Section 8.5 Determining Which Method to Use 397 Check Your Understanding In Exercises 1–4, state which type of parameter is to be estimated, then construct the confidence interval. 1. A simple random sample of size 15 has mean ̄x = 10.34 and standard deviation s = 3.48. The population is normally distributed. Construct a 95% confidence interval for the population standard deviation. Standard deviation; (2.55, 5.49) 2. A simple random sample of size 80 has mean ̄x = 7.31. The population standard deviation is �� = 6.26. Construct a 99% confidence interval for the population mean. Mean; (5.51, 9.11) 3. In a simple random sample of 100 children, 22 had reading skills above their grade level. Construct a 99% confidence interval for the proportion of children who have reading skills above their grade level. Proportion; (0.113, 0.327) 4. A simple random sample of size 25 has mean ̄x = 17.4 and standard deviation s = 5.3. The population is approximately normally distributed. Construct a 95% confidence interval for the population mean. Mean; (15.2, 19.6) Answers are on page 398. SECTION 8.5 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 estimated, then construct the confidence interval. 5. A simple random sample of size 18 has mean ̄x = 71.32 and standard deviation s = 15.78. The population is approximately normally distributed. Construct a 95% confidence interval for the population mean. Mean; (63.47, 79.17) 6. In a simple random sample of 400 voters, 220 said that they were planning to vote for the incumbent mayor in the next election. Construct a 99% confidence interval for the proportion of voters who plan to vote for the incumbent mayor in the next election. Proportion; (0.486, 0.614) 7. A simple random sample of size 8 has mean ̄x = 3.21 and standard deviation s = 1.69. The population is normally distributed. Construct a 99% confidence interval for the population standard deviation. Standard deviation; (0.99, 4.50) 8. A simple random sample of size 12 has mean ̄x = 3.37. The population standard deviation is �� = 1.62. The population is approximately normally distributed. Construct a 95% confidence interval for the population mean. Mean; (2.45, 4.29) 9. In a survey of 250 employed adults, 185 said that they had missed one or more days of work in the past six months. Construct a 95% confidence interval for the proportion of employed adults who missed one or more days of work in the past six months. Proportion; (0.686, 0.794) 10. A simple random sample of size 17 has mean ̄x = 8.44 and standard deviation s = 5.38. The population is normally distributed. Construct a 95% confidence interval for the population standard deviation. Standard deviation; (4.01, 8.19) 11. A simple random sample of size 120 has mean ̄x = 8.45. The population standard deviation is �� = 4.81. Construct a 99% confidence interval for the population mean. Mean; (7.32, 9.58) 12. A simple random sample of size 23 has mean ̄x = 1.48 and standard deviation s = 1.32. The population is approximately normally distributed. Construct a 99% confidence interval for the population mean. Mean; (0.70, 2.26) Working with the Concepts 13. Football players: The weights of 52 randomly selected NFL football players in 2013 are presented below. The sample mean is ̄x = 248.38 and the sample standard deviation is s = 46.68. 305 265 287 285 290 235 300 230 195 236 244 194 190 307 218 315 265 210 194 216 255 300 315 190 185 183 313 246 212 201 308 270 241 242 306 237 315 215 200 295 187 204 257 185 255 318 230 316 200 324 245 185 Source: Chicago Tribune Construct a 95% confidence interval for the mean weight of NFL football players in 2010. (235.38, 261.38) 14. Ages of students: A simple random sample of 100 U.S. college students had a mean age of 22.68 years. Assume the population standard deviation is �� = 4.74 years. Construct a 99% confidence interval for the mean age of U.S. college students. (21.46, 23.90) 15. Calories in bread: Following are the numbers of calories in a random sample of 10 slices of bread. Assume the population is normally distributed. 55 51 49 48 68 52 62 70 67 70 Construct a 95% confidence interval for the standard deviation of the number of calories. (6.26, 16.62)
navidi_monk_elementary_statistics_2e_ch7-9
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