Please help me with B **Flexural Strength Data for Concrete Beams and Cylinders****Concrete Beams:**The flexural strength (MPa) data for concrete beams is as follows:- 5.1, 7.2, 7.3, 6.3, 8.1, 6.8, 7.0, 7.2, 6.5, 7.0, 6.3, 7.9, 9.0- 8.4, 8.7, 7.8, 9.7, 7.4, 7.7, 8.0- 7.7, 8.0, 11.6, 11.3, 11.8, 10.7**Cylinders:**The accompanying strength observations for cylinders (MPa) are:- 6.5, 5.8, 7.8, 7.1, 7.2, 9.2, 6.6, 8.3, 7.0, 8.5- 7.2, 8.1, 7.4, 8.5, 8.9, 9.1- 14.1, 12.6, 11.4**Statistical Analysis of Flexural Strength:**Before collecting data, denote the beam strengths by \( X_1, \ldots, X_m \) and the cylinder strengths by \( Y_1, \ldots, Y_n \). Assume the \( X_i \)'s form a random sample from a distribution with mean \( \mu_1 \) and standard deviation \( \sigma_1 \), and the \( Y_j \)'s form a random sample from another distribution with mean \( \mu_2 \) and standard deviation \( \sigma_2 \).**Part (a): Expected Value Calculation**- Use rules of expected value to show that \( \overline{X} - \overline{Y} \) is an unbiased estimator of \( \mu_1 - \mu_2 \).The correct formula is:\[E(\overline{X} - \overline{Y}) = E(\overline{X}) - E(\overline{Y}) = \mu_1 - \mu_2 **Section (b): Variance and Standard Deviation of the Estimator**To obtain an expression for the variance and standard deviation (standard error) of the estimator from part (a), use the rules of variance:\[ V(\bar{X} - \bar{Y}) = V(\bar{X}) + V(\bar{Y}) = \frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2} \]**Identify the next step in this rule from the options below:**- \( \bigcirc \) \(\frac{\sigma^2_1}{n_1} - \frac{\sigma^2_2}{n_2}\) - \( \bullet \) \(\frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2}\) ✔ - \( \bigcirc \) \(\frac{\sigma_1}{n_1} + \frac{\sigma_2}{n_2}\) - \( \bigcirc \) \(\frac{\sigma_1}{n_1} - \frac{\sigma_2}{n_2}\) **Since standard deviation is the square root of variance, it follows that:**\[ \sigma_{\bar{X} - \bar{Y}} = \sqrt{V(\bar{X} - \bar{Y})} \]**Options:**- \( \bigcirc \) \(\sqrt{\frac{\sigma_1}{n_1} - \frac{\sigma_2}{n_2}}\) - \( \bullet \) \(\sqrt{\frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2}}\) ✔ - \( \bigcirc \) \(\sqrt{\frac{\sigma_1}{n_1} + \frac{\sigma_2}{n_2}}\) - \( \bigcirc \) \(\sqrt{\frac{\sigma^2_1}{n_1} - \frac{\sigma^2_2}{n_2}}\) **Compute the estimated standard error (in MPa), (Round your answer to three decimal places.)**\[ \_\_\_\_\_\_ \text{ MPa} \]**Section (c): Point Estimate

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(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) + (5 =ay² +0,² Identify the next step in this rule from the options below. OV(x-)-1_0₂² n₁ VX-1+%2² 0₁₂ ₂ OVX-1 + 2 1 7₂ O VX--1-02 10₂ Since standard deviation is the square root of variance, it follows that -7√x- V Oºx- ₂ Oox-V 01-02 n₁ 7₂ -₂ 0₂²2²0₂² +9 Oox-₁₂ 2 01+02 n₁ 0₂ Compute 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 answer three decimal places.) 4 (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