Hypothesis Testing for the Mean (s Known) 7.2 SECTION 7.2 Hypothesis Testing for the Mean (s Known) 363 What You Should Learn How to find and interpret P-values How to use P-values for a z-test for a mean m when s is known How to find critical values and rejection regions in the standard normal distribution How to use rejection regions for a z-test for a mean m when s is known Using P@Values to Make Decisions Using P@Values for a z@Test Rejection Regions and Critical Values Using Rejection Regions for a z@Test Using P@Values to Make Decisions In Chapter 5, you learned that when the sample size is at least 30, the sampling distribution for x (the sample mean) is normal. In Section 7.1, you learned that a way to reach a conclusion in a hypothesis test is to use a P@value for the sample statistic, such as x. Recall that when you assume the null hypothesis is true, a P@ value (or probability value) of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme as or more extreme than the one determined from the sample data. The decision rule for a hypothesis test based on a P@value is repeated below. To use a P@value to make a decision in a hypothesis test, compare the P@value with a. 1. If P … a, then reject H0. 2. If P 7 a, then fail to reject H0. Decision Rule Based on P-Value Interpreting a P-Value The P@value for a hypothesis test is P = 0.0237. What is your decision when the level of significance is (1) a = 0.05 and (2) a = 0.01? SOLUTION 1. Because 0.0237 6 0.05, you reject the null hypothesis. 2. Because 0.0237 7 0.01, you fail to reject the null hypothesis. TRY IT YOURSELF 1 The P@value for a hypothesis test is P = 0.0745. What is your decision when the level of significance is (1) a = 0.05 and (2) a = 0.10? Answer: Page A40 The lower the P@value, the more evidence there is in favor of rejecting H0. The P@value gives you the lowest level of significance for which the sample statistic allows you to reject the null hypothesis. In Example 1, you would reject H0 at any level of significance greater than or equal to 0.0237. After determining the hypothesis test’s standardized test statistic and the standardized test statistic’s corresponding area, do one of the following to find the P@value. a. For a left-tailed test, P = (Area in left tail). b. For a right-tailed test, P = (Area in right tail). c. For a two-tailed test, P = 2(Area in tail of standardized test statistic). Finding the P-Value for a Hypothesis Test EXAMPLE 1
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