Question-2 a. A dynamic cone penetrometer DCP is used for measuring material resistance to penetration (mm/blow) as a cone is driven into pavement. A sample of size 52 for DCP values in pavement structure evaluation has a mean of 28.7615 and a standard deviation of 12.2647. Test that the true = average DCP value, μ 30 against that the true average DCP value, μ< 30 using level of significance of 0.02.
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- A series of measurements of the angle of shearing resistance of a sand determined that the parameter had a mean value of 35º, a standard deviation of 3° and that its minimum and maximum values were 28° and 42° respectively. Fit the results to a symmetrical beta distribution.Mr. Matar Al Maqbali measured the concentration of Zinc ion in the wastewater received from Industrial samples on daily basis. He has drawn and consider a Gaussian distribution curve with a population mean of 10.254 mg/L and a population standard deviation of 0.155 mg/L. Find the fraction of measurements expected between 10.525 and 10.575 mg/L if many measurements are made.The finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.03 centimeter. If in a couple of years, the mean and the standard deviation of the nished inside diameter of a piston ring change both to dierent values μ and σ, what proportion of rings will have inside diameters exceeding μ + 2.5σ?
- A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 69 residential customers has a mean monthly consumption of 880 kWh. Assume the population standard deviation is 126 kWh. At α=0.01, can you support the claim? Complete parts (a) through (e). Also find the critical values.A series of measurements in the lab led to an experimental result of 32.9 mL, with a calculated standard deviation of 0.3 mL. What is the standard way to report this result? Select one: 32.6-33.2 mL 32.9 ± 0.3 mL 32.9 ± 0.30 mL = 32.9 mLSolve the problem and draw the normal curve with the shaded region representing the given scenario in the problem. The accountants of a known auditing firm have a mean daily salary Php 850 with a standard deviation of Php 82. Find the median and the mode, and compare it with the given mean value. Determine the intervals within 1, 2 and 3 standard deviations from the mean, that is, the µ ± 1σ, µ ± 2σ, µ ± 3σ. Verify that the empirical rule holds that is, approximately, 68%, 95%, and 99% of the data lie within ± 1σ, ± 2σ, ± 3σ units of the mean, respectively. If an accountant from the firm is chosen at random, what is the probability that he /she earning Php 950 to Php 1,000? What percentage of the accountants will fall in between the salary of Php 300 and Php 500?
- You are studying the velocities of projectiles. Prior experience tells you that standard deviation of velocities is around 9.7 ft/sec. How many independent samples of projectile velocity do you have to measure to estimate the mean velocity within ±±0.98 ft/sec with 92% confidence?The braking ability was compared for two car models. Random samples of two cars were selected. The first random sample of size 64 cars yield a mean of 36 and a standard deviation of 8. The second sample of size 64 yield a sample mean of 33 and a standard deviation of 8. Do the data provide sufficient evidence to indicate a difference between the mean stopping distances for the two models? Use Alpha= 0.01. Ho: µ1 – µ2 = 0 vs. Ha: µ1 – µ2 + 0 .p-value = 0.0017. Reject Ho Но: Д, — м2 — 0 vs. Ha:M1 — M2 + 0. p-value — 0.034. Ассеpt Ho O Ho:µ1 – Hz Но: И — 2 — 0 vs. Ha:M, — нz + 0. p-value —D 0.0017. Ассept Ho Ho: H1 – U2 = 0 vs. Ha: µ1 – µ2 + 0. p-value = 0.034. Reject HoThe slant shear test is widely accepted for evaluating the bond of resinous repair materials to concrete; it utilizes cylinder specimens made of two identical halves bonded at 30°. An article reported that for 12 specimens prepared using wire-brushing, the sample mean shear strength (N/mm2) and sample standard deviation were 18.60 and 1.56, respectively, whereas for 12 hand-chiseled specimens, the corresponding values were 23.19 and 4.07. Does the true average strength appear to be different for the two methods of surface preparation? State and test the relevant hypotheses using a significance level of 0.05. (Use ?1 for wire-brushing and ?2 for hand-chiseling.) H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≤ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0 H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = You may have computed…
- Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for eight specimens under specified conditions, and the resulting mean and standard deviation were 306.11 newtons and 41.94 newtons, respectively. Assuming that it is reasonable to believe that breaking force under these conditions has a distribution that is approximately normal, estimate the mean breaking force for acrylic bone cement under the specified conditions using a 95% confidence interval. (Use a table or technology. Round your answers to three decimal places.) n USE SALT2. Traces of toxic, man-made hexachlorohexanes in North Sea sediments were extracted by a known process and by two new procedures, and measured by chromatography. Method Concentration found Conventional Procedure A (pg/g) 34.4 42.9 Standard deviation (pg/g) 3.6 1.2 Number of replications 6 6 a.) Is the standard deviation for procedure A significantly different from that of the conventional procedure at 95% confidence level? b.) Is the mean concentration found by procedure A significantly different from that of the conventional procedure at 95% confidence level?A machine producesbearings with diameters that are normally distributed with mean 3.0005 inches and standard deviation of 0.0010 inch.Specifications require the bearing diameters to lie in the interval 3.000+-0.0020 inches.Those outside the intzerval are considered scrap and must be processed. With the existing machine setting, what fraction of total production will be scrap?