The resilient moduli of n = 10 samples of a clay mixture of type A are measured and the sample mean is  = 19.50. In addition, the resilient moduli of m = 12 samples of a clay mixture of type B are measured and the sample mean is  = 18.64. Suppose that the experimenter wishes to use values σA = σB = 1.0 for the standard deviations of the resilient modulus of the two types of clay.
(a) What is the exact two-sided p-value for the null hypothesis that the two types of clay have equal average values of resilient modulus?
(b) Construct 90%, 95%, and 99% two-sided confidence intervals for the difference between the average resilient modulus of the two types of clay.