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- 2. Three tensile tests were carried out on an aluminum bar. In each test, the strain was measured at the same values of stress. The results were Stress (MPa) 34.5 69.0 103.5 138.0 Strain (Test 1) 0.46 0.95 1.48 1.93 Strain (Test 2) 0.34 1.02 1.51 2.09 Strain (Test 3) 0.73 1.10 1.62 2.12 Where the units of strain are mm/m. Use linear regression to estimate the modulus of elasticity of the bar (modulus of elasticity = stress/strain). %3DThe compressive strength of an alloy fastener used in aircraft construction is being studied. Ten loads were selected over the range 2500–4300 psi, and a number of fasteners were tested at those loads. The numbers of fasteners failing at each load were recorded. The complete test data are shown in Table E11-14.An automotive engineer subjects a large number of brake pads to a stress test and measures the wear on each. She obtains Y the P-value for testing Ho: µ = 7.0 versus H1: µ#7.0. = 7.4 mm and or = 0.2 mm, Use this information to find
- Japan's high population density has resulted in a multitude of resource-usage problems. One especially serious difficulty concerns waste removal. The article "Innovative Sludge Handling Through Pelletization Thickening"t reported the development of a new compression machine for processing sewage sludge. An important part of the investigation involved relating the moisture content of compressed pellets (y, in %) to the machine's filtration rate (x, in kg-DS/m/hr). Consider the following data. 125.4 98.3 201.6 147.2 146.0 124.5 112.3 120.2 161.1 178.8 y 77.9 76.9 81.3 80.0 78.1 78.5 77.4 77.2 79.9 80.4 159.4 145.7 74.9 151.5 144.2 124.8 198.6 132.6 159.6 110.7 79.7 79.2 76.9 78.1 79.6 78.3 81.7 76.8 79.1 78.5 Relevant summary quantities are X; = 2817.4 Fy, = 1575.5, 5x? = 415,815.84, Fxy, = 222,698.08, Fy? = 124,149.53. Also, x = 140.870, y = 78.78, Sy = 18,928.7020, Sy = 757.395, and SSE = 9.222. The estimated standard deviation is o = 0.716 and the equation of the least squares line is…Q3) An experiment was carried out to investigate variation of solubility of chemical X in water. The quantities in kg that dissolved in 1 liter at various temperatures are show in the table (1). Table (1) Temperature C Mass of X 2.1 2.6 2.9 3.3 15 20 25 30 35 4 50 5.1 70 7 Use the proper methods to answer the following questions: a) Draw a scatter diagram to show the data. b) Estimate the temperature based on the mass of X. c) What quantity might be expected to dissolve at 42 C? Find the quantity that your cquation indicates would dissolve at 10 C and comment on your answer.17.7 Butterfly wings. Researchers studied the morphological attributes of monarch butterflies (Danaus plexippus), a species that undertakes large seasonal migrations over North America. They measured the forewing weight (in milligrams, mg) of a sample of 92 monarch butterflies, all of which had been reared in captivity in identical conditions.° Figure 17.4 shows the output from the statistical software JMP. (The data are also available in the Large.Butterfly the data file if you wish to practice working with your own software.) Estimate with 95% confidence the mean forewing weight of monarch butterflies reared in captivity. Follow the four- step process as illustrated in Example 17.2. 4 STEP そMP FWweight 30 25 20 15 10 11 12 13 14 15 8 9 10 Summary Statistics Mean 11.795652 Std Dev 1.1759413 Std Err Mean 0.1226004 Upper 95% Mean Lower 95% Mean 1 FIGURE 17.4 Software output (JMP) for the forewing weight of monarch 12.039183 11.552122 92 N. butterflies. Count
- A short column has a diameter X₁ and is loaded with an axial compressive load X₂. The ultimate compressive stress of the column is X3. The variables have the following mean and s.d. values: X₁ X₂ X3 Mean 3.5 10.0 2.5 Determine the reliability index of the system. s.d. 0.4 1.0 0.51. As heat is added to a material its temperature rises. The heat capacity is a quantitative statement of the increase in temperature for a specified addition of heat. These data are obtained in X, the measured heat capacity of liquid ethylene glycol at constant pressure and 80° C. Measurements are in calories per gram degree Celsius: .645 .654 .640 .627 .626 .649 .629 .631 .643 .633 .646 .630 .634 .631 .651 .659 .638 .645 .655 .624 .658 .658 .658 .647 .665 Assume that X is normally distributed. Find a 95% confidence interval for µ.In an experiment to investigate oxide charge, Qax on a silicon wafer. The factors thought to induce oxide charge, Qax are cleaning steps and the test location on the wafer where the charge was measured. The results summarized in Table 5. Table 5 Test Location Oxide Charge, Qox Cleaning Method Right (R) Left (L) (x 10" q/cm?) 1.66 R 1.62 1.90 Complete Spin-Rinse-Dry 1.84 1.92 R 1.84 L. -4.21 R -7.58 -1.35 By pass Rinse Cycle R -2.20 -2.08 R -5.36 Evaluate the significance of each factor using t-test. Show formulas and calculation steps of the statistical analysis method.
- I need help with part (c) only, I need t statistic and p value. Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets having diameters smaller than 10 µm (mg/m3): x 88 177 182 354 369 442 970 y 0.39 0.60 0.50 0.66 0.61 0.69 0.92 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? Yes, a scatter plot shows a reasonable linear relationship.No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and…An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm2 for the modified mortar (m = 42) and y = 16.86 kgf/cm for the unmodified mortar (n = 30). Let µ1 and Hz be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o1 = 1.6 and o2 = 1.3, test Ho: µ1 - 42 = 0 versus H3: µ1 – 42 > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Fail to reject Ho: The data does not suggest that the difference in average tension bond strengths exceeds from 0. o Reject Ho: The data does not suggest that the difference in average tension bond…SS 6.15. Control charts for x and R are to be established to control the tensile strength of a metal part. Assume that tensile strength is normally distributed. Thirty samples of size n = 6 parts are collected over a period of time with the following results: 30 30 Στ = 6,000 and Σκ i=1 i=1 = 150 a. Calculate control limits for x and R. b. Both charts exhibit control. The specifications on tensile strength are 200 ± 5. What are your con- clusions regarding process capability?