Four undisturbed samples were taken from a stiff clay deposit. Un- drained triaxial tests on these samples gave the following values for cus the undrained shear strength values: 102, 98, 95, 109 (kN/m²). Determine the minimum number of samples of the clay that should be taken so that, within a 95% probability, the average in-situ undrained shear strength value will be within 5% of the mean test result.
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- The compressive strength of concrete is normally distributed with mean 140 psi and variance 106 psi. A random sample of 54 specimens is collected. What is the standard error of the sample mean? a.)0.191 b.)1.321 c.)1.401 d.)1.744 e.)1.963 f.)14.425A surface reinforced concrete strip foundation, unit weight 24 kN/m³, is 2 m wide, 0.5 m thick and will be subjected to a uniform normal pressure, p, of mean value 500 kN/m² and coefficient of variation, Vp, of 6%. The soil is cohesionless. Unit weight: mean = 18 kN/m³; V₁ = 5% Angle of friction: mean = 40°; V₂ = 2.5% Determine the reliability index against bearing capacity failure.A granular soil has an angle of friction with a mean value of 40° and a coefficient of variation of 2.5%. Determine the corresponding mean and standard deviations values for the bearing capacity coefficient, N..
- A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m?. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed vrith o = 63. Let u denote the true average compressive strength.One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. A quality-control inspector must check that the machine is working properly. The inspector takes a random sample of 40 bottles and measures the volume of liquid in each bottle. We want to test Hg: μ = 180 Ha: 180 where μ = the true mean volume of liquid dispensed by the machine. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. A significance test yields a P-value of 0.0589. Interpret the P-value. Assuming the true mean volume of liquid dispensed by the machine is 180 ml, there is a 0.0589 probability of getting a sample mean of 179.6 just by chance in a random sample of 40 bottles filled by the machine. Assuming the true mean volume of liquid dispensed by the machine is 180 ml, there is a 0.0589 probability of getting a sample mean at least as far from 180 as 179.6 (in either direction) just by chance in a…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 = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 30). Let μ₁ and μ₂ 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 ₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂ : ₁ - ₂ > 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. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…
- 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 = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 32). Let μ₁ and μ₂ 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 0₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: M₁-M₂ > 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. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds…Deep mixing is a ground improvement method developed for soft soils like clay, silt, and peat. Civil engineers investigated the properties of soil improved by deep mixing with lime-cement columns. The mixed soil was tested by advancing a cylindrical rod with a cone tip down into the soil. During penetration, the cone penetrometer measures the cone tip resistance (megapascals, MPa). The researchers established that tip resistance for the deep mixed soil followed a normal distribution with u = 1.7 MPa and a = 1.1 MPa. Complete parts a through c. a. Find the probability that the tip resistance will fall between 1.3 and 4.0 MPa. P(1.3sxs4.0) = 0.6236 (Round to four decimal places as needed.) b. Find the probability that the tip resistance will exceed 1.0 MPa. P(x> 1) =D (Round to four decimal places as needed.)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…
- To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of welds is selected and tests are conducted on each weld in the sample. Weld strength is measured as the force required to break the weld. Suppose that the specifications state that the mean strength of welds should exceed 100 lb/in2 . The inspection team decides to test H0 : μ = 100 versus Ha : μ > 100. Explain why this alternative hypothesis was chosen rather than μ < 100.The compressive strength of concrete is normally distributed with u = 2507 psi and o = 51 psi. A random sample of n = 4 specimens is collected. What is the standard error of the sample mean? Round your final answer to three decimal places (e.g. 12.345). The standard error of the sample mean is psi.An experiment to compare the tenslon 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=10.16 kol/cm for the modified mortar (m = 42) and y= 16.87 kgf/cm for the unmodified mortar (n= 31). Let , and Ha be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (0) Assuming that o, = 1.6 and a, 13, test H -,- o versus H >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.) 2=1377 Pvalue=0 0001 State the conclusion in the problem context. Reject H The data suggests that the difference in average tension bond strengths exceeds d. O Fail to reject H The data does not suggest that the difference in average tension bond strengths exceeds from 0. O Reject H The…