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 = 16.88 kgf/cm2 for the unmodified mortar (n = 31). Let , 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: ₁ - ₂ = 0 versus H₂: H₁-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 = P-value= 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 Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Reject Ho. The data sggests 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 3 = 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=
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 = 16.88 kgf/cm2 for the unmodified mortar (n = 31). Let , 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: ₁ - ₂ = 0 versus H₂: H₁-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 = P-value= 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 Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Reject Ho. The data sggests 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 3 = 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=
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 \(\bar{x} = 18.11 \, \text{kgf/cm}^2\) for the modified mortar \((n = 42)\) and \(\bar{y} = 16.88 \, \text{kgf/cm}^2\) for the unmodified mortar \((n = 31)\). Let \(\mu_1\) and \(\mu_2\) 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 \(\sigma_1 = 1.6\) and \(\sigma_2 = 1.3\), test \(H_0: \mu_1 - \mu_2 = 0\) versus \(H_a: \mu_1 - \mu_2 > 0\) 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.)
\[
z = \underline{\hspace{1em}}
\]
\[
P\text{-value} = \underline{\hspace{1em}}
\]
State the conclusion in the problem context.
- \( \circ \) Fail to reject \(H_0\). The data suggests that the difference in average tension bond strengths exceeds 0.
- \( \circ \) Fail to reject \(H_0\). The data does not suggest that the difference in average tension bond strengths exceeds 0.
- \( \circ \) Reject \(H_0\). The data does not suggest that the difference in average tension bond strengths exceeds 0.
- \( \circ \) Reject \(H_0\). 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 \(\mu_1 - \mu_2 = 1\). (Round your answer to four decimal places.)
\[
\underline{\hspace{1em}}
\]
**(c)** Suppose the investigator decided to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F379782e3-36e2-4b06-9a33-e2601af30423%2Ffd60ada8-04f9-49e6-b0ab-1df0d24de18d%2F9p6qfn_processed.jpeg&w=3840&q=75)
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 \(\bar{x} = 18.11 \, \text{kgf/cm}^2\) for the modified mortar \((n = 42)\) and \(\bar{y} = 16.88 \, \text{kgf/cm}^2\) for the unmodified mortar \((n = 31)\). Let \(\mu_1\) and \(\mu_2\) 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 \(\sigma_1 = 1.6\) and \(\sigma_2 = 1.3\), test \(H_0: \mu_1 - \mu_2 = 0\) versus \(H_a: \mu_1 - \mu_2 > 0\) 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.)
\[
z = \underline{\hspace{1em}}
\]
\[
P\text{-value} = \underline{\hspace{1em}}
\]
State the conclusion in the problem context.
- \( \circ \) Fail to reject \(H_0\). The data suggests that the difference in average tension bond strengths exceeds 0.
- \( \circ \) Fail to reject \(H_0\). The data does not suggest that the difference in average tension bond strengths exceeds 0.
- \( \circ \) Reject \(H_0\). The data does not suggest that the difference in average tension bond strengths exceeds 0.
- \( \circ \) Reject \(H_0\). 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 \(\mu_1 - \mu_2 = 1\). (Round your answer to four decimal places.)
\[
\underline{\hspace{1em}}
\]
**(c)** Suppose the investigator decided to
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