370 CHAPTER 7 Hypothesis Testing with One Sample Using Rejection Regions for a z-Test To conclude a hypothesis test using rejection region(s), you make a decision and interpret the decision according to the next rule. To use a rejection region to conduct a hypothesis test, calculate the standardized test statistic z. If the standardized test statistic 1. is in the rejection region, then reject H0. 2. is not in the rejection region, then fail to reject H0. z 0 z 0 z < z0: Reject H0. Fail to reject H0. z 0 z 0 z > z0: Reject H0. Fail to reject H0. Left-Tailed Test Right-Tailed Test z 0 z 0 −z 0 z < −z0: Reject H0. z > z0: Reject H0. Fail to reject H0. Two-Tailed Test Decision Rule Based on Rejection Region Remember, failing to reject the null hypothesis does not mean that you have accepted the null hypothesis as true. It simply means that there is not enough evidence to reject the null hypothesis. Using Rejection Regions for a z-Test for a Mean M (S Known) In Words In Symbols 1. Verify that s is known, the sample is random, and either the population is normally distributed or n Ú 30. 2. State the claim mathematically State H0 and Ha. and verbally. Identify the null and alternative hypotheses. 3. Specify the level of significance. Identify a. 4. Determine the critical value(s). Use Table 4 in Appendix B. 5. Determine the rejection region(s). 6. Find the standardized test statistic z = x - m s 1n and sketch the sampling distribution. 7. Make a decision to reject or fail to If z is in the rejection region, reject the null hypothesis. then reject H0. Otherwise, fail to reject H0. 8. Interpret the decision in the context of the original claim. GUIDELINES
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