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Chapter 8: 8.44 (page 330)
Explain why the margin of error determines the accuracy with which a sample mean estimates a population mean.
If the margin of error is small, population mean is estimated using and precision of estimate is high.
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Civilian Labor Force. Consider again the problem of estimating the mean age, , of all people in the civilian labor force. In Example on page 328 , we found that a sample size of 2250 is required to have a margin of error of year and a confidence level. Suppose that, due to financial constraints, the largest sample size possible is 900 . Determine the greatest confidence level, given that the margin of error is to be kept at half year. Recall that years.
Medical Marijuana. An issue with legalization of medical marijuana is "diversion," the process in which medical marijuana prescribed for one person is given, traded, or sold to someone who is not registered for medical marijuana use. Researchers S. Sautel et al. study the issue of diversion in the article "Medical Marijuana Use Among Adolescents in Substance Abuse Treatment" . The mean number of days that adolescents in substance abuse treatment used medical marijuana in the last six months was . Assume the population standard deviation is days.
a. Find a confidence interval for the mean number of days, , of diverted medical marijuana use in the last 6 months of all adolescents in substance abuse treatment.
b. Repeat part (a) at a confidence level.
c. Draw a graph similar to Fig. on page to display both confidence intervals.
d. Which confidence interval yields a more accurate estimate of ? Explain your answer.
Civilian Labor Force. Consider again the problem of estimating the mean age, , of all people in the civilian labor force. In Example on page 328 , we found that a sample size of 2250 is required to have a margin of error of year and a confidence level. Suppose that, due to financial constraints, the largest sample size possible is 900 . Determine the smallest margin of error, given that the confidence level is to be kept at . Recall that years.
Assume that the population standard deviation is known and decide weather use of the -interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.
The sample data contain outliers, and the sample size is.
American Alligators. Multi-sensor data loggers were attached to free-ranging American alligators in a study conducted by Y. Watanabe for the article "Behavior of American Alligators Monitored by Multi-Sensor Data Loggers" (Aquatic Biology, Vol. 18 , pp. 1-8). The mean duration for a sample of dives was seconds. Assume the population standard deviation is seconds.
a. Find a confidence interval for the mean duration, of an American-alligator dive.
b. Repeal part (a) at a confidence level.
c. Draw a graph similar to Fig. on page 326 to display both confidence intervals.
d. Which confidence interval yields a more accurate estimate of ? Explain your answer.
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