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 for the modified mortar and for the unmodified mortar . Let m1 and m2 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 s1  1.6 and s2  1.4, test H0: m1 m2  0 versus Ha: m1 m2  0 at level .01.

b. Compute the probability of a type II error for the test of part

(a) when .

c. Suppose the investigator decided to use a level .05 test and wished when . If , what value of n is necessary?

d. How would the analysis and conclusion of part

(a) change if s1 and s2 were unknown but and ?