The diameter of steel rods manufactured on 2 different extrusion machines is being investigated. Two random samples of sizes n1 = 15 and n2 = 17 are chosen, and the sample means and sample variances are x1 = 8.73, s12 = 0.35, x2 = 8.68, and s22 = 0.40, respectively. Suppose that s12 = s22 and that the data are drawn from normal distribution (zero points for not showing your calculations).
a. Is there evidence to support claim that the two machines produce rods with different mean diameters? Employ a P-value in arriving at your conclusion.
b. Develop a 95% confidence interval for the difference in mean rod diameter. Interpret this interval with respect to your answer in part a.