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 inx=18.16kgf/cm²for the modified mortar(m=42)andy=16.88kgf/cm²for the unmodified mortar(n=30).Let₁and₂be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.

(a) Assuming that₁=1.6and₂=1.3,testH₀:₁₂= 0versusH_a:₁₂> 0at level 0.01.

Calculate the test statistic and determine theP-value. (Round your test statistic to two decimal places and yourP-value to four decimal places.)

z=P-value=

State the conclusion in the problem context.

RejectH₀. The data suggests that the difference in average tension bond strengths exceeds 0.

Fail to rejectH₀. The data does not suggest that the difference in average tension bond strengths exceeds from 0.

RejectH₀. The data does not suggest that the difference in average tension bond strengths exceeds 0.

Fail to rejectH₀. The data suggests that the difference in average tension bond strengths exceeds 0.

(b) Compute the probability of a type II error for the test of part (a) when₁₂= 1.(Round your answer to four decimal places.)

(c) Suppose the investigator decided to use a level 0.05 test and wished= 0.10when₁₂= 1.Ifm=42,what value ofnis necessary? (Round your answer up to the nearest whole number.)

n=

(d) How would the analysis and conclusion of part (a) change if₁and₂were unknown buts₁=1.6ands₂=1.3?

Sincen= 30 is not a large sample, it would no longer be appropriate to use the large sample test. A small sampletprocedure should be used, and the appropriate conclusion would follow.

Sincen= 30 is a large sample, it would no longer be appropriate to use the large sample test. Any other test can be used, and the conclusions would stay the same.

Sincen= 30 is not a large sample, it still be appropriate to use the large sample test. The analysis and conclusions would stay the same.

Sincen= 30 is a large sample, it would be more appropriate to use thetprocedure. The appropriate conclusion would follow.

You may need to use the appropriate table in theAppendix of Tablesto answer this question.