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10-17. The diameter of steel rods manufactured on two dif- ferent extrusion machines is being investigated. Two random samples of sizes n, = 15 and n, = 17 are selected, and the sample means and sample variances are ], = 8.73, s = 0.35, X, = 8.68, and $ = 0.40. respectively. Assume that of = of, and that the data are drawn from a normal distribution. (a) Is there evidence to support the claim that the two ma- chines produce rods with different mean diameters? Use o = 0.05 in arriving at this conclusion. (b) Find the P-value for the r-statistic you calculated in part (a). (c) Construct a 95% confidence interval for the difference in mean rod diameter. Interpret this interval.RMAL DISTRIBUTIONS, VARIANCES UNKNOWN 337 (a) Find a 95% confidence interval on the difference in mean active concentrations for the two catalysts. (b) Is there any evidence to indicate that the mean active con- centrations depend on the choice of catalyst? Base your answer on the results of part (a).10-11. The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of cata- lyst used in the process. The standard deviation of active con- centration is known to be 3 grams per liter, regardless of the catalyst type. Ten observations on concentration are taken with each catalyst, and the data follow: Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2. 71.0 Catalyst 2: 66.4, 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.810-3 INFERENCE FOR THE DIFFERENCE IN MEANS OF TWO it. Formulate and test an appropriate hypothesis, using 0 = 0.05. (c) What is the P-value for the test you conducted in part (b)?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 I is of = 1.5, and for Formulation 2 it is of = 1.2. Two random samples of size m = 15 and n, = 20 are tested, and the mean road octane numbers observed are x) = 89.6 and x, = 92.5. Assume normality. (a) Construct a 95% two-sided confidence interval on the difference in mean road octane number. (b) If formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect