A serious drought-related problem for farmers is the spread of aflatoxin, a highly toxic substance caused by mold, which contaminates field corn. In higher levels of contamination, aflatoxin is hazardous to animal and possibly human health. (Officials of the FDA have set a maximum limit of 20 parts per billion aflatoxin as safe for interstate marketing.) Three sprays, A, B, and C, have been developed to control aflatoxin in field corn. To determine whether differences exist among the sprays, ten ears of corn are randomly chosen from a contaminated corn field, and each is divided into three pieces of equal size. The sprays are then randomly assigned to the pieces for each ear of corn, thus setting up a randomized block design. The accompanying table gives the amount (in parts per billion) of aflatoxin present in the corn samples after spraying. Use the Friedman test based on Fr to determine whether there are differences among the sprays for control of aflatoxin. Give approximate bounds for the p-value.
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Mathematical Statistics with Applications
- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.arrow_forwardAs humans we consume food. The body extracts good things such as proteins and vitamins and throws away waste. A typical waste product is uric acid. High levels of uric acid can be an indication of conditions such as gout, kidney disease, and cancer. For females a high level of uric acid is 6 mg/dL or more and for males a high level of uric acid is 7 mg/dL or more. Suppose, over a period of months, an adult female was given 10 blood tests for uric acid. The results of each blood test are shown below. Pisces for Tutoring BVC Student esources results 2.52 4.15 5.91 7.55 7.77 5.4 4.37 3.22 3.48 3.13 hat pogle Drive The distribution of uric acid in healthy adult females is normally distributed with known population standard deviation, o = 2.15 mg/dl. Find a 95% confidence interval for the population mean of uric acid in this adult female's blood. Assume the sample of blood tests were given in a way that's equivalent to a simple random sample. (Round your answers to two decimal places.)…arrow_forwardAs humans we consume food. The body extracts good things such as proteins and vitamins and throws away waste. A typical waste product is uric acid. High levels of uric acid can be an indication of conditions such as gout, kidney disease, and cancer. For females a high level of uric acid is 6 mg/dL or more and for males a high level of uric acid is 7 mg/dL or more. Suppose, over a period of months, an adult male has taken 8 blood test for uric acid. The results of the test are shown below. results 1.54 7.96 7.51 4.84 1.87 6.53 5.99 5.03 The distribution of uric acid in healthy adult males is normally distributed.Find a 95% confidence interval for the population mean of uric acid in this adult male's blood. (Round your answers to two decimal places.)margin of error mg/dL lower limit mg/dL upper limit mg/dLDoes this confidence interval suggest that this adult male has a high level of uric acid? No, since the interval is contained within the acceptable range levels. Yes, since the…arrow_forward
- As humans we consume food. The body extracts good things such as proteins and vitamins and throws away waste. A typical waste product is uric acid. High levels of uric acid can be an indication of conditions such as gout, kidney disease, and cancer. For females a high level of uric acid is 6 mg/dL or more and for males a high level of uric acid is 7 mg/dL or more. Suppose, over a period of months, an adult male has taken 8 blood test for uric acid. The results of the test are shown below. results 5.94 5.79 4.21 6.59 4.59 3.33 5.27 3.27 The distribution of uric acid in healthy adult males is normally distributed.Find a 95% confidence interval for the population mean of uric acid in this adult male's blood. (Round your answers to two decimal places.)margin of error mg/dLlower limit mg/dLupper limit mg/dLarrow_forwardAs humans we consume food. The body extracts good things such as proteins and vitamins and throws away waste. A typical waste product is a uric acid. High levels of uric acid can be an indication of conditions such as gout, kidney disease, and cancer. For females a high level of uric acid is 6 mg/dL or more and for males a high level of uric acid is 7 mg/dL or more. Suppose, over a period of months, an adult female has taken 8 blood test for uric acid. The results of the test are shown below. results 8.9 6.27 3.99 7.42 9.94 8.99 9.17 5.65 Find a 95% confidence interval for the population mean of uric acid in this adult female's blood. (Round your answers to two decimal places.)margin of error mg/dL lower limit mg/dL upper limit mg/dL Does this confidence interval suggest that this adult female has a high level of uric acid? Explain your answer.arrow_forwardArsenic is a naturally occurring chemical that can enter groundwater through eroding granite or from a burned forest. A health organization recommends drinking water should contain no more than 10 parts per billion (ppb) of arsenic. A company produces filters to clean arsenic from private wells that could be affected by the groundwater. The company wants to investigate the effectiveness of a new filter compared to that of an older filter. They will test the filters on a field that is bordered on one side by a granite ledge and on the other side by a burned forest. The field is divided into 88 square plots of equal size, and a well to collect groundwater is drilled in the center of each plot. One filter will be used in each well. The following diagram shows the placement of the wells in the field. The company will use four of each type of filter to conduct the investigation. A randomized block design will be used. (a) Assuming there is a difference in the effectiveness of the two…arrow_forward
