2.) Car insurance companies assume that the longer a person has been driving, the less likely they will be in an accident, and therefore charge new drivers higher insurance premiums than experienced drivers. To determine whether driving experience is related to the amount of car accidents, you survey a random sample of 12 Torontonians and ask them about the number of years they have been driving, and the number of car accidents they have been involved in during the past year. The data are presented below:

Question

2.) Car insurance companies assume that the longer a person has been driving, the less likely they will be in an accident, and therefore charge new drivers higher insurance premiums than experienced drivers.  To determine whether driving experience is related to the amount of car accidents, you survey a random sample of 12 Torontonians and ask them about the number of years they have been driving, and the number of car accidents they have been involved in during the past year.  The data are presented below:

Driver	#ofyrsdriving(X) #accidents (Y)
A	    4.5              3
B	    2.5	             5
C	    1.5              3
D	     3	             3
E	    1.5	             6
F	     5	             2
G	     5	             0
H	     2	             4
I	     3	             1
J	     4 	             2
K	     1	             5
L	     3	             2
	
a.	Determine whether the assumptions of car insurance companies are valid.  Assuming á=0.05, include the hypotheses, critical test statistic, conclusion, and all formulas and calculations.  b.	Is it appropriate to conclude that lack of driving experience causes accidents?  Why or why not?

MathGuru · Answer

To find if there is a statistically significant linear relationship between number of years driving and accidents, try a Pearson r. If the null is rejected, then there is a linear relationship in the population. If the null is not rejected, you cannot conclude a linear relationship in the population.