a) 41 cars equipped with standard carburetors were tested for gas usage and yielded an average of 8.1 km/litre with a standard deviation of 1.2 km/l. 21 of these cars were then chosen randomly, fitted with special carburetors and tested, yielding an average of 8.8 km/l with a standard deviation of 0.9 km/l.
At the 5 percent level of significance, does the new carburetor decrease gas usage?
b) Does the following group of data bear out the same result? Neglect any possibility of interaction between the type of carburetor and other characteristics of the cars.