Ul an ox re being tested to study their road octane numbers. The ce of road octane number for formulation 1 is o = 1.5, r formulation, 2 it is o = 1.2. Two random samples of size 5 and n2 = 20 are tested, and the mean road octane num- bserved are x = 89.6 and x, = 92.5. Assume normality. formulation 2 produces a higher road octane number an formulation 1. the manufacturer would like to detect %3D

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Develop the exercise in minitab

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 of = 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 of = 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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