2. Uniaxial tensile tests were carried on a ceramic. The following strength values were obtained: 310, 380, 400, 415, 448, 455, 475, 489, 500, and 502. a. Calculate the probability of survival or probability of failure for these data. What is the Weibull modulus? Also calculate the characteristic strength. b. What is the tensile strength at 50% survival probability? If the volume was increased three fold, what would be the new strength value at 50% survival probability?
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- To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material. Manufacturer 1 2 3 19 32 23 25 30 22 23 35 26 21 31 25 a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use alpha=0.05. Compute the values below (to 2 decimals, if necessary). Sum of Squares, Treatment ? Sum of Squares, Error ? Mean Squares, Treatment ? Mean Squares, Error ? Calculate the value of the test statistic (to2 decimals)? The p-value is? What is your conclusion? b. At the 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. Calculate Fisher's LSD Value (to 2 decimals)? What conclusion can you draw after carrying out this test?An article discussed the opening of a Market. The following data compared the prices of some kitchen staples at the new Market (group 1) and at the old Market (group 2) located 15 blocks away. ITEM GROUP 1 GROUP 2 HALF GALLON MILK 16.8 22.0 DOZEN EGGS 11.7 15.2 ORANGE JUICE (64OZ) 15.6 18.7 HEAD OF LETTUCE 16.7 15.6 1LB GROUND BEEF 17.5 20.8 6OZ TUNA 18.1 19.5 1LB APPLES 14.1 17.0 LINGUINI 21.8 19.5 SALMON STEAK 1LB 13.9 16.5 WHOLE CHICKEN PER LB 20.8 24.0 A. Using a 0.01 level of signifcance and the p-value approach, what is the p-value? And what is your conclusion? InterpretFour machines M - Mawere each made with three different components B - Bg fitted. The average production capacities [kg / h] of the machines were determined for each component during a test phase. The following values were measured: machine 3 4th B 7.07 8.24 8.43 9.2 B2 9.1 7.98 8.87 8.11 6.07 7th 5.98 6.36 Determine whether there are significant differences in terms of components or machines and calculate the effect sizes, Normal distribution with the same variance can be assumed. Note: q = 14.9477, 1 = 11.0648, 9a =3.5125 Name of the test procedure: O One-way analysis of variance Ot-test for independent samples with homogeneous variances O Two-factor analysis of variance with repeated measures O Two-factor analysis of variance without repetition of measurements Significance level: O 0.5 O 0.05 O 0.01 Overall hypothesis H: O There are no significant differences in terms of components and machines O There are no significant differences in terms of components or machines O There are no…
- Mike Wilde is president of the teachers’ union for Otsego School District. In preparing for upcoming negotiations, he is investigating the salary structure of classroom teachers in the district. He believes there are three factors that affect a teacher’s salary: years of experience, a teaching effectiveness rating given by the principal, and whether the teacher has a master’s degree. A random sample of 20 teachers resulted in the following data. Salary ($ thousands), y Years of Experience, x1 Principal's Rating, x2 Master's Degree,* x3 31.1 8 35 0 33.6 5 43 0 29.3 2 51 1 43.0 15 60 1 38.6 11 73 0 45.0 14 80 1 42.0 9 76 0 36.8 7 54 1 48.6 22 55 1 31.7 3 90 1 25.7 1 30 0 30.6 5 44 0 51.8 23 84 1 46.7 17 76 0 38.4 12 68 1 33.6 14 25 0 41.8 8 90 1 30.7 4 62 0 32.8 2 80 1 42.8 8 72 0…Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (µg/g). Wheat 5.2 4.4 6.1 6.2 6.6 5.8 Barley 6.5 7.9 6.0 7.6 6.0 5.7 Maize 5.8 4.6 6.4 4.9 6.0 5.2 Oats 8.4 6.2 7.8 7.1 5.4 7.2 USE SALT Does this data suggest that at least two of the grains differ with respect to true average thiamin content? Use a level α = 0.05 test. State the appropriate hypotheses. | H₂: M₁ = H₂ = H3 = H4 H₂: all four μ's are unequal • Ho: M₁ = H₂ = H3 = H4 H₂: at least two μ's are unequal ⒸH₂² H₁ H₂ H3 H4 # H: all four μ's are equal O Ho: M₁ #M₂ #H3 H4 H₂: at least two μ's are equal Compute the test statistic value. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O 0.001 < P-value < 0.010 O P-value < 0.001 State the conclusion in the problem context. O Reject Ho. There is not significant evidence…The toll plaza on Route 1 in Dover has four tollbooths open to all vehicles. Ms. Timlin conducted a chi-square goodness of fit test to see if all of the booths are used in equally. A chi-square value of 23.4 was calculated, resulting in a p-value of 0.006. Which of the following is correct? a. There is sufficient evidence to suggest that the tollbooths are not used in equal proportions. Selected:b. There is sufficient evidence to suggest that the tollbooths are used in equal proportions.This answer is incorrect. c. The tollbooths are used in equal proportions. d. There is insufficient evidence to suggest that the tollbooths are used in equal proportions. e. There is insufficient evidence to suggest that the tollbooths are not used in equal proportions.
