Discuss the below:
Q: A car insurance company wishes to investigate the risks that it is incurring when it insures customers who drive two particular types of cars. One part of this investigation is concerned with the ages of claimants. It has therefore collected information on random samples of 12 drivers who drive each of the two types of car and who have made claims during the last year. Their ages in years, to the nearest 6 months are:
Car type A: 27.5, 20.0, 18.0, 28.0, 30.0, 29.5, 28.0, 26.0, 23.5, 27.0, 22.5, 19.0
Car type B: 40.0, 21.5, 30.0, 39.5, 38.0, 25.0, 29.0, 34.5, 30.5, 23.0, 32.0, 18.5.
You can assume that a preliminary analysis of this data has shown that it does NOT have a Normal distribution.
a) Is there any evidence of a significant difference in the age distribution of the drivers claiming for the two types of car? State your null and alternative hypotheses clearly and justify your choice of test.
b) Suppose instead that the insurance companyhad only recorded the agegroup of customers who claimed rather than their individual ages, i.e:
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under 27
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27 and over
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Car A
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6
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6
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|
Car B
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4
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8
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Carry out an appropriate statistical test for a significant difference in the age distribution of drivers who claimed, for the two types of car, and state your conclusion clearly.
c) Comment briefly on the results of your significance tests in parts (a) and (b).