10-7. + 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 ơf = 1.5, and for formulation, 2 it is o = 1.2. Two random samples of size n¡ = 15 and n2 = 20 are tested, and the mean road octane num- bers observed are x = 89.6 and X2 = 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 a = 0.05. What is the P-value? (b) Explain how the question in part (a) could be answered with a 95% confidence interval on the difference in mean %3D %3D %3D road octane number. (c) What sample size would be required in each popula- tion if you wanted to be 95% confident that the error in estimating the difference in mean road octane number is less than 1?

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