Consider the following results of compression test for twelve 28-day concrete cylinder samples from a particular mix batch during ostruction (Note: Th e data are on
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- Problem 5You’re a civil engineer testing the compressive strength of concrete to be used in bridgeconstruction. You test 16 concrete specimens, the resulting in the following compressivestrengths (in psi). DATA:2223 2329 2269 2244 2258 2325 2204 22962316 2272 2302 2342 2307 2205 2208 2311 a. Is the mean compressive strength greater than 2200 psi? Use the critical value approachand the appropriate table with 95% confidence.b. Is the mean compressive strength greater than 2200 psi? Use the p-value approach andExcel with 95% confidence.c. Is the standard deviation of compressive strength less than 50 psi? Use the critical valueapproach with 95% confidence.The determination of the shear strength of spot welds is relatively difficult, whereas measuring the weld diameter of spot welds is relatively simple. As a result, it would be advantageous if shear strength could be predicted from a measurement of weld diameter. The data are as follows: Shear strength (psi) Weld diameter (0.0001 in) 370 400 780 800 1210 1250 1560 1600 1980 2000 2450 2500 3070 3100 3550 3600 3940 4000 3950 4000 a) Test the hypothesis that the slope of the regression line is equal to 1 at the 0.05 level of significance.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?
- An article in the ASCE Journal of Energy Engineering [“Overview of Reservoir Release Improvements at 20 TVA Dams” (Vol. 125, April 1999, pp. 1–17)] presents data on dissolved oxygen concentrations in streams below 20 dams in the Tennessee Valley Authority system. The observations are (in milligrams per liter):The compressive strength of concrete is being studied, and four different mixing techniques are being investigated. The following data have been collected. Mixing Technique Compressive Strength (psi) Observations 1 3129 3000 2865 2890 2 3200 3300 2975 3150 3 2800 2900 2985 3050 4 2600 2700 2600 2765 (a) Test the hypothesis that mixing techniques affect the strength of concrete. Use α=0.05. Calculate to 2 decimal places f0: Does mixing technique affect concrete strength? (b) Find to 2 decimal places the P-value for the F-statistic computed in part (a). P-value = (c) Analyze the following residual plots to determine model adequacy. Does the assumption of normality seem reasonable? Does the assumption of constant variance seem reasonable?QUESTION 6 A new starch polymer foam with high shock absorbent properties is expected to perform better thanthe old foam which can withstand a maximum impact of 1.56 Joule (J). A simple destructive testto quantify shock absorption ability of the new foam is conducted. Table 5 shows the impact energyabsorbed (in J) that the new foam can withstand for each test.Table 51.61 1.5 1.65 1.7 1.4 1.59 1.65 1.5Does the recorded data suggests that the new foam performs better than the old foam? Use 2.5%level of significance.
- PART D ONLY We are using the average bonuses paid to workers on Wall Street from 2000 to 2016 to fit different auto-regressive models. The data is provided below: Year Bonus($000) 2000 100.5 2001 74.1 2002 60.9 2003 99.9 2004 113.5 2005 149.8 2006 191.4 2007 177.8 2008 100.9 2009 140.6 2010 139.0 2011 111.4 2012 142.9 2013 169.8 2014 160.3 2015 136.8 2016 138.2 a. fit a third-order autoregressive model to the bonuses paid and test for the significance of the third-order autoregressive parameter (slope) (Use a = 0.05.) b. if necessary, fit a second-order autoregressive model to the bonuses paid and test for the significance of the second-order autoregressive parameter (slope). (Use a = 0.05.) c. if necessary, fit a first-order autoregressive model to the bonuses paid and test for the significance of the first-order autoregressive parameter (slope). (Use a =…Two different chemical formulations of rocket fuel are considered for the peak thrust they deliver in a particular design for a rocket engine. The thrust/weight ratios (in kilograms force per gram) for each of the two fuels are measured several times. The results are as follows: Fuel A 54.1 52.9 57.9 58.2 53.4 51.4 56.8 55.9 57.9 56.8 58.4 52.9 55.5 51.3 51.8 53.3 Fuel B 55.1 55.5 53.1 50.5 49.7 50.1 52.4 54.4 54.1 55.6 56.1 54.8 48.4 48.3 55.5 54.7 A.Find the P-value. B.Can you conclude at the 5% level that the switch to fuel A should be made?Below you are given a partial Excel output based on a sample of 16 observations. ANOVA df SS MS F Regression 4,853 2,426.5 Residual 485.3 [row intentionally left blank] Coefficients Standard Error Intercept 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 Refer to Exhibit 3. We want to test whether the parameter β1 is significant. The test statistic equals: Select one: a. 5 b. 1.4 c. -1.4 d. 3.6
- The data given below indicate the existence of a linear relationship between the x and y variables. Suppose an analyst who prepared the solutions and carried out the RI measurements was not skilled and as a result of poor technique, allowed intermediate errors to appear. The results are the following:Concentration of solution in percent (x) 10 26 33 50 61Refractive indices (y) 1.497 1.493 1.485 1.478 1.477Step 1. Carefully plot the given x and y values (from the table) on a regular graphing paper. Label then connect the points to observe a zigzag plot due to the scattered points. Step 2: Copy and fill the table given below: x (x - x̄) (x - x̄) 2 y (y - ȳ) (y - ȳ) 2 (x - x̄) (y - ȳ) 10 1.497 26 1.49333 1.48550 1.47861 1.477∑ = ∑ = ∑ = ∑ = ∑ = ∑ = ∑ =x̄= ∑xi ÷ Nx̄= ȳ = ∑yi ÷ Nȳ = Step 3. After completing the table, present following computations and the interpretation.a. Calculate the correlation coefficient (r), using the working formula: r =Σ (x − x ) (y − ȳ)√(Σ(x − x )2)(Σ(y −…Samples are collected from the River X and pH values are observed. 9 different pH values are listed in table 3. Table 3 Concentrations 3.55 4.01 5.38 3.22 8.05 5.25 4.67 3.67 3.5Draw box plot and find a. Bowley’s coefficient of skewness b. Karl Pearson’s coefficient of skewness c. Third moment Rubric Stages of Process Marks Imagine and Plan 2Composition 2Effort 1) The following table shows 10 communities ranked by decayed, missing, or filled (DMF) teeth per 100 children and fluoride concentration in ppm in the public water supply: Rank by DMF Teeth FluorideCommunity per 100 children X Concentration Y 1 8 1 2 9 3 3 7 4 4 3 9 5 2 8 6 4 77 1…