382 CHAPTER 8 Hypothesis Testing Step 7: Make a Decision to Either Reject H0 or Fail to Reject H0 Decision Criteria for the P-Value Method: ■ If P-value … a, reject H0. (“If the P is low, the null must go.”) ■ If P-value 7 a, fail to reject H0. Example: With P@value = 0.106 (rounded) and significance level a = 0.05, we have P@value 7 a, so fail to reject H0. Remember, the P-value is the probability of getting a sample result at least as extreme as the one obtained, so if the P-value is high (greater than a), the sample statistic is not significantly low or significantly high. Decision Criteria for the Critical Value Method: ■ If the test statistic is in the critical region, reject H0. ■ If the test statistic is not in the critical region, fail to reject H0. Example: With test statistic z = 1.25 and the critical region extending to the right from z = 1.645 (as shown in Figure 8-4), the test statistic does not fall within the critical region, so fail to reject H0. Step 8: Restate the Decision Using Simple and Nontechnical Terms Without using technical terms not understood by most people, state a final conclusion that addresses the original claim with wording that can be understood by those without knowledge of statistical procedures. Example: There is not sufficient evidence to support the claim that “most Internet users utilize two-factor authentication to protect their online data.” Wording the Final Conclusion For help in wording the final conclusion, refer to Figure 8-5. CP CP Start No No Yes Yes Reject H0 Fail to reject H0 Wording of Final Conclusion “There is sufficient evidence to support the claim that... (original claim).” “There is not sufficient evidence to support the claim that... (original claim).” Original claim does not contain equality and becomes H1 Original claim contains equality Does the original claim contain the condition or equality? Do you reject H0? No Yes Reject H0 Fail to reject H0 “There is sufficient evidence to warrant rejection of the claim that... (original claim).” (This is the only case in which the original claim is supported.) (This is the only case in which the original claim is rejected.) “There is not sufficient evidence to warrant rejection of the claim that... (original claim).” Do you reject H0? FIGURE 8-5 Hypothesis Tests: Wording of Final Conclusion
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