6. An experiment to compare the tension bond strength of polymer latex modi ed mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodi ed mortar resulted in x  18.12 kgf/cm2 for the modi ed x  .64 y  36,800 x  42,500 y  40,400 x  42,500 X  Y mortar (m  40) and kgf/cm2 for the unmodi ed mortar (n  32). Let m1 and m2 be the true average tension bond strengths for the modi ed and unmodi ed 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 m1  m2  1.

c. Suppose the investigator decided to use a level

.05 test and wished b  .10 when m1  m2  1.

If m  40, what value of n is necessary?

d. How would the analysis and conclusion of part

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

1.6 and s2  1.4?