SECTION 7.1 Introduction to Hypothesis Testing 357 TRY IT YOURSELF 4 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. A consumer analyst reports that the mean life of a certain type of automobile battery is not 74 months. 2. Ha (Claim): A realtor publicizes that the proportion of homeowners who feel their house is too small for their family is more than 24%. Answer: Page A40 The general steps for a hypothesis test using P@values are summarized below. Note that when performing a hypothesis test, you should always state the null and alternative hypotheses before collecting data. You should not collect the data first and then create a hypothesis based on something unusual in the data. 1. State the claim mathematically and verbally. Identify the null and alternative hypotheses. H0: ? Ha: ? 2. Specify the level of significance. a = ? 3. Determine the standardized sampling distribution and sketch its graph. 4. Calculate the test statistic and its corresponding standardized test statistic. Add it to your sketch. 5. Find the P@value. 6. Use this decision rule. Is the P-value less than or equal to the level of significance? Fail to reject H0. Reject H0. Yes No 7. Write a statement to interpret the decision in the context of the original claim. 0 This sampling distribution is based on the assumption that H0 is true. 0 Standardized test statistic Steps for Hypothesis Testing In Step 4 above, the figure shows a right-tailed test. However, the same basic steps also apply to left-tailed and two-tailed tests.
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