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 emulsion5 have been added during mixing) to that of unmodified mortar resulted in x-18.15 ky cm2 or the modified mortar m-42 and y 16.86 kg cm2 ut the unmudified rnorlar n-30 Let 1 and ? be the true average tension bond strengths or the modified and unmodified mortars, respectlvely. Assume that the bond strength distributions are both normal. (a) Assuming that 1-1.6 and 2-1.3, test Ho: 1-H2-0 versus Ha: 1-2 > U 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.) p-value- State the conclusion in the problem context. Fail to reject Ho. The data suggests that the difference in average tension bond strength5 exceeds Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0 Reject Ho- lhe data does not suggest that the difference in average tension bond strengths exceeds 0 Reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. (b Compute the probability of a type II error for the lest of part a when -2 1. Rund your answer tu ur dec mal places. c suppose the investigator decided to use a level o os test and wished 0.10 when 1-12-1. I m 42, what value of n is necessary? Round your answer up to the nearest whole number. (d) How would the analysis and conclusion of part (a) change if 1 and 2 were unknown but s-L5 and s2-1.32 since n-30 is a large sample, it would be more appropriate to use the t procedure. The appropriate conclusion would follow. 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. 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 not a large sample, it still be appropriate to use the large sample test. The analysis and conclusions would stay the same. You may need to use the appropriate table in the Appendix ot Tables to answer this question.

Explanation / Answer

p-value = 0.0001

As p-value is less than significance level of 0.01, we reject the null hypothesis (Option D)

Part B

x1(bar) 18.15 x2(bar) 16.86 s1 1.60 s2 1.30 n1 42 n2 30 SE = sqrt[ (s12/n1) + (s22/n2) ] (s12/n1) 0.0610 (s22/n2) 0.0563 SE 0.3425

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