3. [-/7 Points] DETAILS DEVORESTAT9 6.1.004.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type 5.7 7.2 7.3 6.3 8.1 6.8 7.0 7.4 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 8.0 7.7 11.6 11.3 11.8 10.7 The data below giv low give accompanying strength observations for cylinders. 6.3 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.5 7.6 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.0 Prior to obtaining da eam strengths by X1, w. Xm and the cylinder strengths by Y1. .., Yo. Su d standard deviation #2- (a) Use rules of expect value to show that X - Y is an unbiased estimator of , - #2- O E(X - n) = nm(E(x) - E(n) = #1 - #2 D EX - n = VECX - E() = #1 - H2 DE(X - 1 = =(X) - E() = 1 - M2 DE(X - " - =() - E( = #1 - H2 Calculate the estimate (in MPa) 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 - v) = v(x) + vin = 02 + 02 Identify the next step in this rule from the options below. Dux - n = 1+ 2 Ov(x - n - 1 - 2 Onx - n - 1+ 2 2 onx - n - 1 _ 2 2 Since standard deviation is the square root of variance, It follows that 1+2 Compute the estimated standard error (in MPa). (Round your a imal places.) MPa c) Calculate a point estimate of the ratio , / 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 (in MPa?) of the variance of the difference X - Y between beam strength and cylinder strength. (Round your answer to two decimal places.) MPa2 Need Help? Read " Which Matter