses the evidence provided by data against a null hypothesisH0 and in favor of an alternative hypothesisHa. It provides a method for ruling out chance as an explanation for data that deviate from what we expect under H0.
The hypotheses are stated in terms of population parameters. Usually, H0 is a statement that no effect is present, and Ha says that a parameter differs from its null value 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.
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If the P-value is as small or smaller than a specified value α, the data are statistically signifcant at significance level α.
Significance tests for the hypothesis H0:μ=μ0 concerning the unknown meanμ of a population are based on the zstatistic:
z=ˉx−μ0σ/√n
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 a tests use the table of standard Normal critical values (z* row in Table D).