I need help in figuring out section (b). What have I done wrong? 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 7.5 6.86.57.06.37.9 9.08.9 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7The data below give accompanying strength observations for cylinders.6.8 5.8 7.8 7.1 7.2 9.2 6.68.37.08.77.4 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.3Prior to obtaining data, denote the beam strengths by X,,..., Xm and the cylinder strengths by Y, ..., Y. Suppose that the X's constitute a random sample from a distribution with mean u, and standard deviation o, and that the Y's form a random sample (independent of the X's) from another distribution with mean u, and standard deviation o,.(a) Use rules of expected value to show that X - Y is an unbiased estimator of u, - H.O E(X - Y) = E(X) – E(Y) = H1 - HzO E(X - ) = (E(X) – E(ñ)= H1 - H2E(X - ) = nm( EX) - E()= 41 -H2O E(X - Y) = v E(X) – E(Y) = Hy - H2O E(X – Y)E(X) – E(Y)= 41 - 42nmCalculate the estimate for the given data. (Round your answer to three decimal places.)-0.485MPa(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()= ox + oy22.9668°220n1X -7 =V V(X )2.966820Compute the estimated standard error. (Round your answer to three decimal places.)0.572V MPa(c) Calculate a point estimate of the ratio o,/0, of the two standard deviations. (Round your answer to three decimal places.)0.827(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.)7.302v MPa?

Given, x: beam strengths 5.0, 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, 8.9,…

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 7.5 6.8 6.5 7.0 6.3 7.9 9.0 8.9 8.7 7.8 9.7 7.4 7.7 9.7 7.8 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 8.7 7.4 8.1 74 8.5 8.9 9.8 9.7 14.1 12.6 11.3 rior to obtaining data, denote the beam strengths by X....X and the cylinder strengths by Yg.....Y Suppose that the Xs constitute a random sample from a distribution with mean , and standard deviation e, and that th (a) Use rules of expected value to show that X- Yis an unbiased estimator of - o e -n- VEO - En --2 O E -- - etn 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). vũ -n- vn + vn

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 7.5 6.8 6.5 7.0 6.3 7.9 9.0 8.9 8.7 7.8 9.7 7.4 7.7 9.7 7.8 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 8.7 7.4 8.1 74 8.5 8.9 9.8 9.7 14.1 12.6 11.3 rior to obtaining data, denote the beam strengths by X....X and the cylinder strengths by Yg.....Y Suppose that the Xs constitute a random sample from a distribution with mean , and standard deviation e, and that th (a) Use rules of expected value to show that X- Yis an unbiased estimator of - o e -n- VEO - En --2 O E -- - etn 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). vũ -n- vn + vn

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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…
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) =…
As a bonus assignment a former student checked if your professor gave a statisticallysignificant difference in grades between his male and female students. She based herstudy based on grades assigned in intermediate Econ courses (Econ 303, 305 and 317)and her sample included nm = 485 male students and nf = 264 female students. Theaverage grades received were xm = 84.6 and xf = 85.8 The population standad deviation were σ m = 12.0 and σ f = 11.4 8. From the same extra-credit study as in question 7 see above, this former student found that the proportion of female students in principle courses (Econ 203, 205) was ?̅? = 0.380, while the proportion of female students in intermediate courses (Econ 303, 305, 317) was ?̅? = 0.352. The principle courses sample size was np = 782, while the intermediate courses sample size was ni = 749. Test the hypothesis that female students are less in intermediate courses using a 90% confidence level and the p-value approach.
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.6 8.9 9.7 6.3 11.3 6.3 7.9 6.5 7.0 9.0 9.7 7.3 11.6 7.7 7.4 7.2 7.8 7.0 7.3 8.2 8.7 6.8 11.8 6.8 7.7 10.7 8.1 (a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. [Hint: Σxi = 220.3.] (Round your answer to three decimal places.) (b) Calculate a point estimate of the strength value that separates the weakest 50% of all such beams from the strongest 50%. (c) Calculate a point estimate of the population standard deviation ?. [Hint: Σxi2 = 1871.39.] (Round your answer to three decimal places.) (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.)
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…
In a summary report given by Ing. Pobbi on the lengths of ironrods produced by two machines, he stated that the variability ofmachine A was higher compared to that of machine B. Critiquethe report of the Engineer given data on the length of rodsproduced given as; MachineA(cm): 380 410 280 310 305 360 270 355 400 Machine B(m): 1.1 1.3 1.2 2.0 1.5 1.6 1.4 1.6 1.7
The following statement appeared on a box of Tide laundry detergent: “Individual packages of Tide may weigh slightly more or less than the marked weight due to normal variations incurred with high speed packaging machines, but each day’s production of Tide will average slightly above the marked weight.” (d) Propose procedures to collect data to test the statement.
An article reports the following values for soil heat flux of eight plots covered with coal dust. 37.9 37.8 37.9 35.1 35.5 27.5 18.3 24.1 The mean soil heat flux for plots covered only with grass is 29.0. Assuming that the heat-flux distribution is approximately normal, does the data suggest that the coal dust is effective in increasing the mean heat flux over that for grass? Test the appropriate hypotheses using ? = 0.05.State the appropriate hypotheses. H0: ? = 29Ha: ? > 29H0: ? = 29Ha: ? < 29 H0: ? = 29Ha: ? ≠ 29H0: ? ≠ 29Ha: ? = 29 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. Reject the null hypothesis. There is sufficient evidence to conclude that there was an increase in mean heat flux.Do not reject the null hypothesis. There is sufficient evidence to conclude that…
A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1 2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Amount by Which Speed Limit Was Exceeded MaleDriver FemaleDriver 1.2 -0.1 1.4 0.4 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use μmales − μfemales.Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to…
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 coefficient of variation ?/?. (Round…
A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1 2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Amount by Which Speed Limit Was Exceeded MaleDriver FemaleDriver 1.3 -0.1 1.3 0.4 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use μmales − μfemales.Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to…
An article reported data from a study in which both a baseline gasoline mixture and a reformulated gasoline were used. Consider the following observations on age (yr) and NOx emissions (g/kWh): Engine 1 2 3 4 5 6 7 8 9 10 Age 0 0 2 11 7 16 9 0 12 4 Baseline 1.70 4.38 4.06 1.24 5.29 0.59 3.35 3.45 0.73 1.22 Reformulated 1.86 5.91 5.51 2.70 6.50 0.71 4.95 4.86 0.72 1.41 Construct scatter plots of the baseline NOx emissions versus age. What appears to be the nature of the relationship between these two variables? There is no compelling relationship between the data. As age increases, emissions also increase. As age increases, emissions decrease.