400 Chapter 8 Confidence Intervals 14. Refer to Exercise 13. How large a sample is needed so that a 99% confidence interval will have margin of error of 0.08, using the sample proportion for ̂p? 230 15. Refer to Exercise 13. How large a sample is needed so that a 99% confidence interval will have margin of error of 0.08, assuming no estimate of ̂p is available? 260 Review Exercises 1. Build more parking? A survey is to be conducted in which a random sample of residents in a certain city will be asked whether they favor or oppose the building of a new parking structure downtown. How many residents should be polled to be sure that a 90% confidence interval for the proportion who favor the construction will have a margin of error no greater than 0.05? 271 2. Drill lifetime: A sample of 50 drills had a mean lifetime of 12.68 holes drilled when drilling a low-carbon steel. Assume the population standard deviation is 6.83. a. Construct a 95% confidence interval for the mean lifetime of this type of drill. (10.79, 14.57) b. The manufacturer of the drills claims that the mean lifetime is greater than 13. Does this confidence interval contradict this claim? Explain. No c. How large would the sample need to be so that a 95% confidence interval would have a margin of error of 1.0? 180 Source: Journal of Engineering Manufacture 216:301–305 3. Cost of environmental restoration: In a survey of 189 Scottish voters, 61 said they would be willing to pay additional taxes in order to restore the Affric forest. a. Assuming that the 189 voters who responded constitute a random sample, construct a 99% confidence interval for the proportion of voters who would be willing to pay to restore the Affric forest. (0.235, 0.410) b. Use the results from the sample of size 189 to estimate the sample size needed so that the 99% confidence interval will have a margin of error of 0.03. 1612 c. Another survey is planned, in which voters will be asked whether they would be willing to pay in order to restore the Strathsprey forest. At this point, no estimate of this proportion is available. Find an estimate of the sample size needed so that the margin of error of a 99% confidence interval will be 0.03. 1844 Source: Environmental and Resource Economics 18:391–410 4. More repairs: A sample of six records for repairs of a component showed the following costs: 93 97 27 79 81 87 a. Construct a 90% confidence interval for the mean cost of a repair for this type of component. (56.3, 98.4) b. Is there any evidence to suggest that this confidence interval may not be reliable? Explain. Yes 5. More repairs: Refer to Exercise 4. Would it be appropriate to use these data to construct a confidence interval for �� using the methods of Section 8.4? Explain. No 6. Contaminated water: Polychlorinated biphenyls (PCBs) are a group of synthetic oil-like chemicals that were at one time widely used as insulation in electrical equipment and were discharged into rivers. They were discovered to be a health hazard, and were banned in the 1970s. Assume that water samples are being drawn from a river in order to estimate the PCB concentration. Suppose that a random sample of size 60 has a sample mean of 1.96 parts per billion (ppb). Assume the population standard deviation is �� = 0.35 ppb. a. Construct a 98% confidence interval for the PCB concentration. (1.85, 2.07) b. EPA standards require that the PCB concentration in drinking water be no more than 0.5 ppb. Based on the confidence interval, is it reasonable to believe that this water meets the EPA standard for drinking water? Explain. No c. Estimate the sample size needed so that a 98% confidence interval will have a margin of error of 0.03. 737 7. Defective electronics: A simple random sample of 200 electronic components was tested, and 17 of them were found to be defective. a. Construct a 99% confidence interval for the proportion of components that are defective. (0.034, 0.136) b. Use the results from the sample of 200 to estimate the sample size needed so that the 99% confidence interval will have a margin of error equal to 0.04. 323 c. A simple random sample of a different type of component will be tested. At this point, there is no estimate of the proportion defective. Find a sample size so that the 99% confidence interval will have a margin of error no greater than 0.04. 1037 8. Cost of repairs: A sample of eight repair records for a certain fiber-optic component was drawn, and the cost of each repair, in dollars, was recorded, with the following results: 30 35 19 23 27 22 26 16 a. Construct a dotplot for these data. Are the assumptions for constructing a confidence interval for the mean satisfied? Explain. Yes b. If appropriate, construct a 98% confidence interval for the mean cost of a repair. (18.3, 31.2)
navidi_monk_elementary_statistics_2e_ch7-9
To see the actual publication please follow the link above