If vegetables intended for human consumption contain any pesticides at all, these pesticides should occur in minute quantities. Detection of pesticides in vegetables sent to market is accomplished by using solvents to extract the pesticides from the vegetables and then performing tests on this extract to isolate and quantify the pesticides present. The extraction process is thought to be adequate because, if known amounts of pesticides are added to “clean” vegetables in a laboratory environment, essentially all the pesticide can be recovered from the artificially contaminated extract.
The following data were obtained from a study by Willis Wheeler and colleagues,4 who sought to determine whether the extraction process is also effective when used in the more realistic situation where pesticides are applied to vegetable crops. Dieldrin (a commonly used pesticide) labeled with (radioactive) carbon-14 was applied to growing radishes. Fourteen days later, the extraction process was used, and the extracts were analyzed for pesticide content. A liquid scintillation counterwas used to determine the amount of carbon-14 present in the extract and also the amount left behind in the vegetable pulp. Because the vegetable pulp typically is discarded when analyzing for pesticides, if an appreciable proportion of pesticide remains in this pulp, a serious underassessment of the amount of pesticide could result. The pesticide was the only source of carbon-14; thus, the proportion of carbon-14 in the pulp is likely to be indicative of the proportion of pesticide in the pulp. The following table shows a portion of the data that the researchers obtained when low, medium, and high concentrations of the solvent, acetonitrile, were used in the extraction process.
a Is there sufficient evidence that the mean percentage of carbon-14 remaining in the vegetable pulp differs for the different concentrations of acetonitrile used in the extraction process? Give bounds for, or use the appropriate applet to determine the attained significance level. What would you conclude at the α = .01 level of significance?
b What assumptions are necessary to validly employ the analysis that you performed in part (a)? Relate the necessary assumptions to the specific application represented in this exercise.
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Chapter 13 Solutions
Mathematical Statistics with Applications
- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1arrow_forwardRepeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardExplain the differences between Gaussian elimination and Gauss-Jordan elimination.arrow_forward
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- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?arrow_forwardThe 2019-2020 flu season was especially tough. By the end of the season, an estimated total of 49 million people in the United States had contracted the flu, of whom an estimated 79,000 died from the flu. Assume that the US population was 300,000,000 during the 2019-2020 flu season and that during the season, a total of 2.9 million Americans died from all causes (including the flu). Assume the population of the US remained the same at the midpoint of the season. Report mortality rates per 100,000. Be sure to express the measure in the correct format. a.What was the proportionate mortality rate from flu during the 2019-2020 flu season? b.What was the case fatality rate from flue during the 2019-2020 flu season?arrow_forwardThe 2019-2020 flu season was especially tough.By the end of the season, an estimated total of 49 million people in the United States had contracted the flu, of whom an estimated 79,000 died from the flu. Assume that the US population was 300,000,000 during the 2019-2020 flu season and that during the season, a total of 2.9 million Americans died from all causes (including the flu). Assume the population of the US remained the same at the midpoint of the season. Report mortality rates per 100,000. Be sure to express the measure in the correct format. c.What was the flu-related mortality rate during the 2019-2020 flu season? d.What is the all-cause mortality rate during the 2019-2020 flu season? e.In a country with an age distribution that is much younger than in the US, the proportionate mortality rate from flu in 2019 was 5%. Based on this information alone, can we determine that the risk of dying from flu in 2019 was higher in this country compared to the US? Why or why not?arrow_forward
- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?arrow_forwardOne effect of the pesticide DDT upon birds is to inhibit the production of the enzyme carbonic anhydrase, which controls calcium metabolism. It is believed that this causes eggshells to be thinner and weaker than normal and makes the eggs more prone to breakage. An experiment was conducted where 16 sparrow hawks were fed a mixture of 3 ppm dieldrin and 15 ppm DDT (a combination often found in contaminated prey). The first egg laid by each bird was measured, and the mean shell thickness was found to be 0.19 mm. A “normal” eggshell has a mean thickness of 0.2 mm. What are the null and alternative hypotheses?arrow_forwardAt which point should i place the receiver on this satelite?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning