(b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a).V(X – ) = V(X) + V(Y)= ox? + oy?%D+niox - Y = V V(X )02?+n1Compute the estimated standard error. (Round your answer to three decimal places.)MPа(c) Calculate a point estimate of the ratio 01/02 of the two standard deviations. (Round your answer to three decimal places.)(d) Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate of the variance of the difference X – Y between beam strength and cylinder strength. (Roundyour answer to two decimal places.)MPa? Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.86.57.06.37.9 9.08.8 8.7 7.8 9.7 7.4 7.7 9.7 8.1 7.7 11.6 11.3 11.8 10.7The data below give accompanying strength observations for cylinders.6.7 5.8 7.8 7.1 7.2 9.2 6.68.37.08.87.9 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.7Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . ., Yn. Suppose that the X;'s constitute a random sample from a distribution with mean u1 andstandard deviation o1 and that the Y;'s form a random sample (independent of the X;'s) from another distribution with mean µz and standard deviation o2.(a) Use rules of expected value to show that X - Y is an unbiased estimator of u1 - µ2.E(X - Y)E(X) – E(Y)= µi42nmE(X – Y) = V E(X) – E(Y) = µ1M2E(X – Y)E(X) – E(Y) = H1 – H22O E(X - ) = (EX) – E()= µ1 - µ2O E(X – ) = nm E(X) – E(Y)= H1 - H2Calculate the estimate for the given data. (Round your answer to three decimal places.)MPa

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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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Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.6 8.9 9.7 6.3 11.3 6.3 7.9 6.5 7.0 9.0 9.7 7.3 11.6 7.7 7.4 7.2 7.8 7.0 7.3 8.2 8.7 6.8 11.8 6.8 7.7 10.7 8.1 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Σxi = 220.3.] (Round your answer to three decimal places.) (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. (c) Calculate a point estimate of the population standard deviation ?. [Hint: Σxi2 = 1871.39.] (Round your answer to three decimal places.) (d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 8.3 7.4 7.0 6.8 7.8 9.7 5.0 6.3 6.8 9.0 7.7 7.3 7.4 11.8 6.3 7.7 11.6 7.2 11.3 9.7 10.7 7.0 7.9 8.7 7.9 8.1 6.5 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Σxi = 218.9.] (Round your answer to three decimal places.) MPa(b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPa(c) Calculate a point estimate of the population standard deviation ?. [Hint: Σxi2 = 1851.35.] (Round your answer to three decimal places.) MPa(d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)(e) Calculate a point estimate of the population coefficient of variation ?/?. (Round…
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.3 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 9.0 8.7 7.8 9.7 7.4 7.7 9.7 7.9 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.8 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 9.0 7.6 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.8 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean ?1 and standard deviation ?1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean ?2 and standard deviation ?2. (a) Calculate the estimate for the given data. (Round your answer to three decimal places.) (b) Use rules of variance to obtain an expression for the variance and standard deviation (standard error) of the estimator in part (a). V(X − Y) = V(X) + V(Y) =…
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 6.8 6.5 8.1 7.0 7.0 11.8 6.8 8.6 10.7 7.7 7.2 7.9 7.9 7.3 5.0 11.3 11.6 7.4 9.7 9.0 9.7 7.8 7.7 7.1 6.3 6.3 8.7
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 6.8 6.5 8.1 7.0 7.0 11.8 6.8 8.6 10.7 7.7 7.2 7.9 7.9 7.3 5.0 11.3 11.6 7.4 9.7 9.0 9.7 7.8 7.7 7.1 6.3 6.3 8.7 Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Ex, = 218.9.] (Round your ansver to three decimal places.) MPa State which estimator you used. Os/x Os J Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPa State which estimator you used. Os Calculate a point estimate of the population standard deviation o. [Hint: Ex = 1852.07.] (Round your answer to three decimal places.) MPa Interpret this point estimate. O This estimate describes the bias of the data. O This estimate describes the linearity of the data. O This estimate describes the center of the data. O This estimate describes the spread of the data.
