Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 12.5, Problem 64E
The accompanying data on x = UV transparency index and y = maximum prevalence of infection was read from a graph in the article “Solar Radiation Decreases Parasitism in Daphnia” (Ecology Letters, 2012: 47–54):
| x | 1.3 | 1.4 | 1.5 | 2.0 | 2.2 | 2.7 | 2.7 | 2.7 | 2.8 |
| y | 16 | 3 | 32 | 1 | 13 | 0 | 8 | 16 | 2 |
| x | 2.9 | 3.0 | 3.6 | 3.8 | 3.8 | 4.6 | 5.1 | 5.7 |
| y | 1 | 7 | 36 | 25 | 10 | 35 | 58 | 56 |
Summary quantities include Sxx = 25.5224, Syy = 5593.0588, and Sxy = 264.4882.
- a. Calculate and interpret the value of the sample
correlation coefficient . - b. If you decided to fit the simple linear regression model to this data, what proportion of observed variation in maximum prevalence could be explained by the model relationship?
- c. If you decided to regress UV transparency index on maximum prevalence (i.e., interchange the roles of x and y), what proportion of observed variation could be attributed to the model relationship?
- d. Carry out a test of H0: ρ = .5 versus Ha: ρ > .5 using a significance level of .05. [Note: The cited article reported the P-value for testing H0: ρ = 0 versus H0: ρ ≠ 0.]
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The article "Effect of Environmental Factors on Steel Plate CoIrosion Under Marine
Immersion Conditions" (C. Soares, Y. Garbatov, and A. Zayed, Corrosion Engineering,
Science and Technology, 2011:524-541) descrībes an experiment in which nine steel
specimens were submerged in seawater at various temperatures, and the corrosion rates
were measured. The results are presented in the following table (obtained by digitizing a
graph).
Temperature (*C)
Corrosion (mnm/yr)
26.6
1.58
26.0
1.45
27.4
1.13
21.7
0.96
14.9
0.99
11.3
1.05
15.0
0.82
8.7
0.68
8.2
0.56
Construct a scatterplot of corosion (y) versus temperature (x). Verify that a linear
model is appropriate.
Compute the least-squares line for predicting corrosion from temperature.
Two steel specimens whose temperatures differ by 10°C are submerged in seawater.
By how much would you predict their corrosion rates to differ?
Predict the corrosion rate for steel submerged in seawater at a temperature of 20°C.
Compute the fitted values.…
widely used as dielectrics and coolants in electrical systems in the past. They were found to be a major environmental contaminant in the 1960s. In a study, the mean PCB content at each of thirteen sites was reported for the years 1982 and 1996 (from “The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data”, Journal of Great Lakes Research 24 (1): 12-31, 1998). The data are below.Site:12345678910111213198261.4864.4745.5059.7058.8175.9671.5738.0630.5139.7029.7866.8963.93199613.9918.2611.2810.0221.0017.3628.207.3012.809.4112.6316.8322.74(a) Which test would be more appropriate in this case: a t-test for the difference between two population means, or a paired t-test? Why?(b) Do the data provide sufficient evidence to support the claim that the mean PCB level has decreased in the region? Be sure to check all assumptions, write the null and alternative hypotheses, calculate the appropriate test statistic, calculate the p-value,…
Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on
the foot indicate an increased risk of ulcers. The article "An Intelligent Insole for Diabetic
Patients with the Loss of Protective Sensation" (Kimberly Anderson, M.S. Thesis, Colorado
School of Mines), reports measurements of temperatures, in °F, of both feet for 181
diabetic patients. The results are presented in the following table.
Left Foot
Right Foot
80
80
85
85
75
80
88
86
89
87
87
82
78
78
88
89
89
90
76
81
89
86
87
82
78
78
80
81
87
82
86
85
76
80
88
89
Construct a scatterplot of the right foot temperature (y) versus the left foot temperature
(x). Verify that a linear model is appropriate.
b.
Compute the least-squares line for predicting the right foot temperature from the left
foot temperature.
If the left foot temperatures of two patients differ by 2 degrees, by how much would
you predict their right foot temperatures to differ?
