The diameter of steel rods manufactured on two different extrusion machines is being investigated. two random samples of sizes n1 = 15 and n2 = 17 are selected, and the sample means and sample variances are x = 8.73, s1^2 = 0.35, x2 = 8.68, and s2^2 = 0.40, respectively. assume that sigma1^2 = sigma2^2 and that the data are drawn from a normal distribution. (a) is there evidence to support the claim that the two machines produce rods with different mean diameters? use a p-value in arriving at this conclusion. (b) construct a 95% ci for the difference in mean rod diameter. interpret this interval.