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The following data represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender.

The following data represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. (Source: National Hwy and Traffic Safety Institute)

  1. On the same graph, draw a scatter plot for both males and females. Treat the number of licensed drivers as the explanatory (x) variable.
  2. Based on the scatter plots, do you think the insurance companies are justified in charging two different rates for males and females? Why?
  3. Is there a linear relation between the number of licensed drivers and accidents for males? That is, is the correlation statistically significant? (Compare your correlation to Table II.)
  4. Is there a linear relation between the number of licensed drivers and accidents for females? That is, is the correlation statistically significant? (Compare your correlation to Table II.)
  5. Which gender has the stronger linear relation between the number of licensed drivers and the number fatalities? Why?
  6. Find the least squares regression line for male drivers treating the number of licensed drivers as the explanatory (x) variable and the number of fatal crashes as the response variable.
  7. Interpret the slope and intercept, if appropriate.
  8. Predict the number of crashes if there are 10,000 licensed male drivers.
Age Number of Male Licensed Drivers (000s) (Number of Fatal Crashes Number of Female Licensed Drivers (000s) Number of Fatal Crashes
<16 12 227 12 77
16 - 20 6,424 5,180 6,139 2,113
21 - 24 6,941 5,016 6,816 1,531
25 - 34 18,068 8,595 17,664 2,780
35 - 44 20,406 7,990 20,063 2,742
45 - 54 19,898 7,118 19,984 2,285
55 - 64 14,340 4,527 14,441 1,514
65 - 74 8,194 2,274 8,400 938
>74 4,803 2,022 5,375

980

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