Automobile collision insurance is used to pay for any claims made against the driver in the event of an accident. This type of insurance will typically pay to repair any assets that your vehicle damages.

(a) Collision claims tend to be skewed right. Why do you think this is the case?

(b) A random sample of 40 collision claims of 30- to 59-year-old drivers results in a mean claim of $3669 with a standard deviation of $2029. An independent random sample of 40 collision claims of 20- to 24-year-old drivers results in a mean claim of $4586 with a standard deviation of $2302.

Using the concept of hypothesis testing, provide an argument that justifies charging a higher insurance premium to 20- to 24-year-old drivers.

Perform the appropriate hypothesis test.