1. Suppose the insurance company has found that among its customers, regardless

Question

1. Suppose the insurance company has found that among its customers, regardless of the number of cigarettes smoked, smokers are nearly twice as likely to make an insurance claim (11 claims/year on average) as nonsmokers (6 claims/year). They would like you to test this probability by doing the following:

a) Find the mean number of claims made by the sample of smokers in the group.

b) What's the sample standard deviation for claims made by smokers?

c) Now find the mean number of claims for the nonsmokers.

d) And what is the sample standard deviation of the number of claims made by nonsmokers?

Individual Age Gender (Male=1) Family Size Cigarettes/Day Alcohol/Day Total Claims 1 25 1 2 0 3 1 2 28 0 7 0 1 0 3 20 0 3 10 0 9 4 53 1 1 0 0 5 5 48 0 3 5 2 12 6 54 1 3 0 0 2 7 56 1 4 0 0 0 8 35 1 3 10 1 10 9 50 0 6 0 0 6 10 39 1 6 0 0 1 11 56 1 7 0 3 4 12 29 0 5 0 2 4 13 60 1 1 0 1 3 14 29 1 5 0 1 1 15 21 1 2 20 1 17 16 23 1 4 0 1 1 17 38 1 4 0 1 8 18 62 1 4 0 0 7 19 24 0 1 0 3 7 20 53 0 7 0 1 6

Explanation / Answer

a)No of smokers in the sample = 4

Number of claims made by the of smokers in the group = 9+12+10+17 = 48

Mean Number of claims made by the sample of smokers = 48/4 = 12

b) Let S be the SD for claims made by smokers

S2 = (( 9-12)2 +( 12-12)2 + (10-12)2 + (17-12)2) / 3 therefore S = SQRT(38/3) = 3.5590

c) Mean number of claims made by non-smokers

Number of non-smokers in the sample = 16  

  Number of claims made by the of non-smokers in the sample = 56

  Mean Number of claims made by the sample of smokers = 56/16 = 3.5

d)   sample standard deviation of the number of claims made by non-smokers = 7.466

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