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/cm^{2}

for the modified mortar (*m* = 42) and *y* = 16.84

kgf/cm^{2} for the unmodified mortar (*n* = 30). Let

*Î¼*_{1} and *Î¼*_{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 *Ïƒ*_{1} = 1.6 and

*Ïƒ*_{2} = 1.3, test *H*_{0}:

*Î¼*_{1} âˆ’ *Î¼*_{2} = 0 versus

*H*_{a}: *Î¼*_{1} âˆ’

*Î¼*_{2} > 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 *Î¼*_{1} âˆ’ *Î¼*_{2} = 1.

(Round your answer to four decimal places.)

(c) Suppose the investigator decided to use a level 0.05 test and

wished *Î²* = 0.10 when *Î¼*_{1} âˆ’

*Î¼*_{2} = 1. If *m* = 42, what value of

*n* is necessary? (Round your answer up to the nearest whole

number.)