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=15andn2=20
are tested, and the mean road octane numbers observed are
ẋ1=89.6
and
ẋ2=92.50
. 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. 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 population if you wanted to be 95% confident that the error in estimating the difference in mean road octane number is less than 1?