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# Math 10 – Homework 6 – Answers to homework

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What are the two types of hypotheses used in a hypothesis test? How are they related? Ho: Null Hypotheses – A statement about a population parameter that is assumed to be true for the purposes of testing Ha: Alternative Hypothesis – A statement about a population parameter that is assumed to be true is the Null Hypothesis is rejected during testing. These two Hypotheses are complements of each other. 2. Describe the two types of error possible in a hypothesis test decision. Type I error: Rejecting a true Ho Type II error: Failing to reject a false Ho True or False? In Exercises 3-8, determine whether the statement is true of false. If it is false, rewrite it as a true statement. 3. In a hypothesis test, you assume the alternative hypothesis is true. False, you assume the Null Hypothesis is true. 4. A statistical hypothesis is a statement about a sample. False, it is a statement about a population parameter. 5. If you decide to reject the null hypothesis, you can support the alternative hypothesis. True 6. The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true. True 7. A large P-value in a test will favor a rejection of the null hypothesis. False, a small p-value supports rejecting the null hypothesis. 8. If you want to support a claim, write it as your null hypothesis. False, to support a claim write it as the alternative hypothesis. Stating Hypotheses In Exercises 9-14, use the given statement to represent a claim. Write its complement and state which is Ho and which is Ha. 9. Ha: p >.65 Ho: pζ65 10. Ho:  ζ 128 Ha:  >128 11. Ha: 2 ≠ 5 Ho: 2 = 5 12. Ho:  =1.2 Ha:  ≠1.2 13. Ho: p η 0.45 Ha: p < 0.45 14. Ha:  < 0.21 Ho:  η 0.21 Think about the context of the claim. Determine whether you want to support or reject the claim. a. State the null and alternative hypotheses in words. b. Write the null and alternative hypotheses in appropriate symbols c. Describe in words Type I error (the consequence of rejecting a true null hypothesis.) d. Describe in words Type II error (the consequence of failing to reject a false null hypothesis.) 15. 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 about \$650. How would you write the null and alternative hypotheses?