Home / Questions / Consider the accompanying data on flexural strength MPa for concrete beams of a certain type
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
5.0 | 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 |
8.1 | 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.
6.7 | 5.8 | 7.8 | 7.1 | 7.2 | 9.2 | 6.6 | 8.3 | 7.0 | 8.0 |
7.8 | 8.1 | 7.4 | 8.5 | 8.9 | 9.8 | 9.7 | 14.1 | 12.6 | 11.6 |
Prior to obtaining data, denote the beam strengths by X_{1}, . . . , X_{m} and the cylinder strengths by Y_{1}, . . . , Y_{n}. Suppose that the X_{i}'s constitute a random sample from a distribution with mean Î¼_{1} and standard deviation Ïƒ_{1} and that the Y_{i}'s form a random sample (independent of the X_{i}'s) from another distribution with mean Î¼_{2} and standard deviation Ïƒ_{2}.
(a) Use rules of expected value to show that
X âˆ’ Y
is an unbiased estimator of Î¼_{1} âˆ’ Î¼_{2}.E(X âˆ’ Y) =
Answer: E(X âˆ’ Y) = E(X) âˆ’ E(Y) = Î¼_{1} âˆ’ Î¼_{2 **THIS IS CORRECT**}
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).
Compute the estimated standard error. (Round your answer to three decimal places.)
_____________________ MPa
(c) Calculate a point estimate of the ratio Ïƒ_{1}/Ïƒ_{2} 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 âˆ’ Y between beam strength and cylinder strength. (Round your answer to two decimal places.)
_________________MPa^{2}
Apr 25 2020 View more View Less
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