Suppose that an experimenter wishes to construct a 99% confidence interval with a length no larger than L= 5.0 mm for the difference between the mean thicknesses of two types of plastic sheets. Previous experience suggests that the thicknesses of sheets of type A have a standard deviation of no more than sA= 4.0 mm and that the thicknesses of sheets of type B have a standard deviation of no more than sB= 2.0 mm. determine the appropriate sample sizes n and m, required to obtain a confidence interval of this length