556 CHAPTER 10 Chi-Square Tests and the F -Distribution 20. Carbon Monoxide Emissions An automobile manufacturer claims that the variance of the carbon monoxide emissions for a make and model of one of its vehicles is less than the variance of the carbon monoxide emissions for a top competitor’s equivalent vehicle. A sample of the carbon monoxide emissions of 19 of the manufacturer’s specified vehicles has a variance of 0.008. A sample of the carbon monoxide emissions of 21 of its competitor’s equivalent vehicles has a variance of 0.045. At a = 0.10, can you support the manufacturer’s claim? (Adapted from U.S. Environmental Protection Agency) 21. Golf The table at the left shows a sample of the driving distances (in yards) for two golfers. At a = 0.10, can you conclude that the variances of the driving distances differ between the two golfers? 22. Heart Transplant Waiting Times The table at the left shows a sample of the waiting times (in days) for a heart transplant for two age groups. At a = 0.05, can you conclude that the variances of the waiting times differ between the two age groups? (Adapted from Organ Procurement and Transplantation Network) 23. Science Assessment Tests A state school administrator claims that the standard deviations of science assessment test scores for eighth-grade students are the same in Districts 1 and 2. A sample of 12 test scores from District 1 has a standard deviation of 36.8 points, and a sample of 14 test scores from District 2 has a standard deviation of 32.5 points. At a = 0.10, can you reject the administrator’s claim? (Adapted from National Center for Education Statistics) 24. U.S. History Assessment Tests A state school administrator claims that the standard deviations of U.S. history assessment test scores for eighth-grade students are the same in Districts 1 and 2. A sample of 10 test scores from District 1 has a standard deviation of 30.9 points, and a sample of 13 test scores from District 2 has a standard deviation of 27.2 points. At a = 0.01, can you reject the administrator’s claim? (Adapted from National Center for Education Statistics) 25. Annual Salaries An employment information service claims that the standard deviation of the annual salaries for actuaries is less in California than in New York. You select a sample of actuaries from each state. The results of each survey are shown in the figure. At a = 0.05, can you support the service’s claim? (Adapted from America’s Career InfoNet) s2 = $28,600 n2 = 61 Actuaries in California s1 = $42,800 n1 = 41 Actuaries in New York s2 = $39,100 n2 = 28 Public relations managers in Florida Public relations managers in Louisiana s1 = $27,200 n1 = 24 FIGURE FOR EXERCISE 25 FIGURE FOR EXERCISE 26 26. Annual Salaries An employment information service claims that the standard deviation of the annual salaries for public relations managers is less in Louisiana than in Florida. You select a sample of public relations managers from each state. The results of each survey are shown in the figure. At a = 0.05, can you support the service’s claim? (Adapted from America’s Career InfoNet) Golfer 1 Golfer 2 227 234 235 246 223 268 231 235 245 248 262 257 258 269 253 262 258 265 255 262 TABLE FOR EXERCISE 21 18 – 34 35 – 49 384 326 318 385 371 327 434 415 413 420 408 428 454 392 385 TABLE FOR EXERCISE 22
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