7.1 EXERCISES SECTION 7.1 Introduction to Hypothesis Testing 359 For Extra Help: MyLab® Statistics Building Basic Skills and Vocabulary 1. What are the two types of hypotheses used in a hypothesis test? How are they related? 2. Describe the two types of errors possible in a hypothesis test decision. 3. What are the two decisions that you can make from performing a hypothesis test? 4. Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain. True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 5. In a hypothesis test, you assume the alternative hypothesis is true. 6. A statistical hypothesis is a statement about a sample. 7. If you decide to reject the null hypothesis, then you can support the alternative hypothesis. 8. The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true. 9. A large P@value in a test will favor rejection of the null hypothesis. 10. To support a claim, state it so that it becomes the null hypothesis. Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha. 11. m … 645 12. m 6 128 13. s ≠ 5 14. s 2 Ú 1.2 15. p 6 0.45 16. p = 0.21 Graphical Analysis In Exercises 17–20, match the alternative hypothesis with its graph. Then state the null hypothesis and sketch its graph. 17. Ha: m 7 3 (a) μ 4 3 2 1 18. Ha: m 6 3 (b) μ 4 3 2 1 19. Ha: m ≠ 3 (c) μ 4 3 2 1 20. Ha: m 7 2 (d) μ 4 3 2 1 Identifying a Test In Exercises 21–24, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. 21. H0: m … 8.0 22. H0: s Ú 5.2 Ha: m 7 8.0 Ha: s 6 5.2 23. H0: s 2 = 142 24. H0: p = 0.25 Ha: s 2 ≠142 Ha: p ≠0.25
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