The average gasoline price of one of the major oil companies has been $3.00 per gallon. Because of cost reductions 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 $2.90. Assume that the standard deviation of the population is $0.12.

a. State the null and alternative hypothesis

b. What is the p-value associated with the above sample results? Using the p-value, test their claim Provide interpretation of the p-value

c. What is the beta if the population mean turns out to be $3.00