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 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 d₂ 1.6 and ₂1.3. test Hol H₂H₂O versus H₂H₂-₂0 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. Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 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 test of part (a) when H₂-H₂1. (Round your answer to four decimal places.) (c) Suppose the investigator decided to use a level 0.05 test and wished = 0.10 when H₂-H₂1. If m= 42, what value of n is necessary? (Round your answer up to the nearest whole number.)
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 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 d₂ 1.6 and ₂1.3. test Hol H₂H₂O versus H₂H₂-₂0 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. Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 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 test of part (a) when H₂-H₂1. (Round your answer to four decimal places.) (c) Suppose the investigator decided to use a level 0.05 test and wished = 0.10 when H₂-H₂1. If m= 42, what value of n is necessary? (Round your answer up to the nearest whole number.)
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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 = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 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 0₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: 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 =
P-value =
State the conclusion in the problem context.
O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0.
O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0.
O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 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 test of part (a) when ₁ - ₂ = 1. (Round your answer to four decimal places.)
(c) Suppose the investigator decided to use a level 0.05 test and wished = 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 =
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