SECTION 8.2 Testing the Difference Between Means (Independent Samples, s1 and s2 Unknown) 433 14. Transactions A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World. The results for samples of customer transactions for the two fast food restaurants are shown at the left. At a = 0.05, can you support the magazine’s claim? Assume the population variances are equal. 15. Blue Crabs A marine researcher claims that the stomachs of blue crabs from one location contain more fish than the stomachs of blue crabs from another location. The stomach contents of a sample of 25 blue crabs from Location A contain a mean of 320 milligrams of fish and a standard deviation of 60 milligrams. The stomach contents of a sample of 15 blue crabs from Location B contain a mean of 280 milligrams of fish and a standard deviation of 80 milligrams. At a = 0.01, can you support the marine researcher’s claim? Assume the population variances are equal. 16. Yellowfin Tuna A marine biologist claims that the mean fork length (see figure at the left) of yellowfin tuna is different in two zones in the eastern tropical Pacific Ocean. A sample of 26 yellowfin tuna collected in Zone A has a mean fork length of 76.2 centimeters and a standard deviation of 16.5 centimeters. A sample of 31 yellowfin tuna collected in Zone B has a mean fork length of 80.8 centimeters and a standard deviation of 23.4 centimeters. At a = 0.01, can you support the marine biologist’s claim? Assume the population variances are equal. (Adapted from Fishery Bulletin) 17. Annual Income A politician claims that the mean household income in a recent year is greater in York County, South Carolina, than it is in Elmore County, Alabama. In York County, a sample of 23 residents has a mean household income of $64,900 and a standard deviation of $16,000. In Elmore County, a sample of 19 residents has a mean household income of $59,500 and a standard deviation of $23,600. At a = 0.05, can you support the politician’s claim? Assume the population variances are not equal. (Adapted from U.S. Census Bureau) 18. Annual Income A demographics researcher claims that the mean household income in a recent year is the same in Eagle County, Colorado, and Boulder County, Colorado. In Eagle County, a sample of 18 residents has a mean household income of $85,400 and a standard deviation of $26,100. In Boulder County, a sample of 15 residents has a mean household income of $83,300 and a standard deviation of $18,200. At a = 0.10, can you reject the demographics researcher’s claim? Assume the population variances are not equal. (Adapted from U.S. News) 19. Tensile Strength The tensile strength of a metal is a measure of its ability to resist tearing when it is pulled lengthwise. An experimental method of treatment produced steel bars with the tensile strengths (in newtons per square millimeter) listed below. Experimental Method: 391 383 333 378 368 401 339 376 366 348 The conventional method produced steel bars with the tensile strengths (in newtons per square millimeter) listed below. Conventional Method: 362 382 368 398 381 391 400 410 396 411 385 385 395 371 At a = 0.01, can you support the claim that the experimental method of treatment makes a difference in the tensile strength of steel bars? Assume the population variances are equal. Sample Statistics for Amount Spent by Customers Burger Stop Fry World x1 = $5.46 s1 = $0.89 n1 = 22 x2 = $5.12 s2 = $0.79 n2 = 30 TABLE FOR EXERCISE 14 Fork length FIGURE FOR EXERCISE 16
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