Consider 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 7.2 6.8 6.5 7.0 6.3 7.9 9.0 8.7 8.7 7.8 9.7 7.4 7.7 9.7 8.0 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.6 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.4 7.3 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.3 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2. Compute the estimated standard error. (Round your answer to three decimal places.) (c) Calculate a point estimate of the ratio σ1/σ2 of the two standard deviations. (Round your answer to three decimal places.) (d) Suppose a single beam and a single cylinder are…
Consider 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 The 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 Prior to obtaining data, denote the beam strengths by X,, . Xm and the cylinder strengths by Y,, . Y. Suppose that the X,'s constitute a random sample from a distribution with mean u, and standard deviation o, and that the Y's form a random sample (independent of the X's) from another distribution with mean H2 and standard deviation (a) Use rules of expected value to show that X – Y is an unbiased estimator of µ, - µ. E(X – Y) E(X) – E(Y) = H1 - H2 nm E(X - Y) (E) – E(Y)* = l1 - 42 E(X - Y) = nm( E(X) – E(Yn) = H1 - H2 E(X – Y) E(X - Y) = V E(X) – E(Y) = µ1 – H2 E(X) – E(Y) = µ1 - 42 Calculate the estimate for the given data.…
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 8.7 7.2 7.7 6.5 7.8 7.0 11.8 9.7 7.9 8.1 6.3 7.6 7.8 6.0 11.6 7.0 10.7 7.3 6.8 9.0 6.8 7.7 9.7 6.3 8.6 7.4 11.3 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Ex; = 220.3.] (Round your answer to three decimal places.) MPа State which estimator you used. O s/x (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. MPа State which estimator you used. O s/X (c) Calculate a point estimate of the population standard deviation o. [Hint: Ex;² = 1868.85.] (Round your answer to three decimal places.) MPа Interpret this point estimate. This estimate describes the spread of the data. This estimate describes the bias of the data. This estimate describes the center of the data. This estimate describes the linearity of the data.
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.8 8.7 7.8 9.7 7.4 7.7 9.7 8.1 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.7 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.8 7.9 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.7 Prior 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 deviation o, and that the Y's form a random sample (independent of the X's) from another distribution with mean 42 and standard deviation a Use rules of expected value to show that X - Y is an unbiased estimator of a, - H. O EX - = E - ED. ZH - Ii = O EX -) = VEX) – E(Y) = H, - 42 O EX -) = EX) - EY) = H - 42 O EX - ) = (EX) - En) - H - H2 O EX -) = nm EX) - EM) = 4. - H2 Calculate the estimate for the given data. (Round your answer to…
Consider 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 7.0 6.8 6.5 7.0 6.3 7.9 9.0 8.6 8.7 7.8 9.7| 7.4 7.7 9.7 8.0 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.3 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.7 7.4 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.6 ., Xm and the cylinder strengths by Y,, .., Yo. Suppose that the X's constitute a random sample from a distribution with mean u, Prior to obtaining data, denote the beam strengths by X,, and standard deviation o, and that the Y,'s form a random sample (independent of the X's) from another distribution with mean µ, and standard deviation o,. (a) Use rules of expected value to show that X – Y is an unbiased estimator of µ, - Hg. EX – ) = (E(X) - EC) = H1 - 42 O E(X – ) = V E(X) - E(Y) = H1 - H2 E(X) – E(Y) - O E(X – ): = H1 - H2 nm O E(X – Y) = nm E(X) – E(Y) = H1 - H2 O E(X – Y) = E(X) – E(Y) = µ1 - H2 Calculate the estimate (in…
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 7.0 7.2 6.8 6.5 7.0 6.3 7.9 9.0 9.7 8.1 7.7 11.6 11.3 11.8 10.7 observations for cylinders. 5.9 7.2 7.3 6.3 8.1 6.8 8.4 8.7 7.8 9.7 7.4 7.7 The data below give accompanying strength 6.7 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.1 7.0 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.4 Prior to obtaining data, denote the beam strengths by X₁,..., Xm and the cylinder strengths by Y₁,..., Y. Suppose that the Xi's constitute a random sample from a distribution with mean ₁ and standard deviation 0₁ and that the Y's form a random sample (independent of the X;'s) from another distribution with mean ₂ and standard deviation ₂. (a) Use rules of expected value to show that X - Y is an unbiased estimator of μ₁ - μ₂. O E(X)=√E(X) - E(Y) = μ₁ - H₂ ⒸE(XY) = E(X) - E(X) = 14₁ 14₂ O E(X-= E(X) - E(X) = 11 - 12 nm E(X - Y = nm(E(X) - E()) = μ₁ − 44₂ | E(X) = (E(X) - E(M)² = Calculate the estimate for the given data. (Round your…

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