An experiment to compare the tension bond strength of polymer latex modified mor

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 = 18.67 kgf /cm2 for the modified mortar (m = 40) and ¯y = 17.01 kgf /cm2 for the unmodified mortar (n = 32). 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 1 =1.6 and 2 =1.4, test H0 : µ1 µ2 = 0 vs. Ha : µ1 µ2 > 0 and obtain a p-value.

(b) Take = .05. Compute the power of the test of part (a) when µ1 µ2 = 1. (Note: The observed data play no role in this problem.)

(c) How would the analysis and conclusion of part (a) change if 1 and 2 were unknown but s1 =1.6 and s2 =1.4?

Explanation / Answer

Hypothesis:

H0 : µ1 µ2 = 0 vs. Ha : µ1 µ2 > 0

Test statistic:

x1 = 18.67 , x2 = 17.01 , n1 = 40 , n2 = 32 , s1 = 1.6 ,s2 = 1.4

SE = sqrt[(s1^2/n1) + (s2^2/n2)]
SE = sqrt[(1.6^2/40) + (1.462/32]
= sqrt(3.33 + 9) = sqrt(12.33)
= 0.354

t = [ (x1 - x2) - d ] / SE
= [ (18.67 - 17.01) - 0 ] / 0.354
= 4.69
Now, we need to find p value using t = 4.69 , df = 70

P value = .00001.
As p value is less than 0.05
So, we reject the null hypothesis.

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