Section 9.6 Determining Which Method to Use 463 3. A simple random sample of size 7 has mean ̄x = 32.5 and standard deviation s = 8.27. The population is normally distributed. Can you conclude that the population standard deviation is greater than 6? Use the �� = 0.05 level of significance. Standard deviation; do not reject H0. 4. A simple random sample of size 65 has mean ̄x = 38.16. The population standard deviation is �� = 5.95. Can you conclude that the mean is less than 40? Use the �� = 0.01 level of significance. Mean; reject H0. Answers are on page 464. SECTION 9.6 Exercises Exercises 1– 4 are the Check Your Understanding exercises located within the section. Practicing the Skills In Exercises 5–12, state which type of parameter is to be tested; then perform the hypothesis test. 5. A simple random sample of size 13 has mean ̄x = 7.26 and standard deviation s = 2.45. The population is approximately normally distributed. Can you conclude that the population mean differs from 9? Use the �� = 0.01 level of significance. Do not reject H0. 6. A simple random sample of size 65 has mean ̄x = 57.3. The population standard deviation is �� = 12.6. Can you conclude that the population mean is less than 60? Use the �� = 0.05 level of significance. Reject H0. 7. A simple random sample of size 16 has mean ̄x = 4.1 and standard deviation s = 6.2. The population is normally distributed. Can you conclude that the population standard deviation is greater than 5? Use the �� = 0.05 level of significance. Do not reject H0. 8. In a simple random sample of 120 law students, 54 were women. Can you conclude that less than half of law students are women? Use the �� = 0.01 level of significance. Do not reject H0. 9. A simple random sample of size 23 has mean ̄x = 41.8. The population standard deviation is �� = 3.72. Can you conclude that the population mean differs from 40? Use the �� = 0.05 level of significance. Reject H0. 10. A simple random sample of size 6 has mean ̄x = 5.49 and standard deviation s = 2.37. The population is approximately normally distributed. Can you conclude that the population mean is greater than 4? Use the �� = 0.05 level of significance. Do not reject H0. 11. In a simple random sample of 95 families, 70 had one or more pets at home. Can you conclude that the proportion of families with one or more pets differs from 0.6? Use the �� = 0.01 level of significance. Reject H0. 12. A simple random sample of size 22 has mean ̄x = 91.7 and standard deviation s = 19.3. The population is normally distributed. Can you conclude that the population standard deviation is greater than 15? Use the �� = 0.05 level of significance. Reject H0. Working with the Concepts 13. Saving for college: In a survey of 909 U.S. adults with children conducted in 2012 by the Financial Industry Regulatory Authority, 309 said that they had saved money for their children’s college education. Can you conclude that more than 30% of U.S. adults with children have saved money for college? Use the �� = 0.05 level of significance. Reject H0. 14. Big houses: The U.S. Census Bureau reported that the mean area of U.S. homes built in 2012 was 2505 square feet. Assume that a simple random sample of 20 homes built in 2013 had a mean area of 2581 square feet, with a standard deviation of 225 square feet. Can you conclude that the mean area of homes built in 2013 is greater than that of homes built in 2012? Use the �� = 0.01 level of significance. Do not reject H0. 15. Cookies: Following are the weights of 8 boxes of cookies, each of which is labeled as containing 16 ounces. Assume that the population of weights is normally distributed. 15.91 16.06 16.08 15.97 16.02 15.88 15.89 16.01 Can you conclude that the population standard deviation is less than 0.1? Use the �� = 0.01 level of significance. Do not reject H0. 16. Careers in science: The 2012 General Social Survey asked 514 people whether they had ever considered a career in science, and 178 said that they had. Can you conclude that more than 30% of people have considered a career in science? Use the �� = 0.05 level of significance. Reject H0. 17. Teacher salaries: A random sample of 50 public school teachers in Georgia had a mean annual salary of $48,300. Assume the population standard deviation is �� = $8,000. Can you conclude that the mean salary of public school teachers in Georgia differs from $50,000? Use the �� = 0.01 level of significance. Do not reject H0. 18. Highway speeds: Speeds for a sample of nine cars were measured by radar along a stretch of highway. The results, in miles per hour, were as follows. Assume that the population of speeds is normally distributed. 56 60 53 55 54 51 54 51 56 Can you conclude that the population standard deviation is greater than 2? Use the �� = 0.05 level of significance. Reject H0. 19. Mercury pollution: Mercury is a toxic metal that is used in many industrial applications. Seven measurements, in milligrams per cubic meter, were taken of the mercury concentration in a lake, with the following results. Assume
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