Statistics HW check?

Hey everyone!

I just have a homework assignment (that's graded) and I want to check my answers to make sure they're correct.

Problem: In order to estimate the difference between the average Miles per Gallon of two different models of cars, samples are taken and the following information is collected.

a) Find a 95% confidence interval for the difference between the average Miles per Gallon for the two models.

b) From your answer in Part a), is there conclusive evidence that one model gets a significantly higher average MPG than the other? Why or why not? Explain.

Data: sample size (model a) = 13, sample mean (model a) = 35, sample variance (model a) = 13 | sample size (model b) = 14, sample mean (model a) = 32, sample variance (model b) = 7.

Note: Assume that both populations are normally distributed.