Predict the right foot temperature for a patient whose left…
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 12.1 - The efficiency ratio for a steel specimen immersed...Ch. 12.1 - The article Exhaust Emissions from Four-Stroke...Ch. 12.1 - Bivariate data often arises from the use of two...Ch. 12.1 - The accompanying data on y = ammonium...Ch. 12.1 - The article Objective Measurement of the...Ch. 12.1 - One factor in the development of tennis elbow, a...Ch. 12.1 - The article Some Field Experience in the Use of an...Ch. 12.1 - Referring to Exercise 7, suppose that the standard...Ch. 12.1 - The flow rate y (m3/min) in a device used for...Ch. 12.1 - Suppose the expected cost of a production run is...
Ch. 12.1 - Suppose that in a certain chemical process the...Ch. 12.2 - Refer back to the data in Exercise 4, in which y =...Ch. 12.2 - The accompanying data on y = ammonium...Ch. 12.2 - Refer to the lank temperature-efficiency ratio...Ch. 12.2 - Values of modulus of elasticity (MOE, the ratio of...Ch. 12.2 - The article Characterization of Highway Runoff in...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - The following data is representative of that...Ch. 12.2 - The bond behavior of reinforcing bars is an...Ch. 12.2 - Wrinkle recovery angle and tensile strength are...Ch. 12.2 - Calcium phosphate cement is gaining increasing...Ch. 12.2 - a. Obtain SSE for the data in Exercise 19 from the...Ch. 12.2 - The invasive diatom species Didymosphenia geminata...Ch. 12.2 - Prob. 25ECh. 12.2 - Show that the point of averages (x,y) lies on the...Ch. 12.2 - Prob. 27ECh. 12.2 - a. Consider the data in Exercise 20. Suppose that...Ch. 12.2 - Consider the following three data sets, in which...Ch. 12.3 - Reconsider the situation described in Exercise 7,...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - Exercise 16 of Section 12.2 gave data on x =...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - For the past decade, rubber powder has been used...Ch. 12.3 - Refer back to the data in Exercise 4, in which y =...Ch. 12.3 - Misi (airborne droplets or aerosols) is generated...Ch. 12.3 - Prob. 37ECh. 12.3 - Refer to the data on x = liberation rate and y =...Ch. 12.3 - Carry out the model utility test using the ANOVA...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Verify that if each xi is multiplied by a positive...Ch. 12.3 - Prob. 43ECh. 12.4 - Fitting the simple linear regression model to the...Ch. 12.4 - Reconsider the filtration ratemoisture content...Ch. 12.4 - Astringency is the quality in a wine that makes...Ch. 12.4 - The simple linear regression model provides a very...Ch. 12.4 - Prob. 48ECh. 12.4 - You are told that a 95% CI for expected lead...Ch. 12.4 - Prob. 50ECh. 12.4 - Refer to Example 12.12 in which x = test track...Ch. 12.4 - Plasma etching is essential to the fine-line...Ch. 12.4 - Consider the following four intervals based on the...Ch. 12.4 - The height of a patient is useful for a variety of...Ch. 12.4 - Prob. 55ECh. 12.4 - The article Bone Density and Insertion Torque as...Ch. 12.5 - The article Behavioural Effects of Mobile...Ch. 12.5 - The Turbine Oil Oxidation Test (TOST) and the...Ch. 12.5 - Toughness and fibrousness of asparagus are major...Ch. 12.5 - Head movement evaluations are important because...Ch. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.5 - Prob. 63ECh. 12.5 - The accompanying data on x = UV transparency index...Ch. 12.5 - Torsion during hip external rotation and extension...Ch. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12 - The appraisal of a warehouse can appear...Ch. 12 - Prob. 69SECh. 12 - Forensic scientists are often interested in making...Ch. 12 - Phenolic compounds are found in the effluents of...Ch. 12 - The SAS output at the bottom of this page is based...Ch. 12 - The presence of hard alloy carbides in high...Ch. 12 - The accompanying data was read from a scatterplot...Ch. 12 - An investigation was carried out to study the...Ch. 12 - Prob. 76SECh. 12 - Open water oil spills can wreak terrible...Ch. 12 - In Section 12.4, we presented a formula for...Ch. 12 - Show that SSE=Syy1Sxy, which gives an alternative...Ch. 12 - Suppose that x and y are positive variables and...Ch. 12 - Let sx and sy denote the sample standard...Ch. 12 - Verify that the t statistic for testing H0: 1 = 0...Ch. 12 - Use the formula for computing SSE to verify that...Ch. 12 - In