A random sample of 49 business establishments shows that the average monthly water consumption is 35 cubic meters with a standard deviation of 5 cubic meter. Test the hypothesis that the average monthly water consumption is 34 cubic meters at 1% level of significance.
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- Radon is a gas emitted from the ground that can collect in houses in buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered “acceptable” Radon levels in a house vary from week to week. In one house, a sample of 6 weeks had the following readings for radon level (in pCi/L): 1.9 2.8 3.9 3.9 4.2 5.7 Find the variance and standard deviation (definitional formula). Show your work using a table.Shortleaf Pines. The ability to estimate the volume of a tree based on a simple measurement, such as the diameter of the tree, is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines was reported in C. Bruce and F. X. Schumacher’s Forest Mensuration (New York: McGraw-Hill, 1935) and analyzed by A. C. Akinson in the article “Transforming Both Sides of a Tree” (The American Statistician, Vol. 48, pp. 307–312). The data are provided on the WeissStats site. a. obtain and interpret the standard error of the estimate. b. obtain a residual plot and a normal probability plot of the residuals. c. decide whether you can reasonably consider Assumptions 1–3 for regression inferences met by the two variables under consideration.2.5. A sample of 15 g carbonated salt with density of 2650 kg/m3 is poured into a liter of water to form a suspension. The prepared suspensionwas used to fill up an Andreasen Pipette vessel to the 20 cm mark. Suspension samplesweretaken at:2,8, 16,32, 60,120, 180, 240, 360, 480, 600, and 1440 min. The weight concentrations on10 mL of the every extracted samplewere:0.1465,0.0967,0.0883, 0.0632, 0.0386,0.0294, 0.0178,0.0104, 0.0073,0.0051,0.0030, and 0.0008 g. If every extracted sample drops the height level inthe vessel 0.5 cm, evaluate the median size of the carbonated salt particles.
- 5. mPQ = mSR = 19 mQRT = mPSR = mPS = ach value or measure Sign out DELL %2$ 8. y h g n altArsenic is a chemical element that occurs in many minerals, usually in conjunction with sulfur and metals, and also as a pure elemental crystal. The main use of metallic arsenic is for strengthening alloys of copper and lead. Unfortunately, arsenic occurs in some ground water. In large quantities it is toxic for multicellular life. A mean arsenic level of 8 particles per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested regularly for arsenic. A random sample 37 tests gave a sample mean of 7.2 ppb arsenic with standard deviation of 1.9 ppb. Assume that arsenic levels are normally distributed. We are to use the sample data and test if mean arsenic level in the well in question is less than 8 ppb. a. Test statistic isb. The ? − value of the test isc. At the significance level calculated in part c), we conclude that mean arsenic level in thewell is10. 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 2.21
- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 44 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 8.00 ml/kg for the distribution of blood plasma.The quality control engineer at Palmer Industries is interested in estimating the tensile strength of steel wire based on its outside diameter and the amount of molybdenum in the steel. As an experiment, she selected 25 pieces of wire, measured the outside diameters, and determined the molybdenum content. Then she measured the tensile strength of each piece. The results of the first four are recorded in the table. Tensile Strength Outside Diameter Amount of Molybdenum Place (PSI ) Y (mm) X1 (Units) X2 A 11 0.3 6 B 9 0.2 5 C 16 0.4 8 D 12 0.3 7 Using a statistical software package, the QC engineer determined the multiple regression equation to be Y’=-0.5+20X1+1X2. a) Based on the equation, what is the estimated tensile strength of a steel wire having an outside diameter of .35 mm and 6.4 units of molybdenum? b) Interpret the value of b1 in the equation.