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- The Board of Transportation and Safety (BTS) wants to examine the safety mechanisms of A, B, and C-class cars. Samples of 5 cars for each of the classes were used. The board members collect the pressure exerted overall on the driver’s body during an impact test. The data is listed below. Assume alpha of 0.05. What is N = and G = ? 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)=151Question 1 : Suppose that the probability density function (p.d.f.) of the life (in weeks) of a certain part is f(x) = 3 x 2 (400)3 , 0 ≤ x < 400. (a) Compute the probability the a certain part will fail in less than 200 weeks. (b) Compute the mean lifetime of a part and the standard deviation of the lifetime of a part. (c) To decrease the probability in part (a), four independent parts are placed in parallel. So all must fail, if the system fails. Let Y = max{X1, X2, X3, X4} denote the lifetime of such a system, where Xi denotes the lifetime of the ith component. Show that fY (y) = 12 y 11 (400)12 , y > 0. Hint : First construct FY (y) = P(Y ≤ y), by noticing that {Y ≤ y} = {X1 ≤ y} ∩ {X2 ≤ y} ∩ {X3 ≤ y} ∩ {X4 ≤ y}. (d) Determine P(Y ≤ 200) and compare it to the answer in part (a)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.
- Consider the following 10 measurements about the cohesion of a soil: 12 kPa, 14 kPa, 15 kPa, 14.5 kPa, 16.0 kPa, 18 kPa, 15 kPa, 16.2 kPa, 17. 6 kPa, 13 kPa. Work out the solutions of the following two problems, assuming the cohesion follows the normal and lognormal distributions, respectively. (1) Draw the PDF of the cohesion; (2) Evaluate the probability that the cohesion based on the PDF is less than 5 kPa, 10 kPa, and 15 kPa; (3) Assess the effect of the type of distribution on the results.A statistical program is recommended. Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the material depends on its dielectric properties. The following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relationship with Density,"† was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content. y 4.55 4.49 4.50 4.47 4.47 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.33 4.44 4.40 4.26 4.32 4.34 x 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 6.49 5.70 6.49 6.37 6.51 7.88 6.74 7.08 The following R output is from a simple linear regression of y on x. Estimate Std. Error t value Pr(>|t|) (Intercept) 4.858691 0.059768 81.283 <2e-16 AirVoid −0.074676 0.009923 −7.526 1.21e-06 Residual standard error: 0.03551 on 16 DF Multiple R-squared: 0.7797, Adjusted…The data given is shown below 40 40 43 46 44 49 51 54 46 51 47 49 49 45 45 44 45 41 49 52 51 54 50 51 41 52 53 50 46 56 42 42 40 42 49 47 51 48 46 57 48 55 49 46 57 44 49 43 44 43 51 48 48 46 49 Class width = 6 Find the following: A. Decile (5th) B. Quartile (2nd) C. Skewness D. Kurtosis
- Question 8 Researchers compared the number of chocolate chips in Keebler brand vs. store brand cookies. Number of chocolate chips for keelber and number of cholcalte chips for store brand Grap with question write step by step soulation Question 9The 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?
- 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 1The value of the ___________ is used to estimate the value of the population parameter.Suppose your dependent variable is aggregate household demand for electricity for various cities. To correct for heteroskedasticity you should Select one: a. multiply observations by the square root of the city size b. multiply observations by the city size c. divide observations by the city size d. divide observations by the square root of the city size e. none of these