Question

34. Male versus Female Drivers 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. Age Number of Number Number of Number Male Licensed of Fatal Female Licensed of Fatal Drivers (000s) Crashes Drivers (000s) Crashes 12 6.139 6,816 17664 20,063 19,984 4.441 8,400 5,375 227 5,180 5,016 8,595 7990 7,118 4,527 2,274 2.022 12 6,424 6,941 18,068 20,406 19,898 14,340 8,194 4,803 2,113 1.531 2.780 2.742 2.285 1,514 938 980 16-20 21-24 25-34 35-44 55-64 65-74 74 Source: National Highway and Traffic Safety Institute (a) On the same graph, draw a scatter diagram for both males and females. Be sure to use a different plotting symbol for each group. For example, use a square () for males and a plus sign (+) for females. Treat number of licensed drivers as the explanatory variable. (b) Based on the scatter diagrams, do you think that insurance companies are justified in charging different insurance rates for males and females? Why? (c) Compute the linear correlation coefficient between number of licensed drivers and number of fatal crashes for males. (d) Compute the linear correlation coefficient between number of licensed drivers and number of fatal crashes for females. (e) Which gender has the stronger linear relation between number of licensed drivers and number of fatal crashes Why?

Answer 1

Answer 34)

Therefore, put number of licensed drivers in explanatory variable category and number of fatal crashes in response variable category. Follow the instructions to obtain the scatter plots of both male and female licensed drivers, using Minitab. 1. Enter data in Minitab. 2. Select Graph -Scatterplot. Select Simple. 3. Enter C2 and C4 in Y variables and C1 and C3 in X variables. 4. Select Multiple graphs. Check Overlaid on the same graph. 5. Click OK twice.

The graph window display the scatter plot. The required screen shot is as follows Scatterplot of Fatal Crashe vs Male License, Fatal Crashe vs Female Li 9000 8000 7000 6000 5000 e 4000 3000 2000 1000 Variable Fatal Crashes-m Male Licensed Drivers ● Fatal Crashes-f* Female Licensed Drivers 5000 10000 15000 20000 X-Data From the above output, it shows the Scatterplot. Black dots represent males and red dots represent females

Both the scatter plots display positive, linear relationship between number of licensed drivers and number of fatal crashes. But the scatter plot for male drivers show a strong linear association between the variables, with higher number of fatal crashes with increase in number of licensed drivers. On the other hand, the association between the number of fatal crashes and number of female licensed drivers is strong, but with no extreme number of fatal crashes with increase in number of licensed drivers. Therefore, insurance companies are justified to charge different insurance rates for females and males.

Follow the instructions to find the correlation coefficient, using Minitab. Step 1: Enter the data into the Minitab. Step 2: Select Stat Basic Statistics-Correlation. Step 3: Enter C1 and C2 in Variables. Step 4: Click OK.

The Minitab output is as follows: Correlations: Male Lic ensed Drivers, Fatal Crashes-m Pearson correlation of Male Licensed Drivers and Fatal Crashes-m -0.883 P-value = 0.002 Therefore, the correlation coefficient is 0.883

(cl) Follow C3 and C4 in Variables. The Minitab output is as follows: Correlations: Female Licensed Drivers, Fatal Crashes-f Pearson correlation of Female Licensed Drivers and Fatal Crashes-f- 0.836 the instructions in part (c) and in step2, enter P-value = 0.005 Therefore, the correlation coefficient is0.836

(e)

Males have stronger linear relationship between number of licensed drivers and number of fatal crashes because the correlation coefficient is more for the males than the females (0.883 0.836) Therefore, males have the stronger linear relationship between the number of licensed drivers and number of fatal crashes.