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 = 8.73, s2/1 = 0.35,x = 8.68, and s2/2 = 0.40, respectively. Assume that σ2/1= σ 2/2 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 = 0.05 in arriving at this conclusion.
(b) Find the P-value for the t-statistic you calculated in part (a).
(c) Construct a 95% confidence interval for the difference in mean rod diameter. Interpret this interval.