### Consideration of Data on Flexural Strength for Concrete Beams#### Data OverviewThe data presents the flexural strength (in MPa) for concrete beams of a particular type.**Beam Strength Observations (MPa):**- Values: 5.5, 7.2, 7.3, 6.3, 6.8, 7.0, 7.1, 6.6, 6.5, 7.3, 7.9, 9.0- Sample Size: n = 12**Cylinder Strength Observations (MPa):**- Values: 6.5, 5.8, 7.8, 7.1, 7.2, 6.6, 8.3, 7.0, 8.4, 7.1, 8.1, 7.4, 8.5, 8.9, 9.7, 9.4, 11.2, 12.6, 11.6, 11.5- Sample Size: n = 20#### Analysis Steps**a) Unbiased Estimator Calculation**The goal is to verify and use an unbiased estimator for the difference in means (\( \mu_1 - \mu_2 \)).- Chosen equation for unbiased estimator: \[ E(\overline{X} - \overline{Y}) = E(\overline{X}) - E(\overline{Y}) = \mu_1 - \mu_2 \]- Calculated estimate for the data: \(-0.443 \, \text{MPa}\)**b) Variance and Standard Deviation**Derive an expression for the variance and standard deviation (standard error) of the estimator.- Variance formula: \[ V(\overline{X} - \overline{Y}) = V(\overline{X}) + V(\overline{Y}) = \frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} \]- Standard error: \[ \sigma_{\overline{X} - \overline{Y}} = \sqrt{V(\overline{X} - \over

Name: ### Consideration of Data on Flexural Strength for Concrete Beams####
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Description: ### Consideration of Data on Flexural Strength for Concrete Beams#### Data OverviewThe data presents the flexural strength (in MPa) for concrete beams of a particular type.**Beam Strength Observations (MPa):**- Values: 5.5, 7.2, 7.3, 6.3, 6.8, 7.0,

x y 5.5 6.5 7.2 5.8 7.3 7.8 6.3 7.1 8.1 7.2 6.8 9.2 7.0 6.6 7.1 8.3 6.8 7.0 6.5…

Math

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onsider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.5 7.2 7.3 6.3 8.1 6.8 7.0 7.1 6.8 6.5 7.0 6.3 7.9 9.0 8.9 8.7 7.8 9.7 7.4 7.7 9.7 7.9 7.7 11.6 11.3 11.8 10.7 he data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.4 7.1 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.5 rior to obtaining data, denote the beam strengths by X,. ....,X, and the cylinder strengths by Y,...., Y. Suppose that the X's constitute a random sample from a distribution with mean u, and standard ample (independent of the X;s) from another distribution with mean u, and standard deviation o. (a) Use rules of expected value to show that X – Y is an unbiased estimator of #, - H2. O EX - - EX) – E(Ý) nm O EX – 7) = (EX) – E()* = "1 = #2 O EX – ) = nm( EX) - E(Y) = ", - H2 • EX – ) = EX) – E(Ÿ) = #1 = H2 O EX – ) = VE(X) – E(Y) = H1 – H2 Calculate the estimate for the given data. (Round your answer to three decimal places.) -0.443 MPa (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). vũ - ) = VX) + V)

onsider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.5 7.2 7.3 6.3 8.1 6.8 7.0 7.1 6.8 6.5 7.0 6.3 7.9 9.0 8.9 8.7 7.8 9.7 7.4 7.7 9.7 7.9 7.7 11.6 11.3 11.8 10.7 he data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.4 7.1 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.5 rior to obtaining data, denote the beam strengths by X,. ....,X, and the cylinder strengths by Y,...., Y. Suppose that the X's constitute a random sample from a distribution with mean u, and standard ample (independent of the X;s) from another distribution with mean u, and standard deviation o. (a) Use rules of expected value to show that X – Y is an unbiased estimator of #, - H2. O EX - - EX) – E(Ý) nm O EX – 7) = (EX) – E()* = "1 = #2 O EX – ) = nm( EX) - E(Y) = ", - H2 • EX – ) = EX) – E(Ÿ) = #1 = H2 O EX – ) = VE(X) – E(Y) = H1 – H2 Calculate the estimate for the given data. (Round your answer to three decimal places.) -0.443 MPa (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). vũ - ) = VX) + V)

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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