354 CHAPTER 7 Estimating Parameters and Determining Sample Sizes 16.Comparing Waiting Lines a. The values listed below are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Construct a 95% confidence interval for the population standard deviation s. 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7 b. The values listed below are waiting times (in minutes) of customers at the Bank of Providence, where customers may enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation s. 4.2 5.4 5.8 6.2 6.7 7.7 7.7 8.5 9.3 10.0 c. Interpret the results found in parts (a) and (b). Do the confidence intervals suggest a difference in the variation among waiting times? Which arrangement seems better: the single-line system or the multiple-line system? Determining Sample Size. In Exercises 17–20, assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 7-2 on page 351 to find the indicated sample size. 17.IQ of Data Scientists You want to estimate s for the population of IQ scores of data scientists. Find the minimum sample size needed to be 99% confident that the sample standard deviation s is within 20% of s. Is this sample size practical? 18.Blood Pressure You want to estimate s for the population of diastolic blood pressures of air traffic controllers in the United States. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 1% of s. Is this sample size practical? 19.Aspirin Tablets You want to estimate s for the population of weights of the aspirin in Bayer tablets. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 10% of s. Is this sample size practical? 20.Pulse Rates You want to estimate s for the population of pulse rates for the population of marathon runners. Find the minimum sample size needed to be 99% confident that the sample standard deviation s is within 50% of s. Is this sample size practical? Large Data Sets from Appendix B. In Exercises 21 and 22, use the data set in Appendix B. Assume that each sample is a simple random sample obtained from a population with a normal distribution. 21.Comparing Waiting Lines Refer to Data Set 30 “Queues” in Appendix B. Construct separate 95% confidence interval estimates of s using the two-line wait times and the single-line wait times. Do the results support the expectation that the single line has less variation? Do the wait times from both line configurations satisfy the requirements for confidence interval estimates of s? 22.Birth Weights Refer to Data Set 6 “Births” in Appendix B. a. Use the 205 birth weights of girls to construct a 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained. b. Repeat part (a) using the 195 birth weights of boys. c. Compare the results from part (a) and part (b). 23.Finding Critical Values In constructing confidence intervals for s or s 2, Table A-4 can be used to find the critical values x2 L and x2 R only for select values of n up to 101, so the number of degrees of freedom is 100 or smaller. For larger numbers of degrees of freedom, we can approximate x2 L and x2 R by using x2 = 1 2 3 {za>2 + 22k - 142 7-3 Beyond the Basics
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