Question

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 x = 18.12 kgf/cm2 for the modified mortar (m = 40) and y = 16.87 kgf/cm2 for the unmodified mortar (n = 32). Let ?1 and ?2 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 ?1 = 1.6 and ?1 = 1.4, test H0: ?1 - ?2 =0 versus Ha: ?1 - ?2 > 1 at level 0.01.

b) Compute the probability of a type II error for the test of part (a) when Ha: ?1 − ?2 =1.

c) Suppose the investigator decided to use a level 0.05 test and wished ? =0.10 when Ha: ?1 - ?2 = 1 If m = 40, what value of n is necessary?

d) How would the analysis and conclusion of part (a) change if ?1 and ?2 were unknown but ?1 = 1.6 and ?1 =1.4?

Answer 1