- QUA For Numbers 11 to 15: To determine the efficacy and lethal dosage of cardiac relaxants, anesthetized guinea pigs are infused with a drug (A, B, C, or D) until death occurs. Each drug was randomly assigned to ten guinea pigs, and the total dosage required for death of each guinea pig was recorded (smaller lethal doses are considered more effective). The software output of the analysis are given below: ANOVA Assumption Checks ANOVA - total_dosage Homogeneity of Variances Test (Levene's) Sum of Squares Mean Square df1 df2 df 36 0.307 drug 265 88.49 9.87 <001 1.25 3 Residuals 323 36 8.97 Normality Test (Shapiro-Wilk) Statistic 0.979 0.670 11. Which of the following is (are) TRUE about the design of the experiment? I. The experiment has an unbalanced design. II. The experiment was laid out in CRD without subsampling. A. I only B. Il only C. Both I and II D. Neither I nor II 12. At 5% level of significance, which of the following statement(s) is(are) TRUE about the test of assumptions of…A psychologist would like to examine the effects of different testing methods on the final performance of college students. One group has regular quizzes, one group has three large exams, and the third group only has a final exam. At the end of the course, the psychologist interviews each student to get a measure of the student's overall knowledge of the material. Do these data indicate any significant differences among the three methods? Do the following computations: a. Compute and report the F Ratio at a a = .05 b. Compute and report the Tukey's HSD to determine exactly which methods are significantly different. Quizzes 4 6 3 7 T = 20 SS = 10 Exams 1 4 5 2 T = 12 SS= 10 Final Only 0 2 0 2 T=4 SS=4 G=36 EX² = 164 ✩Convert to raw-scores μ = 3,0 = 2 Z 0.50 -1.00 2.37 -0.75 -1.49 2.64 -1.47 2.64 Blank 1; Blank 2; Blank 3; Blank 4; Blank 5; Blank 6; Blank 7; Blank 8 Blank 1 Blank 2 Blank 3 Blank 4 Blank 5 Blank 6 Blank 7 Blank 8 Add your answer Add your answer Add your answer Add your answer Add your answer Add your answer Add your answer Add your answer Br
- The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Presented is the data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (°C) 1515 1616 1717 1818 1919 2020 2121 2222 2323 2424 2525 2626 2727 2828 2929 3030 Percent heat loss from beak 3232 3636 3636 3333 3535 4747 5757 5151 4242 5353 4646 5252 5959 5959 6363 6262 (a) What is the equation of the least‑squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature? (Use…The ratio of the lengths of the second and the fourth fingers, denoted 2D:4D, is an indicator of the level of prenatal testosterone. It is known that higher prenatal testosterone levels are associated with a lower 2D:4D value. Since testosterone levels are known to be related to behavioural traits, it has been conjectured that certain types of aggressive and dominant behaviours may be associated with lower 2D:4D values. van der Meij et al. (2012) conducted a study that investigated the possible relationship between 2D:4D and so-called "sociable" and "aggressive" dominance. For the study, 84 male students completed two questionnaires, measuring sociable and aggressive dominance respectively, on which high scores related to increased aggression. After some adjustments, a score between 1 and 6 was recorded for each subject on each questionnaire. The participants' hands were scanned and measurements taken, on which a 2D:4D measure could be recorded per subject by averaging the ratio for…Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data: MOE 29.7 33.1 33.6 35.2 35.4 36.2 36.2 36.3 37.4 37.8 Strength 5.8 7.1 7.2 6.2 8.0 6.9 7.1 7.7 6.7 6.4 МОЕ 38.6 38.7 39.7 40.9 42.7 42.7 43.6 45.7 45.9 46.8 Strength 7.1 6.4 8.0 8.9 8.3 8.8 7.9 9.6 7.3 7.6 МОЕ 47.9 49.2 51.6 62.7 69.7 79.6 80.1 Strength 9.8 7.7 7.8 11.5 11.4 11.9 10.6 Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in the data above resulted in ý = 7.589, s, = 0.180 when x = 40 and ý = 9.749, s, = 0.255 for x = 60. The simple linear regression model also resulted in a value of s = 0.8718. (a) Explain why s, is larger when x = 60 than when x = 40. O The closer x is to…