- You work for the U.S. Food and Drug Administration. You have gotten word that a drug manufacturing is not accurately reporting the contents of their liquid cold medication. Under Federal Regulations, "Variations from stated quantity of contents shall not be unreasonably large" (see section q of the regulation by clicking here).The company that produces cold medication is claiming that each bottle contains 355 milliliters of cold medication, which is about 12 fluid ounces. In order to determine if they are accurate in their reporting, you decide to randomly select 20 different bottles of cold medication and measure the amount of cold medication in each bottle (in milliliters). The results of each sample are shown below. Bottle Number 1 2 3 4 5 6 7 8 9 10 Milliliters 343 345 349 360 349 358 346 357 351 347 Bottle Number 11 12 13 14 15 16 17 18 19 20 Milliliters 344 341 358 346 346 350 347 341 353 352 a) Use the data shown above to construct a 96% confidence interval…arrow_forwardAn article on the PureEnergySystems.com website written by Louis LaPoint discusses a product called acetone. The article stated that “Acetone 1CH3COCH32 is a product that can be purchased inexpensively in most locations around the world, such as in common hardware, auto parts, or drug stores. Added to the fuel tank in tiny amounts, acetone aids in the vaporization of the gasoline or diesel, increasing fuel efficiency, engine longevity, and performance—as well as reducing hydrocarbon emissions.” To test whether this product actually does increase fuel efficiency in passenger cars, a consumer group has randomly selected 5 people to participate in the study. The following procedure is used: People are to bring their cars into a specified gasoline station and have the car filled with regular, unleaded gasoline at a particular pump. Nothing extra is added to the gasoline at this fill-up. The car’s odometer is recorded at the time of fill-up. When the tank is nearly empty, the person is…arrow_forwardThere are three types of contaminants that spoils water. Organic pollutants (O), volatile solvents (V), and chlorinated compounds (C). A new analytical method to detect (D) contaminants in water is being tested. The makers of the test claim that it can detect high levels of organic pollutants with 98% accuracy, volatile solvents with 99% accuracy, and chlorinated components with 89% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% with traces of chlorinated compounds. A test sample is selected randomly. (a) What is the probability that the test will signal? (b) If the test signals, what is the probability that volatile solvents are present? (c) If the test does not signal, what is the probability that chlorinated compounds are present? Note: Use the notations in the brackets to describe the events.arrow_forward
- ABC Textiles, Inc. has a textile production facility located in Palm City, FL. It lies along a river that is used for drinking water for the surrounding town and is therefore tested regularly for chemical contaminants according to EPA standards. There is also a recreational beachfront with swimming and boating located ½ mile downstream of the plant. Over the last ten years, the incidence of a skin reaction called allergic dermatitis has increased dramatically for swimmers at the recreational beachfront. Due to public concern, the local water utility began checking for elevated levels of several pollutants that cause skin reactions. Over the course of a year, they collected 45 water samples from a location adjacent to the output of the industrial plant. These samples were tested and elevated levels of chromium were identified. The EPA’s Maximum Contaminant Level (MCL) for chromium is 0.1 mg/L. With the knowledge that chromium pollution can result from fabric dyeing within textile…arrow_forwardABC Textiles, Inc. has a textile production facility located in Palm City, FL. It lies along a river that is used for drinking water for the surrounding town and is therefore tested regularly for chemical contaminants according to EPA standards. There is also a recreational beachfront with swimming and boating located ½ mile downstream of the plant. Over the last ten years, the incidence of a skin reaction called allergic dermatitis has increased dramatically for swimmers at the recreational beachfront. Due to public concern, the local water utility began checking for elevated levels of several pollutants that cause skin reactions. Over the course of a year, they collected 45 water samples from a location adjacent to the output of the industrial plant. These samples were tested and elevated levels of chromium were identified. The EPA’s Maximum Contaminant Level (MCL) for chromium is 0.1 mg/L. With the knowledge that chromium pollution can result from fabric dyeing within textile…arrow_forwardABC Textiles, Inc. has a textile production facility located in Palm City, FL. It lies along a river that is used for drinking water for the surrounding town and is therefore tested regularly for chemical contaminants according to EPA standards. There is also a recreational beachfront with swimming and boating located ½ mile downstream of the plant. Over the last ten years, the incidence of a skin reaction called allergic dermatitis has increased dramatically for swimmers at the recreational beachfront. Due to public concern, the local water utility began checking for elevated levels of several pollutants that cause skin reactions. Over the course of a year, they collected 45 water samples from a location adjacent to the output of the industrial plant. These samples were tested and elevated levels of chromium were identified. The EPA’s Maximum Contaminant Level (MCL) for chromium is 0.1 mg/L. With the knowledge that chromium pollution can result from fabric dyeing within textile…arrow_forward