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- A textile fiber manufacturer is investigating a newdrapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The companywishes to test the hypothesis Ho:u = 12 against H1 :µ < 12, using a random sample of 4 specimens. Round your answers to 4 decimal places. (a) What is the type l error probability if the critical region is defined asa < I1.5 kilograms? The type l error probability is (b) Find ßfor the case where the true mean elongation is 11.28 kilograms. ß = 1 (C) Find ßfor the case where the true mean is 11.5 kilograms. Statistical Tables and ChartsAn engineer measures the diameter of 20 tubes selected at random from a large shipment. The sample mean is 48.5 mm and S- 9.4 mm. The manufacturer of the tubes claims that 2 = 42.1 mm. Is this claim supported by data set? for 90% probability? where a' is the true or the estimate value O No O yesA temperature measurement system has the following specifications: -128 to 781°C Range Linearity error 0.29% FSO Hysteresis error 0.12% FSO Sensitivity error 0.04% FSO Zero drift 0.32% FSO FSO stands for "Full Scale Output". Estimate the overall instrument uncertainty for this system based on the available information. Use the maximum possible output range over the FSO in your computations.
- A small sample (N = 7) of the static coefficient of friction (µ) between two materials is measured with the following data set: 0.0043 0.0050 0.0053 0.0047 0.0031 0.0051 0.0049 Test the data for outliers. Determine the mean value and its confidence.You have been given the following set of data from a soil-geotextile friction test: Normal stress (kPa) Peak shear strength (kPa) Residual shear strength (kPa) 17 20.2 13 35 31 22 70 52 39.5 140 94 74.5 (a) Plot the Mohr-Coulomb failure envelope (x-axis=normal stress; y-axis=shear stress) (b) Determine the peak friction angle, and the residual friction angle, . (c) Determine the peak adhesion and the residual adhesion. (d) Calculate the fabric efficiency based on a soil friction angle of = 35-degrees using the peak friction angle. **HINT: the equation for efficiency of soil friction angle mobilization is:As an engineer working for a water bottling company, you collect the following data in order to test the performance of the bottling systems. Assume normal distribution. Milliliters of Water in the Bottle Frequency 485 490 milliliters 495 500 505 510 515 What is the mean (in milliliters)? milliliters What is the standard deviation (in milliliters)? What is the z value corresponding to 490 milliliters? Z = 6 12 20 33 18 11 00 8
- Pressure distribution measurements are made on a two-dimensional wing model placed in a wind tunnel. The difference between the static pressure sockets on the surface and the static pressure of the free stream is measured. 30 data is taken at each measurement point. The average of the values measured from one of the sockets near the trailing edge was calculated as 2.30 Pa, and the standard deviation was calculated as 2.65 Pa. After applying the Chauvenet criterion to these measurement values, it was decided to eliminate 3 measurements and the new mean value was found to be 2.18 Pa and the standard deviation was 2.42. It was verified that the unexcluded data fit the normal distribution curve. Data above how many Pa and below how many Pa were eliminated? Estimate how many data have negative value (?<0) after elimination.A gentleman used a spring scale to measure his luggage weight 3 times in different time under fixed condition and found the results were 42.1, 41.8 and 42.5 lbf, respectively. From the above results, estimate the nearest zero order uncertainty? All solutions are not correct 0.05 O 0.2 0.1An electrical firm manufactures light bulbs that have a lifetime that is approximately normally distributed with a standard deviation of 36 hours. A lifetime test of n=36 samples resulted in the sample average of 1510 hours. Assume the significance level of 0.05. (a) Test the hypothesis HO:µ=1500 versus H1:µ#1500using ap-value. (10pts) (b) Calculate the power of the test if the true mean lifetime is 1510. (10pts)
- Areas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal Distribution Function of Excel Note that the standard normal curve is symmetrical about the mean. z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 1 0.95 0.96 0.97 0.98 0.99 1.01 1.02 1.03 1.04 1.05 Mean - 0 1.06 1.07 1.08 1.09 A 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.0398 0.0438 0.0478 A 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 Z 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 1.12 1.13 1.14 1.15 1.16 1.17 A z 0.0517 0.0557 0.26 0.27 0.28 0.29 0.0596 0.0636 0.0675 0.3 0.0714 0.31 0.0753 0.32 0.0793 0.33 0.0832 0.34 0.0871 0.35 0.0910 0.0948 0.0987 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 A 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.36 0.3830 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.37…Home work for tensile test The following data was obtained from a tensile test on 135 Load (kN) Extension (mm) 16 32 56 72 95 110 132 142 140 0.2 0.4 0.7 0.9 1.5 2.5 5.0 8.5 10.0 12.0 a specimen of 10mm diameter and gauge length 60mm. Using the graph paper supplied, plot the load-extension diagram and determine: (1) The tensile strength (2) 0.1% Proof Stress (3) Young's Modulus for the specimen7. Repeat the experiment using a second and third rod of different material. Data Table: T; °C Lo m Aluminum 0.30 Material AL m T; °C AT °C 5.44 x 10-4 24.6 100.2 0.29 4.21 x 10-4 23.5 99.9 Brass 0.30 3.83 х 104 25.0 100 Copper Data Analysis Table Experimental a Accepted a /°C 24 x 10-6 Material Error % Aluminum 19 х 106 Brass 17x 10-6 Сopper