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
Videos
Textbook Question
thumb_up100%
Chapter 12.1, Problem 3E
Bivariate data often arises from the use of two different techniques to measure the same quantity. As an example, the accompanying observations on x = hydrogen concentration (ppm) using a gas chromatography method and y = concentration using a new sensor method were read from a graph in the article “A New Method to Measure the Diffusible Hydrogen Content in Steel Weldments Using a Polymer Electrolyte-Bused Hydrogen Sensor” (Welding Res., July 1997: 251s–256s).
| x | 47 | 62 | 65 | 70 | 70 | 78 | 95 | 100 | 114 | 118 |
| y | 38 | 62 | 53 | 67 | 84 | 79 | 93 | 106 | 117 | 116 |
| x | 124 | 127 | 140 | 140 | 140 | 150 | 152 | 164 | 198 | 221 |
| y | 127 | 114 | 134 | 139 | 142 | 170 | 149 | 154 | 200 | 215 |
Construct u
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
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…
The depth of wetting of a soil is the depth to which water content will increase owing to
extemal factors. The article "Discussion of Method for Evaluation of Depth of Wetting in
Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and
Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of
wetting beneath a structure and the age of the structure. The article presents measurements
of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the
following table.
Age
Depth
7.6
4
4.6
6.1
9.1
3
4.3
7.3
5.2
10.4
15.5
5.8
10.7
4
5.5
6.1
10.7
10.4
4.6
7.0
6.1
14
16.8
10
9.1
8.8
Compute the least-squares line for predicting depth of wetting (y) from age (x).
b. Identify a point with an unusually large x-value. Compute the least-squares line that
results from deletion of this point.
Identify another point which can be classified as an outlier. Compute the least-squares
line that results from deletion of the outlier,…
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.
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
- Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?arrow_forwardWire electrical-discharge machining (WEDM) is a process used to manufacture conductive hard metal components. It uses a continuously moving wire that serves as an electrode. Coating on the wire electrode allows for cooling of the wire electrode core and provides animproved cutting performance. The article “High-Performance Wire Electrodes for Wire Electrical-Discharge Machining—A Review” (J. of Engr. Manuf.,2012: 1757–1773) gave the following sample observationson total coating layer thickness (in mm) of eightwire electrodes used for WEDM:21 16 29 35 42 24 24 25Calculate a 99% CI for the standard deviation of thecoating layer thickness distribution. Is this interval validwhatever the nature of the distribution? Explain.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_forward
- The cetane number is a critical property in specifying the ignition quality of a fuel used in a diesel engine. Determination of this number for a biodiesel fuel is expensive and time- consuming. The article "Relating the Cetane Number of Biodiesel Fuels to Their Fatty Acid Composition: A Critical Study" (J. of Automobile Engr., 2009: 565–583) included the following data on x = iodine value (g) and y = cetane number for a sample of 15 biofuels The iodine value (x) is the amount of iodine necessary to saturate a sample of 100 g of oil. The article's authors fit the simple linear regression model to this data, so let' s does the same. 132.0 129.0 120.0 113.2 105.0 92.0 84.0 88.4 59.0 80.0 81.0 81.5 71.0 69.2 63.0 y 46.0 48.0 51.0 52.1 54.0 52.0 59.0 58.7 61.6 64.0 61.4 54.6 58.8 58.0 51.4 Construct a scatter plot for the data. Identify and state which is dependent and independent variable. What is the purpose of the scatter plot/diagram? 2. Fit a simple linear regression line/ equation to…arrow_forwardThe cetane number is a critical property in specifying the ignition quality of a fuel used in a diesel engine. Determination of this number for a biodiesel fuel is expensive and time- consuming. The article "Relating the Cetane Number of Biodiesel Fuels to Their Fatty Acid Composition: A Critical Study" (J. of Automobile Engr., 2009: 565–583) included the following data on x = iodine value (g) and y = cetane number for a sample of 15 biofuels The iodine value (x) is the amount of iodine necessary to saturate a sample of 100 g of oil. The article's authors fit the simple linear regression model to this data, so let' s does the same. 132.0 129.0 120.0 113.2 105.0 92.0 84.0 88.4 59.0 80.0 81.0 81.5 71.0 69.2 63.0 y 46.0 48.0 51.0 52.1 54.0 52.0 59.0 58.7 61.6 64.0 61.4 54.6 58.8 58.0 51.4 3) Estimate the correlation coefficient (Pearson coefficient), r, between x and y and explain briefly the strength of r and its direction and comment the p-value. 4) Construct a 95% two-sided confidence…arrow_forwardIn the article “Groundwater Electromagnetic Imaging in Complex Geological and Topographical Regions: A Case Study of a Tectonic Boundary in the French Alps” (S. Houtot, P. Tarits, et al., Geophysics, 2002:1048–1060), the pH was measured for several water samples in various locations near Gittaz Lake in the French Alps. The results for 11 locations on the northern side of the lake and for 6 locations on the southern side are as follows: Northern side: 8.1 8.2 8.1 8.2 8.2 7.4 7.3 7.4 8.1 8.1 7.9 Southern side: 7.8 8.2 7.9 7.9 8.1 8.1 Find a 98% confidence interval for the difference in pH between the northern and southern side.arrow_forward
- Foot ulcers are 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 18 diabetic patients. The results are presented in the Table QI. Table Q1: Measurements of temperatures, in °F of left foot Vs right foot for 18 diabetic patients Left Foot 80 foo Right Foot Right Foot 81 Left Foot (a) berature m80 85 76 85 89 86 9 marks) 75 80 87 82 88 foot temper 86sof 89 would thei 87 ht foo temp 80ures will 78s differ by 278reespredict by 81 (b) 87 82 87 82 I marks) 78 right foot to9erature for 76 tient whose 0 foot tmperature 78 86 85 (c) 88 89 90 88 89 (I marks) (d) Test the slope, ß1 = 1 at 5% level of significance. (e) Calculate the coefficient of correlation r and r² and then interpret their valuesarrow_forwardThe removal of ammoniacal nitrogen is an important aspect of treatment of leachate at landfill sites. The rate of removal (in percent per day) is recorded for several days for each of several treatment methods. The results are presented in the following table. (Based on the article "Removal of Ammoniacal Nitrogen from Landfill Leachate by Irrigation onto Vegetated Treatment Planes," S. Tyrrel, P. