Laboratory experiments designed to measure LC50 (lethal concentration killing 50%of the test species) values for the effect of certain toxicants on fish are run by two different methods. One method has water continuously flowing through laboratory tanks, and the other method has static water conditions. For purposes of establishing criteria for toxicants, the Environmental Protection Agency (EPA) wants to adjust all results to the flow-through condition. Thus, a model is needed to relate the two types of observations. Observations on toxicants examined under both static and flow-through conditions yielded the data in the accompanying table (measurements in parts per million, ppm). Fit the model Y = β0 + β1x + ε.
- a What interpretation can you give to the results?
- b Estimate the flow-through value for a toxicant with an LC50 static value of x = 12 ppm.
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Chapter 11 Solutions
Mathematical Statistics with Applications
- Maple syrup is a non-negligible nutritional source of manganese. It is made from the sap of two species of maple: the sugar maple and the black maple. To see if there is a significant difference between the manganese content of these two species of maple, we measured the manganese content (in mg per 100g syrup) for a sample of sugar maples and a sample of black maples. The data is summarized by the Minitab output below: Two-sample T for Sugar Maple Black Maple group N Mean St Dev SE Mean Sugar Maple 20 Black Maple 12 3.55 0.29 Find: (i) a point estimate for ₁-2, where ₁ and 2 are the average manganese contents of the sugar maple, respectively the black maple; (ii) the standard error of X₁ - X₂. A) (i) -0.07; (ii) 0.101 C) (i) -0.26; (ii) 0.097 E) (i) -0.07; (ii) 0.035 3.29 0.22 0.049 0.084 B) (i) -0.26; (ii) 0.188 D) (i) -0.26; (ii) 0.101arrow_forwardDistress in EMSworkers. The Journal consulting and Clinical Psychology reported on a study of emergency service (EMS) rescue workers who responded to the I-880 freeway collapse during a San Francisco earthquake. The goal of the study was to identify the predictors of symptomatic distress in the EMS workers. One of the distress variables studied was the Global Symptom Index (GSI). Several models for GSI, y, were considered based on the following independent variables: x1 = Critical Incident Exposure scale (CIE) x2 = Hogan Personality Inventory—Adjustment scale (HPI-A) x3 = Years of experience (EXP) x4 = Locus of Control scale (LOC) x5 = Social Support scale (SS) x6 = Dissociative Experiences scale (DES) x7 = Peritraumatic Dissociation Experiences Questionnaire, self-report (PDEQ-SR) (a) Write a first-order model for E(y) as a function of the first five independent variables, x1 –x5. (b) The model of part a, fitted to data collected for n = 147 EMS workers, yielded the following results:…arrow_forwardAn experiment is conducted to see the effect of light intensity on plant growth, what is the dependent variable in this scenario?arrow_forward
- Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. An article in Urban Ecosystems, "Urbanization and Warming of Phoenix (Arizona, USA): Impacts, Feedbacks and Mitigation" (2002, Vol. 6, pp. 183-203), mentions that Phoenix is ideal to study the effects of an urban heat island because it has grown from a population of 300,000 to approximately 3 million over the last 50 years and this is a period with a continuous, detailed climate record. The 50-year averages of the mean annual temperatures at eight sites in Phoenix are shown below. Check the assumption of normality in the population with a probability plot. Construct a 95% confidence interval for the standard deviation over the sites of the mean annual temperatures. Site Sky Harbor Airport 23.3 Phoenix Greenway 21.7 Phoenix Encanto 21.6 Waddell Litchfield Laveen Average Mean Temperature (°C) Maricopa Harlquahala i 21.7 21.3 20.7 20.9 20.1 Round the answers to three…arrow_forwardThe authors of a paper compared two different instruments for measuring a person's capacity for breathing out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. The Wright meter is thought to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. Use of the mini-Wright meter could be recommended as long as there is not convincing evidence that the mean reading for the mini-Wright meter is different from the mean reading for Wright meter. For purposes of this exercise, you can assume that it is reasonable to consider the 17 people who participated in this study as representative of the population of interest. Data values from this paper are given in the accompanying table.…arrow_forwardThe authors of a paper compared two different instruments for measuring a person's capacity for breathing out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter. The Wright meter is thought to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. Use of the mini-Wright meter could be recommended as long as there is not convincing evidence that the mean reading for the mini-Wright meter is different from the mean reading for Wright meter. For purposes of this exercise, you can assume that it is reasonable to consider the 17 people who participated in this study as representative of the population of interest. Data values from this paper are given in the accompanying table.…arrow_forward
- Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. An article in Urban Ecosystems, "Urbanization and Warming of Phoenix (Arizona, USA): Impacts, Feedbacks and Mitigation" (2002, Vol. 6, pp. 183–203), mentions that Phoenix is ideal to study the effects of an urban heat island because it has grown from a population of 300,000 to approximately 3 million over the last 50 years and this is a period with a continuous, detailed climate record. The 50-year averages of the mean annual temperatures at eight sites in Phoenix are shown below. Check the assumption of normality in the population with a probability plot. Construct a 95% confidence interval for the standard deviation over the sites of the mean annual temperatures. Site Sky Harbor Airport 23.3 Average Mean Temperature (°C) Phoenix Greenway 21.7 Phoenix Encanto Waddell 21.6 21.7arrow_forwardDDT (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.arrow_forwardI am determining how effective a Drug is at reducing inflammation in individuals infected with a virus. the serum levels of antibody are measured as a measure of inflammation (less antibodies means less inflammation which decreases virus mortality) in 30 people given placebo, 30 people given 1 unit of the drug, and 30 people given 2 units of the drug. I would like to determine what levels of the drug are effective, and if there are sex-specific effects. What are the dependent and independent variables in this experiment? age _________ sex __________ antibody level _____________ treatment ___________arrow_forward
- Cell Phone Radiation Listed below are the measured radiation absorption rates (in W/kg) corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the Federal Communications Commission (FCC). The media often report about the dangers of cell phone radiation as a cause of cancer. The FCC has a standard that a cell phone absorption rate must be 1.6 W/kg or less. If you are planning to purchase a cell phone, are any of the measures of center the most important statistic? Is there another statistic that is most relevant? If so, which one?arrow_forwardA researcher is investigating the effectiveness of two weight loss treatments. The number of patients attending Treatment A and Treatment B are 30 and 32 respectively. The patients’ weight losses (in Kg) after a two-month treatment period are recorded and shown in Table 1: What type of research design you think this research should be classified? Explain your answer. Based on the research objective of the study, identify the: Independent and dependent variables of this research. Scale of measurement of each of the independent and dependent variables. For EACH of the treatment, determine/construct the following measures and histograms of weight losses using SPSS or any suitable statistical analysis tool: Mean Median Range Histogram d. Based on the histograms of weight losses produced in (c), briefly describe: The shape of distribution of weight losses for EACH treatment. How does the distribution of Treatment A differ from Treatment B e.…arrow_forwardData from the US Department of Energy’s US Energy Information Administration (eia.doe.gov) provides a look at the energy-related carbon dioxide emissions by end use sector (residential, commercial, industrial, transportation) from years 1990 to 2009. (Report # DOE/EIA0573(2009)). Here we would like to see if the CO2 emissions from the Industrial sector are less than that from the Transportation sector. Below are the results: 14. What type of study is this? a. Paired b. Two-Sample Independent 15. What type of plot would we use? a. Histogram of the differences b. Side-by-side boxplots c. Pie chart d. Bar graph 16. Was the HOV/pooled test used above (hint: look at the df)? YES NO 17. Is there evidence that the CO2 emissions from the Industrial sector are less than that from the Transportation sector? YES NO 18. If we were to test to see if there was a difference between the CO2 emissions from the Industrial sector and the Transportation sector, what would be the p-value? (report to 3…arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt