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|  Previous AnswersDevoreStat9 9.E.006.

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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/cm² for the modified mortar (m = 42) and y = 16.85 kgf/cm²for 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 σ₁ = 1.6 and σ₂ = 1.3, test H₀: μ₁ − μ₂ = 0 versus H_a: μ₁ − μ₂ > 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 H₀. The data does not suggest that the difference in average tension bond strengths exceeds 0.Fail to reject H₀. The data does not suggest that the difference in average tension bond strengths exceeds from 0.    Reject H₀. The data suggests that the difference in average tension bond strengths exceeds 0.Fail to reject H₀. 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) when μ₁ − μ₂ = 1. (Round your answer to four decimal places.)


(c) Suppose the investigator decided to use a level 0.05 test and wished β = 0.10 when μ₁ − μ₂ = 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 σ₁ and σ₂ were unknown but s₁ = 1.6 and s₂ = 1.3?

Since n = 32 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 = 32 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 = 32 is a large sample, it would be more appropriate to use the t procedure. The appropriate conclusion would follow.Since n = 32 is not a large sample, it still be appropriate to use the large sample test. The analysis and conclusions would stay the same.

An experiment to co pare the tension bond s rength of polyr er late modified morter Portland cement mortar to which poly er latex emulsions have beer added during ixing to that o un dified mortar esulted in x Ⅲ 18.1 7 kgf/cm for the unmodified mortar n-32 Let μ and 2 be the true a era e tension bond stren ths for the modified and unmodified mortars respectively. Assume that the bond stren th distributions are both normal for the modified mortar m 42 and y·16.85 kgf/cm (a) Assuming that σ1 . 1.6 and σ2" 1.3, test HO: μ1-#2·O versus Mai μ1-#2 > O 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.) Pvalue 0010 State the conclusion in the problem context. 3083 @ Reject Н0-The data does not suggest that the difference in average tension bond strengths exceeds 0. Fail to reject Ho. The data does not supgest that the difference in average tension bond strengths exceeds from 0 O Reject Mo The data suggests that the difference in average tension bond strengths exceeds 0 @ Fail to reject mo. The data suggests that the difference in average tension bond strengths exceeds О. (b) Compute the probability of a type II error for the test of part (a) when μ1-μ2-1.(Round your answer to four dec mal places.) 4288x c) Suppose the investigator decided to use a leve, o os test and wished O 10 when μ1-เ 2·1.ท m·42 what value of n is necessary, (Round your answer up to the nearest v hole number. (d) How would the analysis and condusion of part (a) change if σ1 and σ2 were unknown but si-1.6 and S2-1.37 Since n-32 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 foillow. Since n . 32 i5 ฮ large sample· it vould no longer be appropriate to use the large 5ample test. Any other test can be used, and the condsons would stay the same. Since n- 32 is a large sample, it would be more appropriate to use the t procedure. The appropriate condusion would follow. Since n 32 is not a large sample, it still be appropriate to use the large sample test. The analysis and conclusions would stay the same.

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