Sintering, one of the most important techniques of materials science, is used to convert powdered material into a porous solid body. The following two measures characterize the final product:

When V_v = 100%, the product is completely solid—i.e., it contains no pores. Both V_v and S_v are estimated by a microscopic examination of polished cross sections of sintered material. The accompanying table gives the mean and standard deviation of the values of S_v (in squared centimeters per cubic centimeter) and V_v (percentage) for n = 100 specimens of sintered nickel for two different sintering times.

a. Find a 95% confidence interval for the mean change in S_v between sintering times of 10 minutes and 150 minutes. What inference would you make concerning the difference in mean sintering times?

b. Repeat part a for V_v.

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Vy = Percentage of total volume of final product that is solid Solid volume 100 Porous volume + Solid volume Sy = Solid-pore interface area per unit volume of the product