An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in  = 18.12 kgf/cm2 for the modified mortar (m = 40) and = 16.87 kgf/cm2 for the unmodified mortar (n = 32). Let µ1 and µ2 be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.

a. Assuming that σ1 = 1.6 and σ2 = 1.4, test H0: µ1 - µ2 = 0 versus Ha: µ1- µ2 > 0 at level .01.

b. Compute the probability of a type II error for the test of part (a) when µ1 - µ2 = 1.

c. Suppose the investigator decided to use a level .05 test and wished β 5 .10 when µ1 - µ2 = 1. If m = 40, what value of n is necessary?

d. How would the analysis and conclusion of part (a) change if σ1 and σ2 were unknown but σ1 = 1.6 and σ2 = 1.4?