The chemist responsible for a ceramics factory evaluated the presence of Cadmium in the vessels produced by the company using a standard leaching test, and the following results were obtained: [Cd] (mg/L) 0,4887 0,4758 0,5506 0,4838 0,4901 0,4954 The limit value for Cd in the leaching test is established by standard as 0.5000 mg/L. Is there evidence that the average Cadmium content in ceramics is lower than the reference value established by the standard with 95% confidence? Formulate the null and alternative hypotheses, present the critical/tabled values, calculated and complete the test in full
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The chemist responsible for a ceramics factory evaluated the presence of Cadmium in the vessels produced by the company using a standard leaching test, and the following results were obtained:
[Cd] (mg/L) |
0,4887 |
0,4758 |
0,5506 |
0,4838 |
0,4901 |
0,4954 |
The limit value for Cd in the leaching test is established by standard as 0.5000 mg/L. Is there evidence that the average Cadmium content in ceramics is lower than the reference value established by the standard with 95% confidence? Formulate the null and alternative hypotheses, present the critical/tabled values, calculated and complete the test in full
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- The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. 1. For what value of z does exactly 95% of the area under a Gaussian curve lie between ± z? Use this multiplier to find the range of measured cholesterol concentrations that would include 95% of the trials from the “parent population” (μ and σ) given above. 2. Calculate z for a trial in which the measured total cholesterol concentration is 6.302 mmol/L. 3. What is the probability that a trial will give a cholesterol…The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. **Please show written work! It is difficult to understand "text" work/answers with mathematical/statistical problems** 1. For what value of z does exactly 95% of the area under a Gaussian curve lie between ± z? Use this multiplier to find the range of measured cholesterol concentrations that would include 95% of the trials from the “parent population” (μ and σ) given above. 2. Calculate z for a trial in which the…The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. In three trials, you obtained the following cholesterol concentrations (all in mmol/L): 6.476, 6.590, 6.338. 1. Showing all work, calculate a 95% confidence interval for your measured cholesterol concentration and write it as an intermediate result (with guard digits). Does your measurement differ from μ at 95% confidence? 2. Repeat part 1 for 90% confidence and explain any change in your conclusion. 3. Another…
- 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.The differential is a standard measurement made during a blood test. It consists of classifying white blood cells into the following five categories: (1) basophils, (2) eosinophils, (3) monocytes, (4) lymphocytes, and (5) neutrophils. The usual practice is to look at 100 randomly selected cells under a microscope and to count the number of cells within each of the five categories. Assume that a normal adult will have the following proportions of cells in each category: basophils, 0.5%; eosinophils, 1.5%; monocytes, 4%; lym- phocytes, 34%; and neutrophils, 60%. *5.25 An excess of eosinophils is sometimes consistent with a violent allergic reaction. What is the exact probability that a normal adult will have 5 or more eosinophils? *5.26 An excess of lymphocytes is consistent with vari- ous forms of viral infection, such as hepatitis. What is the probability that a normal adult will have 40 or more lymphocytes? *5.27 What is the probability a normal adult will have 50 or more lymphocytes?Listed below are pulse rates (beats per minute) from samples of adult males and females. Does there appear to be adifference? Find the coefficient of variation for each of the two samples; then compare the variation. A. The coefficient of variation for the male pulse rates iS (Type an integer or decimal rounded to one decimal place as needed.) B. The coefficient of variation for the female pulse rates is (Type an integer or decimal rounded to one decimal place as needed.)
- 1.56 Longleaf pine trees. The Wade Tract in Thomas County, Georgia, is an old-growth forest of longleaf pine trees (Pinus palustris) that has survived in a relatively undisturbed state since before the settlement of the area by Europeans. A study collected data on 584 of these trees. One of the variables measured was the diameter at breast height (DBH). This is the diameter of the tree at 4.5 feet, and the units are centimeters (cm). Only trees with DBH greater than 1.5 cm were sampled. Here are the diameters of a random sample of 40 of these trees: PINES 27 10.5 13.3 26.0 18.3 52.2 9.2 26.1 17.6 40.5 31.8 47.2 11.4 2.7 69.3 44.4 16.9 35.7 5.4 44.2 2.2 4.3 7.8 38.1 2.2 11.4 51.5 4.9 39.7 32.6 51.8 43.6 2.3 44.6 31.5 40.3 22.3 43.3 37.5 29.1 27.9 (a) Find the five-number summary for these data. (b) Make a boxplot. (c) Make a histogram. (d) Write a short summary of the major features of this distribution. Do you prefer the boxplot or the histogram for these data?A builder can choose between two different types of brick-red and yellow. Here are the results of tests on the strength of the bricks (in psi). Red brick: 1200, 1270, 1600, 1005, 1300, 1550, 1270, 1165, 1390, 1580, 1280, 1150, 1170, 1230, 1050, 1295, 1065, 1600, 1500, 1450, 1355, 1260, 1070, 1185, 1300. Yellow brick: 1400, 1200, 1000, 1250, 1340, 1210, 1000, 1090, 980, 800, 1020, 1275, 1345, 1195, 1095, 995, 1350, 1280, 1355, 1350, 1050, 950, 890, 1005, 980. a) Find out the five number summary for the datasets above. b) Develop box and whisker plot for the above datasets. What type of brick will you advise the builder to choose and why?In a manufacturing company, a new production process is being considered to replace the old process presently used. This new process was tested for 10 consecutive hours with the following results: 128, 120, 118, 122, 124, 126, 110, 125, 118. If the average outputs per hour using the old process is 120 units, is the management's claim justified in stating the output per hour can be increased with the new process? Use a = 0.01. a. Null and alternative hypothesis b. Level of significance c. Test statistics to be used and decide whether a one-tailed test or two-tailed test d. Critical value and the rejection region/s e. Compute for the value of test statistic. f. State the decision g. State the conclusion.
- Coke is a solid fuel made by heating coal in the absence of air so that the volatile components are driven off. For screened coke, the porosity factor is measured by the difference in weight between dry and soaked coke. A certain supply of screened coke from a supplier is claimed to have a porosity factor of 1.8 kilograms. Ten samples of the screened coke obtained from this supplier are tested for porosity factors and the results are as follows : 1.7 , 1.9 , 1.8 , 1.9 , 2.1 , 2.1 , 2.0 , 1.8 , 1.7 , 2.0 . Is there sufficient evidence to indicate that the actual coke from the supplier is more porous than what is claimed? Use Assume that the porosity factor is a normally distributed variable. Use the following format in your presentation. Show the values of the mean and the standard deviation which you calculate using the formulas or directly through your calculator stat or through Excel. Ho : HA : Test Statistic Critical Value : Test Statistic Calculated Value : (show the…Riboflavin (Vitamin B2) is determined in a cereal sample by measuring its fluorescence intensity(형광세기) in 5% acetic acid solution. A calibration curve was prepared by measuring the fluorescence intensities of a series of standards of increasing concentrations. The following data were obtained. Riboflavin (μg/mL) 0.000 0.100 0.200 0.400 0.800 Unknown sample Fluorescence intensity 0.0 5.8 12.2 22.3 43.3 15.4 (a) Use the method of least squares to obtain the best straight line through these five points (n=5). (b) Make a graph showing the experimental data and the calculated straight line. (c) An unknown sample gave an observed fluorescence intensity of 15.4. Calculate the concentration of Riboflavin (Vitamin B2) in the unknown sample (μg/mL). (d) Calculate the coefficient of determination (R2).A sample of ore is found to be 0.0022% gold and 0.059% silver. What is the percentage of matter in the ore that is neither gold or silver?