354 CHAPTER 7 Hypothesis Testing with One Sample The P@value of a hypothesis test depends on the nature of the test. There are three types of hypothesis tests—left-tailed, right-tailed, and two-tailed. The type of test depends on the location of the region of the sampling distribution that favors a rejection of H0. This region is indicated by the alternative hypothesis. 1. If the alternative hypothesis Ha contains the less-than inequality symbol 162, then the hypothesis test is a left-tailed test. 2 3 1 −1 −2 −3 0 Standardized test statistic H0: ≥ k μ Ha: < k μ P is the area to the left of the standardized test statistic. Left-Tailed Test 2. If the alternative hypothesis Ha contains the greater-than inequality symbol 172, then the hypothesis test is a right-tailed test. 2 3 1 −1 −2 −3 0 Standardized test statistic H0: ≤ k μ Ha: > k μ P is the area to the right of the standardized test statistic. Right-Tailed Test 3. If the alternative hypothesis Ha contains the not-equal-to symbol 1≠2, then the hypothesis test is a two-tailed test. In a two-tailed test, each tail has an area of 1 2P. 2 3 1 −1 −2 −3 0 Standardized test statistic Standardized test statistic The area to the left of the negative standardized test statistic is P. The area to the right of the positive standardized test statistic is P. H0: = k μ Ha: ≠ k μ 1 2 1 2 Two-Tailed Test DEFINITION The smaller the P@value of the test, the more evidence there is to reject the null hypothesis. A very small P@value indicates an unusual event. Remember, however, that even a very low P@value does not constitute proof that the null hypothesis is false, only that it is probably false. Study Tip The third type of test is called a two-tailed test because evidence that would support the alternative hypothesis could lie in either tail of the sampling distribution.
RkJQdWJsaXNoZXIy NjM5ODQ=