(a) Assuming that σ₁ = 1.6 and ₂ = 1.3, test Ho: M₁ M₂ = 0 versus H₂ : ₁ - ₂ > 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 = 4.74 x P-value = State the conclusion in the problem context. 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. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. O Fail to 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 μg - H₂ 1. (Round your answer to four decimal places.) (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=

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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 = 18.18 kgf/cm² for the modified mortar (m = 42) and y = 16.85 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 ₂ = 1.3, test Ho: M₁ M₂ = 0 versus Ha: M₁ M₂ > 0 at level 0.01.
1
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 = 4.74
X
P-value =
State the conclusion in the problem context.
Ⓒ 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.
O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0.
O Fail to 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 μ₁ - M₂ = 1. (Round your answer to four decimal places.)
(c) Suppose the investigator decided to use a level 0.05 test and wished ß = 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 =
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 = 18.18 kgf/cm² for the modified mortar (m = 42) and y = 16.85 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 ₂ = 1.3, test Ho: M₁ M₂ = 0 versus Ha: M₁ M₂ > 0 at level 0.01. 1 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 = 4.74 X P-value = State the conclusion in the problem context. Ⓒ 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. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. O Fail to 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 μ₁ - M₂ = 1. (Round your answer to four decimal places.) (c) Suppose the investigator decided to use a level 0.05 test and wished ß = 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 =
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