358 CHAPTER 7 Hypothesis Testing with One Sample Strategies for Hypothesis Testing In a courtroom, the strategy used by an attorney depends on whether the attorney is representing the defense or the prosecution. In a similar way, the strategy that you will use in hypothesis testing should depend on whether you are trying to support or reject a claim. Remember that you cannot use a hypothesis test to support your claim when your claim is the null hypothesis. So, as a researcher, to perform a hypothesis test where the possible outcome will support a claim, word the claim so it is the alternative hypothesis. To perform a hypothesis test where the possible outcome will reject a claim, word it so the claim is the null hypothesis. Writing the Hypotheses A medical research team is investigating the benefits of a new surgical treatment. One of the claims is that the mean recovery time for patients after the new treatment is less than 96 hours. 1. How would you write the null and alternative hypotheses when you are on the research team and want to support the claim? How should you interpret a decision that rejects the null hypothesis? 2. How would you write the null and alternative hypotheses when you are on an opposing team and want to reject the claim? How should you interpret a decision that rejects the null hypothesis? SOLUTION 1. To answer the question, first think about the context of the claim. Because you want to support this claim, make the alternative hypothesis state that the mean recovery time for patients is less than 96 hours. So, Ha: m 6 96 hours. Its complement, H0: m Ú 96 hours, would be the null hypothesis. If you reject H0, then you will support the claim that the mean recovery time is less than 96 hours. H0: m Ú 96 and Ha: m 6 96 (Claim) 2. First think about the context of the claim. As an opposing researcher, you do not want the recovery time to be less than 96 hours. Because you want to reject this claim, make it the null hypothesis. So, H0: m … 96 hours. Its complement, Ha: m 7 96 hours, would be the alternative hypothesis. If you reject H0, then you will reject the claim that the mean recovery time is less than or equal to 96 hours. H0: m … 96 (Claim) and Ha: m 7 96 TRY IT YOURSELF 5 1. You represent a chemical company that is being sued for paint damage to automobiles. You want to support the claim that the mean repair cost per automobile is less than $650. How would you write the null and alternative hypotheses? How should you interpret a decision that rejects the null hypothesis? 2. You are on a research team that is investigating the mean temperature of adult humans. The commonly accepted claim is that the mean temperature is about 98.6°F. You want to show that this claim is false. How would you write the null and alternative hypotheses? How should you interpret a decision that rejects the null hypothesis? Answer: Page A40 EXAMPLE 5
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