biofiltration of wastewater, air discharged...Ch. 12 - Normal hatchery processes in aquaculture...Ch. 12 - Prob. 86SECh. 12 - Prob. 87SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 5.21) ▼ The accompanying data on x head circumfer- ence z score (a comparison score with peers of the same age-a positive score suggests a larger size than for peers) at age 6 to 14 months and y = volume of cerebral grey matter (in ml) at age 2 to 5 years were read from a graph in the article described in the chapter introduction (Jour- nal of the American Medical Association [2003]). Head Circumfer- Cerebral Grey ence z Scores at Matter (ml) 2–5 yr 6-14 Months 680 -.75 690 1.2 700 -.3 720 .25 740 .3 740 1.5 750 1.1 750 2.0 760 1.1 780 1.1 790 2.0 810 2.1 815 2.8 820 2.2 825 .9 835 2.35 840 2.3 845 2.2 a. Construct a scatterplot for these data. b. What is the value of the correlation coefficient? c. Find the equation of the least-squares line. by using Sor mulas.arrow_forwardAn article in Environment International ["influence of Water Temperature and Shower Head Office Size on the release Radon During Showering" (1992, Vol. 18(4)] described an experiment in which the amount of radon released in showers was imvestigated. Radon-enriched water was used in the experiment, and six different orifice diameters were tested in shower heads. The data from the experiment are shown in the following table. 5. Orifice Diameter 0.37 0.51 0.71 1.02 Radon Released () 83 75 73 72 83 85 79 79 74 76 77 67 74 74 1.40 62 62 67 69 1.99 60 64 66 (a) Does the size of the orifice affect the mean percentage of radon released? Use a=0.05. (b) Find a 95% confidence interval on the mean percent of radon released when the orifice diameter is 1.40.arrow_forward5.47 The paper "Crop Improvement for Tropical and Subtropical Australia: Designing Plants for Difficult Climates" (Field Crops Research (1991]: 113–139) gave the following data on x = crop duration (in days) for soy- beans and y = crop yield (in tons per hectare): 92 100 102 96 1.9 92 y 1.7 2.3 2.0 1.5 102 106 106 121 143 1.7 1.6 1.8 1.0 0.3 Σ 1060 Ey = 15.8 a = 5.20683380 E xy = 1601.1 b = -0.3421541 a. Construct a scatterplot of the data. Do you think the least-squares line will give accurate predictions? Explain. b. Delete the observation with the largest x value from the sample and recalculate the equation of the least-squares line. Does this observation greatly affect the equation of the line? c. What effect does the deletion in Part (b) have on the value of r2? Can you explain why this is so?arrow_forward
- The article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142–148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.arrow_forwardAn article described an experiment in which observations on various characteristics were made using minichambers of three different types: (1) cooler (PVC frames covered with shade cloth), (2) control (PVC frames only), and (3) warmer (PVC frames covered with plastic). One of the article's authors kindly supplied the accompanying data on the difference between air and soil temperatures (°C). Cooler Control Warmer 1.59 1.92 2.57 1.43 2.00 2.60 1.88 2.19 1.93 1.26 1.12 1.58 1.91 1.78 2.30 1.86 1.84 0.84 1.90 2.45 2.65 1.57 2.03 0.12 1.79 1.52 2.74 1.72 0.58 2.53 2.41 1.90 2.13 2.34 2.86 0.96 2.31 1.34 1.91 1.76 (a) Compare measures of center for the three different samples. Cooler=_____________ Control=____________ Warmer=____________ (b) Calculate the standard deviations for the three different samples. (Round your answers to three decimal places.) Coolers=_______________ Controls=______________ Warmers=______________…arrow_forwardThe paper "A Cross-National Relationship Between Sugar Consumption and Major Depression?" (Depression and Anxiety [2002]: 118-120) concluded that there was a correlation between refined sugar consumption (calories per person per day) and annual rate of major depression (cases per 100 people) based on data from 6 countries. The following data were read from a graph that appeared in the paper: рaper: Depression Sugar Consumption Rate Country Korea 150 2.3 United States 300 3.0 France 350 4.4 Germany 375 5.0 Canada 390 5.2 New Zealand 480 5.7 Compute and interpret the correlation coefficient for this data set. . Is it reasonable to conclude that increasing sugar consumption leads to higher rates of depression? Explain. Do you have any concerns about this study that would make you hesitant to generalize these conclusions to other countries?arrow_forward
