ONLY THE LAST ONE Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.5.97.27.36.38.16.87.07.56.86.57.06.37.99.08.48.77.89.77.47.79.78.27.711.611.311.810.7The data below give accompanying strength observations for cylinders.6.55.87.87.17.29.26.68.37.08.37.88.17.48.58.99.89.714.112.611.9Prior 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.(a) Use rules of expected value to show that X − Y is an unbiased estimator of μ1 − μ2.E(X − Y) = E(X) − E(Y) = μ1 − μ2E(X − Y) = E(X) − E(Y) 2 = μ1 − μ2 E(X − Y) = nm E(X) − E(Y) = μ1 − μ2E(X − Y) = E(X) − E(Y)nm = μ1 − μ2E(X − Y) = E(X) − E(Y) = μ1 − μ2Calculate the estimate for the given data. (Round your answer to three decimal places.) MPa(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) =σX2 + σY2 =σ21 n1 + σ22n2 σX − Y= V(X − Y) = σ21 n1 + σ22n2 Compute the estimated standard error. (Round your answer to three decimal places.) MPa(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 randomly selected. Calculate a point estimate of the variance of the difference X − Y between beam strength and cylinder strength. (Round your answer to two decimal places.) MPa2

d) Point estimate of the variance of the difference X − Y σx-y2=V(X)n1+V(Y)n2 Consider, V(X)=2.7564,…

Answered: ONLY THE LAST ONE Consider the…

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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ONLY THE LAST ONE

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	7.5	6.8	6.5	7.0	6.3	7.9	9.0
8.4	8.7	7.8	9.7	7.4	7.7	9.7	8.2	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	8.3
7.8	8.1	7.4	8.5	8.9	9.8	9.7	14.1	12.6	11.9

Prior to obtaining data, denote the beam strengths by X₁, . . . , X_m and the cylinder strengths by Y₁, . . . , Y_n. Suppose that the X_i's constitute a random sample from a distribution with mean μ₁ and standard deviation σ₁ and that the Y_i's form a random sample (independent of the X_i's) from another distribution with mean μ₂ and standard deviation σ₂.

(a) Use rules of expected value to show that

X − Y

is an unbiased estimator of μ₁ − μ₂.

E(X − Y) = E(X) − E(Y) = μ₁ − μ₂

E(X − Y) =

E(X) − E(Y)

	2

= μ₁ − μ₂

E(X − Y) = nm

E(X) − E(Y)

= μ₁ − μ₂

E(X − Y) =

E(X) − E(Y)

= μ₁ − μ₂

E(X − Y) =

E(X) − E(Y)

= μ₁ − μ₂

Calculate the estimate for the given data. (Round your answer to three decimal places.)
MPa

(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)

σ_X² + σ_Y²

σ21

n₁

σ₂²

σ_X − Y

V(X − Y)

σ21

n₁

σ₂²

Compute the estimated standard error. (Round your answer to three decimal places.)
MPa

(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 randomly selected. Calculate a point estimate of the variance of the difference X − Y between beam strength and cylinder strength. (Round your answer to two decimal places.)
MPa²

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