6 Chapter Quiz 340 CHAPTER 6 Confidence Intervals Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book. 1. The winning times (in hours) for a sample of 20 randomly selected Boston Marathon Women’s Open Division champions from 1980 to 2019 are shown in the table at the left. Assume the population standard deviation is 0.068 hour. (Source: Boston Athletic Association) (a) Find the point estimate of the population mean. (b) Find the margin of error for a 95% confidence level. (c) Construct a 95% confidence interval for the population mean. Interpret the results. (d) Does it seem likely that the population mean could be greater than 2.52 hours? Explain. 2. You wish to estimate the mean winning time for Boston Marathon Women’s Open Division champions. The estimate must be within 2 minutes of the population mean. Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Use the population standard deviation from Exercise 1. 3. The data set represents the amounts of time (in minutes) spent checking email for a random sample of employees at a company. 7.5 2.0 12.1 8.8 9.4 7.3 1.9 2.8 7.0 7.3 (a) Find the sample mean and the sample standard deviation. (b) Construct a 90% confidence interval for the population mean. Interpret the results. Assume the times are normally distributed. (c) Repeat part (b), assuming s = 3.5 minutes. Compare the results. 4. In a random sample of 12 senior-level civil engineers, the mean annual earnings were $133,326 and the standard deviation was $36,729. Assume the annual earnings are normally distributed and construct a 95% confidence interval for the population mean annual earnings for senior-level civil engineers. Interpret the results. (Adapted from Salary.com) 5. You research the salaries of senior-level civil engineers and find that the population mean is $131,935. In Exercise 4, does the t-value fall between -t0.95 and t0.95? 6. In a survey of 1010 U.S. adults, 838 say that the energy situation in the United States is very or fairly serious. (Adapted from Gallup) (a) Find the point estimate for the population proportion. (b)Construct a 90% confidence interval for the population proportion. Interpret the results. (c) Would it be unusual for the population proportion to be between 90% and 95% of the point estimate? Explain. (d)Find the minimum sample size needed to estimate the population proportion at the 99% confidence level to ensure that the estimate is accurate within 4% of the population proportion. 7. Refer to the data set in Exercise 3. Assume the population of times spent checking email is normally distributed. Construct a 95% confidence interval for (a) the population variance and (b) the population standard deviation. Interpret the results. Women’s Open Division winning times (in hours) 2.42 2.38 2.44 2.67 2.44 2.57 2.39 2.49 2.39 2.41 2.49 2.40 2.42 2.53 2.39 2.45 2.44 2.54 2.49 2.42 TABLE FOR EXERCISE 1
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