Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octane number for formulation 1 is = 1.5, and for formulation 2 it is 2/2 = 1.2. Two random samples of size n1 = 15 and n2 = 20 are tested, and the mean road octane numbers observed are = 89.6 and = 92.5. Assume normality.
(a) Construct a 95% two-sided confidence interval on the difference in mean road octane number.
(b) If formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect it. Formulate and test an appropriate hypothesis, using
a =c) What is the P-value for the test you conducted in part (b)?