APPENDIX D 799 and Best Actors typically appeared in different movies, we should not expect that there would be a correlation between their ages at the time that they won the awards. 21. r = 0.990. P@value = 0.000 (Table: 60.01). Critical values: r = {0.632. There is sufficient evidence to support the claim that there is a linear correlation between New York City prices of a slice of pizza and a subway ride. 23. r = 0.857. P@value = 0.007 (Table: 60.01). Critical values: r = {0.707. There is sufficient evidence to support the claim that there is a linear correlation between footprint lengths and heights of males. The given results suggest that police can use a footprint length to estimate the height of a male. 25. r = 0.174. P@value = 0.681 (Table: 70.05). Critical values: r = {0.707. There is not sufficient evidence to support the claim that there is a linear correlation between the numbers of cars sold (thousands) and the numbers of points scored in the Super Bowl. Common sense suggests that it would be unreasonable to expect a correlation between car sales and points scored in the Super Bowl. 27. r = -0.959. P-value = 0.010. Critical values: r = {0.878. There is sufficient evidence to support the claim that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates. The results do not suggest any cause-effect relationship between the two variables. 29. r = 0.571. P@value = 0.000 (Table: 60.05). Critical values found from technology: r = {0.074. There is sufficient evidence to support the claim that there is a linear correlation between the time of the ride and the tip amount. It does appear that riders base their tips on the time of the ride. While the smaller sample of eight pairs of data listed in Exercise 15 did not provide sufficient evidence to support a claim of a linear correlation, the larger data set of 703 pairs of data does provide sufficient evidence to support that claim. 31. r = 0.934. P@value = 0.000 (Table: 60.05). Critical values found from technology: r = {0.074. There is sufficient evidence to support the claim that there is a linear correlation between the distance of the ride and the fare. The smaller sample of eight pairs of data leads to the same conclusion as the larger data set of 703 pairs of data, and the values of the linear correlation coefficient r are not dramatically different. 33. Answers vary, but the following is typical. Resampling 1000 times, there are 108 results that are at least as extreme as r = 0.532 found from the sample data. (The results “at least as extreme” are those with r = 0.532 or greater and those that with r = -0.532 or lower.) It appears that the likelihood of getting a result at least as extreme as the one obtained is 0.108, so there is not sufficient evidence to support the claim that there is a linear correlation between lottery jackpots and numbers of tickets sold. 35. Answers vary, but the following is typical. Resampling 1000 times, there are 473 results that are at least as extreme as r = 0.298 found from the sample data. (The results “at least as extreme” are those with r = 0.298 or greater and those that with r = -0.298 or lower.) It appears that the likelihood of getting a result at least as extreme as the one obtained is 0.473, so there is not sufficient evidence to support the claim that there is a linear correlation between the time of the ride and the tip amount. 7. Yes. r = 0.319 and with n = 56, the critical values are {0.263 (Table: {0.254 approximately). There is sufficient evidence to support the claim that there is a linear correlation between the numbers of words spoken in a day by men and women in couple relationships. 9. a. Answer varies. Because there appears to be an upward pattern, it is reasonable to think that there is a linear correlation. b. r = 0.906. P-value = 0.000 (Table: 60.01). Critical values: r = {0.632 (for a 0.05 significance level). There is sufficient evidence to support the claim of a linear correlation. c. r = 0. P-value = 1.000 (Table: 70.05). Critical values: r = {0.666 (for a 0.05 significance level). There is not sufficient evidence to support the claim of a linear correlation. d. The effect from a single pair of values can be very substantial, and it can change the conclusion. 11. a. b. r = 0.816. P-value = 0.002 (Table: 60.01). Critical values: r = {0.602 assuming a 0.05 significance level. There is sufficient evidence to support the claim of a linear correlation between the two variables. c. The scatterplot reveals a distinct pattern that is not a straightline pattern. 13. r = 0.532. P@value = 0.114 (Table: 70.05). Critical values: r = {0.632. There is not sufficient evidence to support the claim that there is a linear correlation between lottery jackpots and numbers of tickets sold. The pair of data in the last column correspond to a point in the scatterplot that is an outlier. The outlier had a significant effect on the results and the conclusion changed from the one reached in Example 4. Also, the added pair of values represent a huge jackpot of 400 million dollars, but the relatively low number of ticket sales is not consistent with known lottery behavior. It appears that the added pair of values is in error. 15. r = 0.298. P@value = 0.473 (Table: 70.05). Critical values: r = {0.707. There is not sufficient evidence to support the claim that there is a linear correlation between the time of the ride and the tip amount. It does not appear that riders base their tips on the time of the ride. 17. r = 0.986. P@value = 0.000 (Table: 60.01). Critical values: r = {0.707. There is sufficient evidence to support the claim that there is a linear correlation between the distance of the ride and the fare. 19. r = -0.139. P@value = 0.667 (Table: 70.05). Critical values: r = {0.576. There is not sufficient evidence to support the claim that there is a significant linear correlation between the ages of Best Actresses and Best Actors. Because Best Actresses
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