A86 ODD ANSWERS 11. ny = -0.086x + 10.450 x y Age (in years) Hours of sleep 20 30 40 50 60 70 80 4 5 6 7 8 9 (a) It is not meaningful to predict the value of y when x = 16 because x = 16 is outside the range of the original data. (b) 8.3 hours (c) It is not meaningful to predict the value of y when x = 85 because x = 85 is outside the range of the original data. (d) 6.15 hours 13. 0.203. About 20.3% of the variation is explained. About 79.7% of the variation is unexplained. 15. 0.412. About 41.2% of the variation is explained. About 58.8% of the variation is unexplained. 17. (a) 0.876. About 87.6% of the variation is explained by the relationship between the time to accelerate from 0 to 60 miles per hour and top speed for electric cars and about 12.4% of the variation is unexplained. (b) 9.411. The standard error of estimate of the top speed for a specific time to accelerate from 0 to 60 miles per hour is about 9.411 miles per hour. 19. 196.393 6 y 6 212.635 You can be 90% confident that the total amount of milk produced will be between 196.393 billion pounds and 212.635 billion pounds when the average number of cows is 9275. 21. 4.866 6 y 6 8.294 You can be 95% confident that the hours slept will be between 4.866 and 8.294 hours for an adult who is 45 years old. 23. 73.727 6 y 6 150.357 You can be 99% confident that the top speed of an electric car will be between 73.727 miles per hour and 150.357 miles per hour when it has a time of 5.9 seconds to accelerate from 0 to 60 miles per hour. 25. (a) ny = 1.639 + 3.469x 1 - 32.326x2 (b) 0.838 (c) 0.943 The standard error of estimate of the carbon monoxide content given specific contents of tar and nicotine is about 0.838 milligram. The multiple regression model explains about 94.3% of the variation. 27. (a) 21.705 miles per gallon (b) 25.21 miles per gallon (c) 30.1 miles per gallon (d) 25.86 miles per gallon Quiz for Chapter 9 (page 520) 1. The data appear to have a positive linear correlation. As x increases, y tends to increase. x Secondary school teachers’ salaries (in thousands of dollars) Elementary school teachers’ salaries (in thousands of dollars) y 50 54 58 62 66 70 50 52 54 56 58 60 62 64 66 68 70 2. 0.995. Strong positive linear correlation. As the average annual salaries of secondary school teachers increase, the average annual salaries of elementary school teachers tend to increase. 3. Reject H0. There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between the average annual salaries of secondary school teachers and the average annual salaries of elementary school teachers. 4. ny = 0.976x - 0.604 x Secondary school teachers’ salaries (in thousands of dollars) Elementary school teachers’ salaries (in thousands of dollars) y 50 54 58 62 66 70 50 52 54 56 58 60 62 64 66 68 70 5. $61,372 6. 0.991. About 99.1% of the variation in the average annual salaries of elementary school teachers can be explained by the relationship between the average annual salary of secondary school teachers and elementary school teachers and about 0.9% of the variation is unexplained. 7. 0.372. The standard error of estimate of the average annual salaries of elementary school teachers for a specific average annual salary of secondary school teachers is about $372. 8. 60.486 6 y 6 62.283 You can be 95% confident that the average annual salary of elementary school teachers will be between $60,486 and $62,283 when the average annual salary of secondary school teachers is $63,500. 9. (a) $95.26 (b) $70.28 (c) $67.74 (d) $59.46
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