Discuss the below:
Auto Insurance Commissioner
Q: Auto insurance premiums in Massachusetts depend on the age of the driver and the driver's record but are not supposed to depend on gender. The state insurance commissioner wants to investigate whether there is any difference in the average premium that company A charges males and the average premium for females.
(a) State the null hypothesis that the insurance commissioner is interested in testing and provide a suitable alternative hypothesis. Explain your choice of alternative.
(b) The commissioner takes a simple random sample of 40 insured females and 40 insured males. The sample of 40 males has average annual premium $483.44 and standard deviation $126.62. The sample of 40 females has average annual premium $414.34 and standard deviation $105.98. Find the p-value for testing the commissioner's null hypothesis (Note, the sample sizes are large).
(c) What conclusion do you reach about the null hypothesis? Explain.
(d) Explain in words what the p-value tells the commissioner.