On August 8,2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a random sample of n = 10 gas stations in the state of Illinois were recorded at that time. The mean price for the sampled gas stations was $3.975, with standard deviation $0.2266.
a) Is it reasonable to use the t-distribution to perform a test about the average gas price in Illinois (on August 8, 2012)?
b) Test, at the 5% level, if there is evidence that the average gas price in Illinois (on August 8, 2012) was significiantly higher than the national average. Include all of the details of the test.
c) Construct a 95% confidence interval for the mean gas price in Illinois ( on August 8,2012). Round your margin of error to three decimal places.