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 = 16.82 kgf/cm² for the unmodified mortar (n = 32). Let #₁ and ₂ 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 a₁ = 1.6 and 2 = 1.3, test Ho: M1 M2 = 0 versus Ha: #1 - H₂> 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 = (No Response) P-value (No Response) State the conclusion in the problem context. Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. O Reject Ho. The 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. O Fail o reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. (b) Compute the probability of a type II error for the test of part (a) when #₁ #2 = 1. (Round your answer to four decimal places.) 0.1560 X (c) Suppose the investigator decided to use a level 0.05 test and wished ß = 0.10 when #₁ - 2 = 1. If m = 42, what value of n is necessary? (Round your answer up to the nearest whole number.) n = 107 X (d) How would the analysis and conclusion f part (a) change if ₁ and 2 were unknown but s₁ = 1.6 and s₂ = 1.3? ● Since n = 32 is a large sample, it would be more appropriate to use the t procedure. The appropriate conclusion would follow.
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 = 16.82 kgf/cm² for the unmodified mortar (n = 32). Let #₁ and ₂ 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 a₁ = 1.6 and 2 = 1.3, test Ho: M1 M2 = 0 versus Ha: #1 - H₂> 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 = (No Response) P-value (No Response) State the conclusion in the problem context. Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. O Reject Ho. The 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. O Fail o reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. (b) Compute the probability of a type II error for the test of part (a) when #₁ #2 = 1. (Round your answer to four decimal places.) 0.1560 X (c) Suppose the investigator decided to use a level 0.05 test and wished ß = 0.10 when #₁ - 2 = 1. If m = 42, what value of n is necessary? (Round your answer up to the nearest whole number.) n = 107 X (d) How would the analysis and conclusion f part (a) change if ₁ and 2 were unknown but s₁ = 1.6 and s₂ = 1.3? ● Since n = 32 is a large sample, it would be more appropriate to use the t procedure. The appropriate conclusion would follow.
A First Course in Probability (10th Edition)
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Transcribed Image Text: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 = 16.82 kgf/cm² for the unmodified mortar (n = 32). Let μ₁ and ₂ 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: M₁ M2 = 0 versus Ha: M1 M₂ > 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 = (No Response)
P-value = (No Response)
State the conclusion in the problem context.
O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0.
O Reject Ho. The 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.
Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 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.)
0.1560 X
(c) Suppose the investigator decided to use a level 0.05 test and wished ß = 0.10 when M₁ M₂ = 1. If m = 42, what value of n is necessary? (Round your answer up to the nearest whole number.)
n = 107 X
(d) How would the analysis and conclusion of part (a) change if 0₁ and 2 were unknown but s₁ = 1.6 and s₂ = 1.3?
● 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 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 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 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 of Tables to answer this question.
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