SECTION 7.1 Introduction to Hypothesis Testing 355 z 0 P-value area 1 2 P-value area 1 2 Standardized test statistic P-value area z 0 Standardized test statistic P-value area z 0 Standardized test statistic Identifying the Nature of a Hypothesis Test For each claim, state H0 and Ha in symbols and in words. Then determine whether the hypothesis test is a left-tailed test, right-tailed test, or two-tailed test. Sketch a normal sampling distribution and shade the area for the P@value. 1. A school publicizes that the proportion of its students who are involved in at least one extracurricular activity is 61%. 2. A car dealership announces that the mean time for an oil change is less than 15 minutes. 3. A company advertises that the mean life of its furnaces is more than 18 years. SOLUTION In Symbols In Words 1. H0: p = 0.61 The proportion of students who are involved in at least one extracurricular activity is 61%. Ha: p ≠0.61 The proportion of students who are involved in at least one extracurricular activity is not 61%. Because Ha contains the ≠ symbol, the test is a two-tailed hypothesis test. The figure at the left shows the normal sampling distribution with a shaded area for the P@value. In Symbols In Words 2. H0: m Ú 15 min The mean time for an oil change is greater than or equal to 15 minutes. Ha: m 6 15 min The mean time for an oil change is less than 15 minutes. Because Ha contains the 6 symbol, the test is a left-tailed hypothesis test. The figure at the left shows the normal sampling distribution with a shaded area for the P@value. In Symbols In Words 3. H0: m … 18 yr The mean life of the furnaces is less than or equal to 18 years. Ha: m 7 18 yr The mean life of the furnaces is more than 18 years. Because Ha contains the 7 symbol, the test is a right-tailed hypothesis test. The figure at the left shows the normal sampling distribution with a shaded area for the P@value. TRY IT YOURSELF 3 For each claim, state H0 and Ha in symbols and in words. Then determine whether the hypothesis test is a left-tailed test, right-tailed test, or two-tailed test. Sketch a normal sampling distribution and shade the area for the P@value. 1. A consumer analyst reports that the mean life of a certain type of automobile battery is not 74 months. 2. An electronics manufacturer publishes that the variance of the life of its home theater systems is less than or equal to 2.7. 3. 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 EXAMPLE 3
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