# 14 Two different formulas of an oxygenated motor fuel are being tested to study their road octane numbers.

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Question 14Two different formulas of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octane number for formula 1 is Of = 1.5, and for formula 2 it is Oz = 1.2.Two random samples of size /1 = 13 and 2 – 20 are tested, and the mean octane numbers observed are X1 -89.0 fluid ounces and X2 = 92.1 fluid ounces. Assume normality.(a) Test the hypotheses #o: H1 = #2 versus #1: #1 &lt; #2 using @ – 0.05. Round your answer to three decimal places (e.g. 98.765).Zo(b) Calculate a 95% two-sided confidence interval on the mean difference road octane number, *1 2. Round your answer to three decimal places (e.g. 98.765).SH1 – #25(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?m1 = 02 =Round your answer up to the nearest integer.Statistical Tables and Charts