Can u help find the answer for b and explain d? (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)=(x+v= 0x² +0,²Identify the next step in this rule from the options below.OVX-5 đi t0₁VX-1+ °2²7₂ ₂OVX-1 + 21 7₂7₂OV--1-271 7₂Since standard deviation is the square root of variance, it follows that-√x-VOox-n₁7₂10₁ ²0₂ ²Oox-₁₂Oox-1201 02n₁ ₂Compute the estimated standard error (in MPa). (Round your answer to three decimal places.)MPa(c) Calculate a point estimate of the ratio ₁/₂ of the two standard deviations. (Round your answerthree decimal places.)4(d) Suppose a single beam and a single cylinder are randomly selected. Calculate a point estimate (in MPa2) of the variance of the difference X - Y between beam strength and cylinder strength. (Round your answer to two decimal places.)MPa2 Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.6.8 7.0 7.2 6.88.4 8.7 7.8 9.7 7.4 7.7 9.7 8.0 7.7 11.6The data below give accompanying strength observations for cylinders.5.1O7.27.3 6.3 8.16.5 5.8 7.8 7.1 7.2 9.2 6.6 8.37.2 8.1 7.4 8.5 8.9 9.8 9.7 14.1O E(X-Y)=√E(X) - E(X)=H₁-H₂O EX-- (EX-EM)²-1₂-1₂O E(X)=E(X) - E()=H₁-H₂nmE(X-Y)= E(X) - E(Y) = H₁ - 1₂E(X-= nm (EX) - E() -μ₁-1₂6.5***7.0 8.512.6 11.47.0 6.3 7.9Prior to obtaining data, denote the beam strengths by X₁, Xm and the cylinder strengths by Y₁, Y Suppose that the X's constitute a random sample from a distribution with mean , and standard deviationo, and that the Y's form a random sample (independent of the X's) from another distribution with mean , and standard deviation a%1(a) Use rules of expected value to show that X - Y is an unbiased estimator of #₁ - 2.11.311.8 10.79.0Calculate the estimate (in MPa) for the given data. (Round your answer to three decimal places.)-474✓MPa

It is given that X1, X2, …, Xm denotes the beam strengths with mean, μ1 and standard deviation, σ1,…

Answered: (b) Use rules of variance to obtain an…

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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Flexural strength is a measure of a material's ability to resist failure in bending. The accompanying data are on flexural strength of concrete (in MegaPascal, MPa, where 1 Pa (Pascal) = 1.45 ⨯ 10−4 psi): 5.7 7.2 7.3 6.2 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.5 11.8 10.6 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) What appears to be a representative strength value? Do the observations appear to be highly concentrated about the representative value or rather spread out? highly concentrated around the representative value spread out with a large range    (b) Does the display appear to be reasonably symmetric about a representative value, or would you describe its shape in some other way? reasonably symmetric positive skewness     negative skewness completely random distribution (c) Do there appear to be any outlying…
Flexural strength is a measure of a material's ability to resist failure in bending. The accompanying data are on flexural strength of concrete (in MegaPascal, MPa, where 1 Pa (Pascal) = 1.45 ⨯ 10−4 psi): 5.6 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 8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.2 11.8 10.5 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Answer: Stems Leaves 5 6 7 8 9 10 11 What appears to be a representative strength value?Answer:____________ MPaDo the observations appear to be highly concentrated about the representative value or rather spread out? Answer: ______highly concentrated around the representative value ______spread out with a large range     (b) Does the display appear to be reasonably symmetric about a representative value, or would you describe its shape in some other way? Answer: _____reasonably…
. Two soft drink dispensing machines should dispense 8 oz of your selection into a cup. The table below shows the data Machine 1   9.52 6.41 10.07 5.85 8.15                            Machine 2   8.01 7.99 7.95 8.03 8.02 Which is more consistent in dispensing soda base on the measures of dispersion? Show all solutions.
The population (in millions) and the violent crime rate (per 1000) were recorded for 10 metropolitan areas. The data are shown in the following table. Do these data provide evidence to reject the null hypothesis that ? = 0 in favor of ? ≠ 0 at ? = .05? (Give your answers correct to three decimal places.) Population 10 2.3 1.4 6 2.7 6 1.9 1.7 2.1 6.7 Crime Rate 12.4 6.7 7.8 7.4 8 7 8.9 9.1 8 7.7 (ii) Calculate the critical region. (smaller value) (larger value)
Refer to Exercise 6. Assume that c = 448 J/kg°C and ΔQ = 1210 J are known with negligible uncertainty. Assume the mass is m = 0.75 ± 0.01 kg. Estimate ΔT, and find the relative uncertainty in the estimate.
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. 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…
An article in the Journal of Applied Polymer Science (Vol. 56, pp. 471–476, 1995) studied the effect of the mole ratio of sebacic acid on the intrinsic viscosity of copolyesters.- The data follows: Viscosity 0.45 0.2 0.34 0.58 0.7 0.57 0.55 0.44 Mole ratio 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 (a) Construct a scatter diagram of the data.
A crayon manufacturer is comparing the effects of two kinds of yellow dye on the brittleness of crayons. Dye B is more expensive than dye A, but it is thought that it might produce a stronger crayon. Four crayons are tested with each kind of dye, and the impact strength (in joules) is measured for each. The results are as follows: Dye A: 1.0 2.0 1.2 3.0 Dye B: 3.0 3.2 2.6 3.4 a) Can you conclude that the mean strength of crayons made with dye B is greater than that of crayons made with dye A? b) Can you conclude that the mean strength of crayons made with dye B exceeds that of crayons made with dye A by more than 1 J?
The data given is shown below 40 40 43 46 44 49 51 54 46 51 47 49 49 45 45 44 45 41 49 52 51 54 50 51 41 52 53 50 46 56 42 42 40 42 49 47 51 48 46 57 48 55 49 46 57 44 49 43 44 43 51 48 48 46 49 Class width = 6 Find the following: A. Decile (5th) B. Quartile (2nd) C. Skewness D. Kurtosis
A river was contaminated with waste materials. Specimens of these materials were collected andtheir physical appearance recorded as shown in Table 3. Is there evidence of association betweencolor and texture for these waste materials based on the given hypothesis? Explain your findings.Use ? = 0.05.H0: No relationship between texture and colourH1: Relationship exist between texture and colour colour colour colour texture light medium dark fine 4 20 8 medium 5 23 12 coarse 21 23 4
SOLVE QUESTIONS D & E ONLY!!!! 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…

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