The average gasoline price of one of the major oil companies has been $2.20 per gallon. Because of cost reduction measures, it is believed that there has been a significant reduction in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.14. Assume that the standard deviation of the population is $0.12.

a. Conduct a hypothesis test to ascertain the validity of the company's claim. Use a 0.03 level of significance.

b. Construct a 95% confidence interval for the average price of gasoline.