460 Chapter 9 Hypothesis Testing Check Your Understanding 1. A random sample of size 20 from a normal distribution has standard deviation s = 50. Test H0 : �� = 45 versus H1: �� > 45 at the �� = 0.05 level. Do you reject H0? No 2. A random sample of size 12 from a normal distribution has standard deviation s = 7. Test H0 : �� = 15 versus H1: �� < 15 at the �� = 0.01 level. Do you reject H0? Yes 3. A random sample of size 28 from a normal distribution has standard deviation s = 5. Test H0 : �� = 3 versus H1: �� ≠ 3 at the �� = 0.01 level. Do you reject H0? Yes 4. A random sample of size 5 from a normal distribution has standard deviation s = 28. Test H0 : �� = 40 versus H1: �� ≠ 40 at the �� = 0.05 level. Do you reject H0? No Answers are on page 461. SECTION 9.5 Exercises Exercises 1– 4 are the Check Your Understanding exercises located within the section. Understanding the Concepts In Exercises 5 and 6, fill in each blank with the appropriate word or phrase. 5. To test a hypothesis about a standard deviation using a sample of size 15, we use a chi-square distribution with degrees of freedom. 14 6. The method described for testing hypotheses about standard deviations should be used only when the distribution of the population is almost exactly . normal In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement. 7. When a test for a standard deviation is performed, it does not matter whether the population is normal, so long as the sample is large. False 8. Hypothesis tests for a standard deviation may be either oneor two-tailed. True Practicing the Skills 9. A random sample of size 11 from a normal distribution has standard deviation s = 98. Test H0 : �� = 70 versus H1: �� > 70. Use the �� = 0.05 level of significance. Reject H0. 10. A random sample of size 29 from a normal distribution has standard deviation s = 49. Test H0 : �� = 55 versus H1: �� < 55. Use the �� = 0.01 level of significance. Do not reject H0. 11. A random sample of size 24 from a normal distribution has standard deviation s = 29. Test H0 : �� = 35 versus H1: �� < 35. Use the �� = 0.01 level of significance. Do not reject H0. 12. A random sample of size 13 from a normal distribution has standard deviation s = 83. Test H0 : �� = 60 versus H1: �� > 60. Use the �� = 0.05 level of significance. Reject H0. 13. A random sample of size 25 from a normal distribution has standard deviation s = 51. Test H0 : �� = 30 versus H1: �� ≠ 30. Use the �� = 0.05 level of significance. Reject H0. 14. A random sample of size 8 from a normal distribution has standard deviation s = 75. Test H0 : �� = 50 versus H1: �� ≠ 50. Use the �� = 0.01 level of significance. Do not reject H0. Working with the Concepts 15. Babies: A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of 4.3 pounds. Assume that the population of weights is normally distributed. A pediatrician claims that the standard deviation of the weights of one-year-old girls is less than 5 pounds. Do the data provide convincing evidence that the pediatrician’s claim is true? Use the �� = 0.05 level of significance. Do not reject H0. Based on data from the National Health Statistics Reports 16. Watching TV: The 2012 General Social Survey asked a large number of people how much time they spent watching TV each day. The mean number of hours was 3.09 with a standard deviation of 2.87. Assume that in a sample of 40 teenagers, the sample standard deviation of daily TV time is 2.0 hours, and that the population of TV watching times is normally distributed. Can you conclude that the population standard deviation of TV watching times for teenagers is less than 2.87? Use the �� = 0.01 level of significance. Reject H0. 17. IQ scores: Scores on an IQ test are normally distributed. A sample of 25 IQ scores had standard deviation s = 8. The developer of the test claims that the population standard deviation is �� = 15. Do these data provide sufficient evidence to contradict this claim? Use the �� = 0.05 level of significance. Reject H0. 18. SAT scores: Scores on the math SAT are normally distributed. A sample of 20 SAT scores had standard deviation s = 87. Someone says that the scoring system for the SAT is designed so that the population standard deviation will be �� = 100. Do these data provide sufficient evidence to contradict this claim? Use the �� = 0.05 level of significance. Do not reject H0. 19. How much is in that can? A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in each can is
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