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 = 18.17 kgf/cm2
for the modified mortar (m = 42) and y = 16.84
kgf/cm2 for the unmodified mortar (n = 30). 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 = 1.3, test H0:
μ1 − μ2 = 0 versus
Ha: μ1 −
μ2 > 0 at level 0.01.
Calculate the test statistic and determine the P-value.
(Round your test statistic to two decimal places and your
P-value to four decimal places.)
(b) Compute the probability of a type II error for the test of
part (a) when μ1 − μ2 = 1.
(Round your answer to four decimal places.)
(c) Suppose the investigator decided to use a level 0.05 test and
wished β = 0.10 when μ1 −
μ2 = 1. If m = 42, what value of
n is necessary? (Round your answer up to the nearest whole
number.)
