For a 20 specimens' sample of reinforced concrete beams to be tested under three non-mutually exelusive tests which are, compression (A), absorption(B), and cement content (C). The percentages of failure of the above sample beams are given below in the three Venn Diagrams., P(A UBUC)=0.42, P(ANB) -0.1, P(BNC) =0.13, P(ANC) -0.12 P(A)=0.24, P(B)=0.22, P(C)=0.26, Find the following probabilities: 1- P(ANBNC), 2- P(A UBNC), 3-P(Cn A U B)
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- Past research has indicated that the average age of death row inmates is 41 years old. researcher would like to determine if the average age has changed. She randomly selects 50 death row inma s and ds their average age to be 37 years old. The hypothesis the statistician wants to test is: a. Ho: µ=37 vs_ Ha: µ ± 41. b. Ho: µ=41 vs Ha: µ< 41. Ho: u = 41 vs. H: u 41 d. Ho: µ=37 vs_Ha: µ< 41. C. 2. If a player at a casino is playing roulette and betting on red, there is a 18 / 38 or 0.474 chance that he will win on any spin of the roulette wheel. If we take a random sample of 300 players betting on red, then p is the proportion of times that the player wins. What is the mean of the sampling distribution of p? t' a. b. What is the standard deviation (os) of the sampling distribution of p? c. If repeated samples of 300 players are taken, what would be the range of the sample proportion of players victories according to the 95 part of the 68-95-99.7 rule" pts) 3. The z statistic for a…Let XXN(u. 16). How much should the sample size he for testing HeiH = 24 rs. He = 25 ata = 0.025 and ß = 0.409 (a) 77 (b) 48 (c) 35 (d) 28 (e) NoneThe Board of Transportation and Safety (BTS) wants to examine the safety mechanisms of A, B, and C-class cars. Samples of 10 cars for each class were used. The board members collect the pressure exerted overall on the driver’s body during an impact test. Assume alpha of 0.05. What is dfbetween = ? What is dfwithin = ? What is the critical test statistic: ? A B C 27 21 48 13 23 39 11 10 22 15 27 30 34 34 31 n(A) = 5 n(B) = 5 n(B) = 5 T(A)=100 T(B)=115 T(C)=170 SS(A)=86 SS(B)=135 SS(C)=151 What is the MSbetween=? What is the MSwithin=? What is the calculated test statistic? Given the values of your critical test statistic and calculated test statistic, do you reject the null?
- 2. To investigate the effect of pH and catalyst concentration on product viscosity (sSt). Two levels of pH were used 5.6 and 5.9 and two catalyst concentration 2.5 and 2.7. Four products were tested with each combination of pH and catalyst. a. Use the estimate table below to test for main effects and interaction using a = 0.05. What are your conclusions? Predictor Constant Coefficient SDCoeff 191.563 165.49 pH 2.937 1.158 2.52 Catalyst -0.062 1.158 -0.05 pH*Catalyst 5.812 1.158 5.02 b. What is the value for the overall average viscosity? c. Write the regression model for this experiment. d. Below the interaction plot for the experiment. Discuss the information provided by the plot. To maximize viscosity what would be the recommended setting? Interaction Plot for Viscosity Data Mears 200 195 190- 185 Catalyst Concentration Mean Product Viscosity (cSt)10. An engineering study was undertaken to determine the optimum thickness of aluminum to be used to construct cans to be used for cat food. Cans made of aluminum of thickness 2.10 mm and 1.90 mm were tested to determine the maximum load each would sustain before collapsing. The sample data is summarized below. Use a = 0.05 to test the claim that the thicker cans are stronger (will withstand a higher load). 2.10 mm thick 1.90 mm thick sample size 175 170 mean maximum load (kg) 28.18 26.71 standard deviation of maximum load (kg) | 2.78 2.21Following are measurements of soil concentrations (in mg /kg) of chromium (Cr) and nickel (Ni) at20 sites in the area of Cleveland, Ohio. These data are taken from the article "Variation in NorthAmerican Regulatory Guidance for Heavy Metal Surface Soil Contamination at Commercial andIndustrial Sites" (A. Jennings and J. Ma, J. Environment Eng, 2007:587-609). Cr: 260 19 36 247 263 319 317 277 319 264 23 29 61 119 33 281 21 35 64 30Ni: 435 377 359 53 38 38 54 188 397 33 92 490 28 35 799 347 321 32 74 508 (a) Construct a histogram for each set of concentrations. (b) Find the 1st, 2nd and 3rd quartiles for the Cr concentrations (c) Find the 1st, 2nd and 3rd quartiles for the Ni concentrations.
- 20. Find the coefficient of skewness from the tollowing intormation : Difference of two quartiles = 8 Mode = 11 eboM %3D Sum of two quartiles = 22 Mean = 8 %3DDetermine the following ; Conclusion HYPOTHESIS CalculationTo evaluate the coagulation effects of three drugs, 30 healthy volunteers were randomly assigned into 3 groups and injected with different drugs. Their relevant coagulation times were measured as follows A(group=1): 36.8 34.4 34.3 35.7 33.2 31.1 34.3 29.8 35.4 31.2B(group=2): 40.0 35.5 36.7 39.3 40.1 36.8 33.4 38.3 38.4 39.8C(group=3): 32.9 37.9 30.5 31.1 34.7 37.6 40.2 38.1 32.4 35.6Questions: ① If you want to evaluate whether the coagulation effects of the three drugs are different, which method should be used? and what are the model assumptionsfor the application of this method?② Compare the difference of the coagulation effects among three drugs by SPSS,present the main results and make interpretation.③ Make pairwise comparisons of the efficacy of the three drugs, write out the method of pairwise comparison you adopted (just write one method) and the corresponding p-values.
- The authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement"† compared two different instruments for measuring a person's ability to breathe out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. Subject Mini-WrightMeter WrightMeter Subject Mini-WrightMeter WrightMeter 1 512 494 10 445 433 2 430 395 11 432 417 3 520 516 12 626 656 4 428 434 13 260 267 5 500 476 14 477 478 6 600 557 15 259 178 7 364 413 16 350 423 8 380 442 17 451 427 9 658 650 (a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce…Your company manufactures plastic wrap for food storage. The tear resistance of the wrap, denoted by X, must be controlled so that the wrap can be torn off the roll without too much effort but it does not tear too easily when in use. In a series of tests (see data table below), 15 rolls of wrap are made under carefully controlled conditions and the tear resistance of each rool is measured. The results are used as the basis of a quality assurance specification. If X for a subsequently produced roll falls more than two standard deviations away from the test period average, the process is declared out of specification and production is suspended for routine maintenance. Roll 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 X 134 131 129 133 135 131 134 130 131 136 129 130 133 130 133 a)What is the mean tear resistance? Enter your answer to the correct number of significant figures. b)What is the…