- Body Fat. In the paper “Total Body Composition by Dual- Photon (153 Gd) Absorptiometry” (American Journal of Clinical Nutrition, Vol. 40, pp. 834–839), R. Mazess et al. studied methods for quantifying body composition. Eighteen randomly selected adults were measured for percentage of body fat, using dual-photon absorptiometry. Each adult’s age and percentage of body fat are shown on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain the coefficient of determination. c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. d. State how useful the regression equation appears to be for making predictions.arrow_forwardAn article described an experiment in which observations on various characteristics were made using minichambers of three different types: (1) cooler (PVC frames covered with shade cloth), (2) control (PVC frames only), and (3) warmer (PVC frames covered with plastic). One of the article's authors kindly supplied the accompanying data on the difference between air and soil temperatures (°C). Cooler 1.59 1.43 1.88 1.26 1.91 1.86 1.90 1.57 1.79 1.72 2.41 2.34 0.94 1.34 1.76 Control 1.92 2.00 2.19 1.12 1.78 1.84 2.45 2.03 1.52 0.49 1.90 Warmer 2.57 2.60 1.93 1.58 2.30 0.84 2.65 0.15 2.74 2.53 2.13 2.86 2.31 1.91 (a) Compare measures of center for the three different samples. Cooler X = 1.76 Control X = 1.90 Warmer X = 2.305 (b) Calculate the standard deviations for the three different samples. (Round your answers to three decimal places.) Cooler S = 0.395 Control S = 0.522 Warmer S = 0.772 X x Interpret and compare the standard deviations for the three different samples.arrow_forwardThe decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' (Trans. Amer. Fisheries Soc. (1991: 405-420) gave the accompanying data on 10 values for the data sets where y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Here is the computer software printout of the summary: Coefficients: Estimate Std. Error t value Pr(> |t|) (Intercept) −89.010 16.703 −5.329 0.000 Length 0.705 0.046 15.293 0.000 Using this information, compute a 95% confidence interval for the slope. Assume that we have normal distribution and choose the resulting interval. a) [0.356, −54.814] b) [−121.749, −56.271] c) [0.611, 0.799] d) [−122.951, −55.069] e)…arrow_forward
- The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' (Trans. Amer. Fisheries Soc. (1991: 405-420) gave the accompanying data on 10 values for the data sets where y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Here is the computer software printout of the summary: Coefficients: Estimate Std. Error t value Pr(> |t|) (Intercept) −89.010 16.703 −5.329 0.000 Length 0.705 0.046 15.293 0.000 Using this information, compute a 95% confidence interval for the slope. a) [0.356, −54.814] b) [−121.749, −56.271] c) [0.611, 0.799] d) [−122.951, −55.069] e) [0.629, 0.781]arrow_forwardAn article23 summarized results from the Nurses’ Health Study and the Health Pro- fessionals Follow-Up Study. The article reported (with RR = relative risk) that “Com- pared with nonregular use, regular aspirin use was associated with lower risk of overall cancer (RR 0.97; 95% CI 0.94, 0.99), which was primarily due to a lower incidence of gastrointestinal cancers, especially colorectal cancers (RR 0.81; 95% CI 0.75, 0.88).” Identify the response variables and the explanatory variable for these two results. Explain how to interpret the confidence interval about colorectal cancers. Would the association with overall cancer be considered (i) significant or non- significant? (ii) strong or weak? Explain. question 1 and 2arrow_forwardConsider a Qunat vars and Y and suppose we have collected data on both of them from an underlying population: PowerPoint Slide Show-LinearReg.pptx]-PowerPoint Bivariate Analysis: Modelling a Linear Relation b= After checking their scatter graph and correlation, if the amount of linear relation between the two was high enough, we can model the relation using a linear function: Y=f(X)=a+bX To that end, we need to estimate a and b. x1,x2,...,xn У1. Уг...... Уп a = nΣ(xy) - ExΣy nΣx²-(x)² Σy-bΣx n MULTIPLE CHOICE QUESTION If the amount if linear association was not high, we do not use SLR True False Rewatch Submitarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY