The management of a taxi cab company is trying to decide if they should switch from bias tires to radial tires to improve fuel economy. Each of 10 taxis was equipped with one of the two tire types and driven on a test course. Without changing drivers, tires were then switched to the other tire type and the test course was repeated. The fuel economy (in mpg) for the 10 cars are given below. Let μR be the mean number of miles per gallon for taxis using radial tires, and let μB be the mean number of miles per gallon for taxis using bias tires. Car Radial Bias
1 32.1 27.1
2 36.1 31.5
3 32.3 30.4
4 29.5 26.9
5 34.3 29.9
6 31.9 28.7
7 33.4 30.2
8 34.6 31.8
9 35.2 33.6
10 32.7 29.9

Required:
a. Because switching tires on the taxi fleet is expensive, management does not want to switch unless a hypothesis test provides strong evidence that the mileage will be improved. State the appropriate null and alternate hypotheses, and find the P-value.
b. A cost-benefit analysis shows that it will be profitable to switch to radial tires if the mean mileage improvement is greater than 2 mpg. State the appropriate null and alternate hypotheses, and find the P-value, for a hypothesis test that is designed to form the basis for the decision whether to switch.