The engine capacity in liters and the fuel efficiency in mil

The engine capacity (in liters) and the fuel efficiency (in miles per gallon) of a random sample of 10 petrol-driven cars are:

Capacity 1.0 1.2 1.4 1.6 2.0 2.4 2.5 2.8 3.2 4.0

Fuel efficiency 44 47 41 37 33 30 25 26 23 21

a) Determine the regression equation and test the hypothesis that the population slope is zero using 1% level of significance.

b) Construct a 99% confidence interval for the mean fuel efficiency of cars with an engine capacity of 1.8 liters.

c) Construct a 99% prediction interval for the fuel efficiency of a single car with an engine capacity of 1.8 liters.