SECTION 6.3 Summary

• A test of significance assesses the evidence provided by data against a null hypothesis and in favor of an alternative hypothesis . It provides a method for ruling out chance as an explanation for data that deviate from what we expect under .
• The hypotheses are stated in terms of population parameters. Usually, is a statement that no effect is present, and 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 -value is the probability, computed assuming that is true, that the test statistic will take a value at least as extreme as that actually observed. Small -values indicate strong evidence against . Calculating -values requires knowledge of the sampling distribution of the test statistic when is true.

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• If the -value is as small or smaller than a specified value , the data are statistically signifcant at significance level .
• Significance tests for the hypothesis concerning the unknown mean of a population are based on the statistic:
  

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