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 σ1 2 = 1.5, and for formulation, 2 it is σ2 2 = 1.2 . Two random samples of size n1 = 15 and n2 = 20 are tested, and the mean road octane numbers observed are x̅1 = 89.6 and x̅2 = 92.5. Assume normality. (a) 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 α = 0.05.

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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 σ1

2 = 1.5, and for

formulation, 2 it is σ2

2 = 1.2 . Two random samples of size n1 = 15 and n2 = 20 are tested, and
the mean road octane numbers observed are x̅1 = 89.6 and x̅2 = 92.5. Assume normality.
(a) 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 α =
0.05.

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