An auto manufacturer makes a type of car that is known to have an average mileage of 31.5 miles per gallon on the highway. They want to put a smaller engine in this type of car, and they want to see if this increases the average mileage. They test the new engine on a random sample of eight cars. The mileages for this sample of cars are shown below:

32.831.930.433.332.231.633.631.0

The sample mean and sample standard deviation are calculated to be 32.1 mpg and 1.1 mpg, respectively. Mileages are known to follow a normal distribution.

(a) Calculate a 95% confidence interval for the true mean mileage with the new smaller engine.

(b) Provide an interpretation of the interval in (a).