Question: 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

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)?

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