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 = 18.11 kgf/cm2 for the modified mortar (m = 42) and y = 16.84 kgf/cm2 for the unmodified mortar (n = 30). Let uy and My 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 01 = 1.6 and 02 = 1.3, test Ho: 41 - U2 = 0 versus Ha: 41 - 42 > 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.) z = P-value = State the conclusion in the problem context. Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds o. Reject Ho. The data suggests that the difference in average tension bond strengths exceeds o. Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds o. (b) Compute the probability of a type II error for the test of part (a) when 41 – Hl2 = 1. (Round your answer to four decimal places.) (C) Suppose the investigator decided to use a level 0.05 test and wished B = 0.10 when M1 - U2 = 1. If m = 42, what value of n is necessary? (Round your answer up to the nearest whole number.) n = (d) How would the analysis and conclusion of part (a) change if 01 and 2 were unknown but $1 = 1.6 and 52 = 1.3? Since n = 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. O Since n = 30 is not a large sample, it still be appropriate to use the large sample test. The analysis and conclusions would stay the same. Since n = 30 is not a large sample, it would no longer be appropriate to use the large sample test. A small sample t procedure should be used, and the appropriate conclusion would follow. Since n = 30 is a large sample, it would be more appropriate to use the t procedure. The appropriate conclusion would follow.

Answer 1

a)

		pop 1	pop 2
sample mean x =		18.11	16.84
std deviation σ=		1.600	1.300
sample size n=		42	30
std error σx1-x2=√(σ21/n1+σ22/n2)    =			0.342
test stat z =(x1-x2-Δo)/σx1-x2     =			3.71
p value : =			0.0001	(from excel:1*normsdist(-3.71)

b)

for 0.01 level and right tail critival Zα=			2.33
rejecf Ho if x>= Δo +Zα*σx or x>=			0.798
P(Type II error) =P(Xbar<0.798| Δ=1)=P(Z<(0.798-1)/0.342)=P(Z<-0.59)=0.2776

c)

n=31