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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 ơf = 1.5, and for formulation, 2 it is ož = 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 x, = 92.5. Assume normality. (a) If formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect 10-7. %3D it. Formulate and test an appropriate hypothesis using ɑ = 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 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?

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 ož = 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 x, = 92.5. Assume normality. (a) If formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect 10-7. %3D it. Formulate and test an appropriate hypothesis using ɑ = 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 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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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 o = 1.5, and for formulation, 2 it is o = 1.2. Two random samples of size n = 15 and n = 20 are tested, and the mean road octane num- bers observed are X¡ = 89.6 and x, = 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 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?
Transcribed Image Text: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 o = 1.5, and for formulation, 2 it is o = 1.2. Two random samples of size n = 15 and n = 20 are tested, and the mean road octane num- bers observed are X¡ = 89.6 and x, = 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 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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