Insurance companies are asking themselves, are average repair costs for SUVs with less than three-star rating larger than repair costs for SUVs with three-star rating?

This question can be replied using statistical techniques developed to test for differences in means of two populations.

a. If the automotive analyst wished to show that damage to SUVs with less than three-star rating cost over $1500 more than SUVs with three-star rating, how would you set up null and alternative hypotheses?
b. If random sample of 25 SUVs with three-star rating which were engaged in collisions showed average damage amount of $5810 and random sample of 25 SUVs with less than three-star rating also involved in collisions showed average damage amount of $8000, would these data support alternative hypothesis in question a? Use significance level of 10%. Suppose that data are from normally distributed populations with known standard deviations of $1450 for SUVs with three-star ratings and $1625 for SUVs with less than three-star ratings.
c. Assume that in question b, standard deviations of $1450 and $1625 were computed from sample. Using a t test, would results of test change? Describe.
d.Create the 90% confidence interval for difference in average damage amount for two kinds of SUVs. Interpret this interval.