Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 13.4, Problem 12E
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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DDT (dichlorodiphenyltrichloroethane) was used extensively from 1940 to 1970 as an insecticide. It still sees limited use for control of disease. But DDT was found to be harmful to plants and animals, including humans, and its effects were found to be lasting. The amount of time that DDT remains in the environment depends on many factors, but the following table shows what can be expected of 200 kilograms of DDT that has seeped into the soil.
t = time in yearssince application
D = DDT remaining,kilograms
0
200.00
1
190.00
2
180.50
3
171.48
(a) Show that the data are exponential.
The ratio from year 0 to year 1 is ______ , from year 1 to year 2 is ____ , and from year 2 to year 3 is_____ (rounded to two decimal places). Because these successive ratios are all , a) different b)the same , the data are exponential.
There 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
65% of them are contaminated with organic
pollutants, 20% with volatile solvents, and
15% 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
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.
One 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?
Chapter 13 Solutions
Mathematical Statistics with Applications
Ch. 13.2 - The reaction times for two different stimuli in a...Ch. 13.2 - Prob. 2ECh. 13.4 - State the assumptions underlying the ANOVA of a...Ch. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Suppose that independent samples of sizes n1, n2,,...Ch. 13.4 - Four chemical plants, producing the same products...Ch. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - A clinical psychologist wished to compare three...
Ch. 13.4 - It is believed that women in the postmenopausal...Ch. 13.4 - If vegetables intended for human consumption...Ch. 13.4 - One portion of the research described in a paper...Ch. 13.4 - The Florida Game and Fish Commission desires to...Ch. 13.4 - Prob. 15ECh. 13.4 - An experiment was conducted to examine the effect...Ch. 13.5 - Prob. 17ECh. 13.5 - Refer to Exercise 13.17 and consider YiYi for i ...Ch. 13.5 - Refer to the statistical model for the one-way...Ch. 13.7 - Refer to Examples 13.2 and 13.3. a Use the portion...Ch. 13.7 - Refer to Examples 13.2 and 13.4. a Use the portion...Ch. 13.7 - a Based on your answers to Exercises 13.20 and...Ch. 13.7 - Refer to Exercise 13.7. a Construct a 95%...Ch. 13.7 - Prob. 24ECh. 13.7 - Prob. 25ECh. 13.7 - Prob. 26ECh. 13.7 - Prob. 27ECh. 13.7 - Prob. 28ECh. 13.7 - Prob. 29ECh. 13.7 - Prob. 30ECh. 13.7 - Prob. 31ECh. 13.7 - Prob. 32ECh. 13.7 - Prob. 33ECh. 13.7 - Prob. 34ECh. 13.7 - Prob. 35ECh. 13.8 - Prob. 36ECh. 13.8 - Prob. 37ECh. 13.8 - Prob. 38ECh. 13.8 - Prob. 39ECh. 13.8 - Prob. 40ECh. 13.9 - Prob. 41ECh. 13.9 - The accompanying table presents data on yields...Ch. 13.9 - Refer to Exercise 13.42. Why was a randomized...Ch. 13.9 - Prob. 44ECh. 13.9 - Prob. 45ECh. 13.9 - Prob. 46ECh. 13.9 - Prob. 47ECh. 13.9 - Prob. 48ECh. 13.9 - Prob. 49ECh. 13.9 - Prob. 50ECh. 13.9 - Prob. 51ECh. 13.10 - Prob. 52ECh. 13.10 - Prob. 53ECh. 13.10 - Prob. 54ECh. 13.10 - Refer to Exercise 13.46. Construct a 95%...Ch. 13.10 - Prob. 56ECh. 13.10 - Prob. 57ECh. 13.11 - Prob. 58ECh. 13.11 - Prob. 59ECh. 13.11 - Prob. 60ECh. 13.11 - Prob. 61ECh. 13.11 - Prob. 62ECh. 13.12 - Prob. 63ECh. 13.12 - Prob. 64ECh. 13.12 - Prob. 65ECh. 13.12 - Prob. 66ECh. 13.12 - Prob. 67ECh. 13.12 - Prob. 68ECh. 13.13 - Prob. 69ECh. 13.13 - Prob. 70ECh. 13.13 - Refer to Exercise 13.42. Answer part (a) by...Ch. 13.13 - Refer to Exercise 13.45. Answer part (b) by...Ch. 13 - Prob. 73SECh. 13 - Prob. 74SECh. 13 - Prob. 75SECh. 13 - Prob. 77SECh. 13 - A study was initiated to investigate the effect of...Ch. 13 - Prob. 79SECh. 13 - A dealer has in stock three cars (models A, B, and...Ch. 13 - In the hope of attracting more riders, a city...Ch. 13 - Prob. 84SECh. 13 - Prob. 85SECh. 13 - Prob. 86SECh. 13 - Prob. 87SECh. 13 - Prob. 88SECh. 13 - Prob. 89SECh. 13 - Prob. 90SECh. 13 - Prob. 92SECh. 13 - Prob. 94SE
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