356 CHAPTER 7 Hypothesis Testing with One Sample Making a Decision and Interpreting the Decision To conclude a hypothesis test, you make a decision and interpret that decision. For any hypothesis test, there are two possible outcomes: (1) reject the null hypothesis or (2) fail to reject the null hypothesis. To decide to reject H0 or fail to reject H0, you can use the following decision rule. 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 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. To support a claim, state it so that it becomes the alternative hypothesis. To reject a claim, state it so that it becomes the null hypothesis. The table will help you interpret your decision. Claim Decision Claim is H0. Claim is Ha. Reject H0. There is enough evidence to reject the claim. There is enough evidence to support the claim. Fail to reject H0. There is not enough evidence to reject the claim. There is not enough evidence to support the claim. Interpreting a Decision You perform a hypothesis test for each claim. How should you interpret your decision if you reject H0? If you fail to reject H0? 1. H0 (Claim): A school publicizes that the proportion of its students who are involved in at least one extracurricular activity is 61%. 2. Ha (Claim): A car dealership announces that the mean time for an oil change is less than 15 minutes. SOLUTION 1. The claim is represented by H0. If you reject H0, then you should conclude “there is enough evidence to reject the school’s claim that the proportion of students who are involved in at least one extracurricular activity is 61%.” If you fail to reject H0, then you should conclude “there is not enough evidence to reject the school’s claim that the proportion of students who are involved in at least one extracurricular activity is 61%.” 2. The claim is represented by Ha, so the null hypothesis is “the mean time for an oil change is greater than or equal to 15 minutes.” If you reject H0, then you should conclude “there is enough evidence to support the dealership’s claim that the mean time for an oil change is less than 15 minutes.” If you fail to reject H0, then you should conclude “there is not enough evidence to support the dealership’s claim that the mean time for an oil change is less than 15 minutes.” EXAMPLE 4 Study Tip In this chapter, you will learn that there are two types of decision rules for deciding whether to reject H0 or fail to reject H0. The decision rule described on this page is based on P-values. The second type of decision rule is based on rejection regions. When the standardized test statistic falls in the rejection region, the observed probability (P-value) of a type I error is less than a. You will learn more about rejection regions in the next section.
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