580 CHAPTERS 9&10 CUMULATIVE REVIEW CHAPTER 10 Chi-Square Tests and the F-Distribution 1. The table below shows the winning times (in seconds) for the men’s and women’s 100-meter runs in the Summer Olympics from 1932 to 2020. (Source: Olympic Channel Services) Men, x 10.30 10.30 10.30 10.40 10.50 10.20 10.00 Women, y 11.90 11.50 11.90 11.50 11.50 11.00 11.40 Men, x 9.90 10.14 10.06 10.25 9.99 9.92 9.96 Women, y 11.00 11.07 11.08 11.06 10.97 10.54 10.82 Men, x 9.84 9.87 9.85 9.69 9.63 9.81 9.80 Women, y 10.94 11.12 10.93 10.78 10.75 10.71 10.61 (a) Display the data in a scatter plot, calculate the correlation coefficient r, and describe the type of correlation. (b) At a = 0.05, is there enough evidence to conclude that there is a significant linear correlation between the winning times for the men’s and women’s 100-meter runs? (c) Find the equation of the regression line for the data. Draw the regression line on the scatter plot. (d) Use the regression equation to predict the women’s 100-meter time when the men’s 100-meter time is 9.90 seconds. 2. The table at the right shows the residential natural gas expenditures (in dollars) in one year for a random sample of households in four regions of the United States. Assume that the populations are normally distributed and the population variances are equal. At a = 0.10, can you reject the claim that the mean expenditures are the same for all four regions? (Adapted from U.S. Energy Information Administration) 3. The equation used to predict the annual sweet potato yield (in pounds per acre) is ny = 17,106 - 0.318x 1 + 0.303x2, where x1 is the number of acres planted and x2 is the number of acres harvested. Use the multiple regression equation to predict the annual sweet potato yields for the values of the independent variables. (Adapted from U.S. Department of Agriculture) (a) x1 = 110,000, x2 = 100,000 (b) x1 = 125,000, x2 = 115,000 Northeast Midwest South West 1091 318 403 499 529 734 312 425 654 471 609 853 884 859 597 391 775 652 738 229 1150 987 455 273 533 656 417 435 528 614 868 505
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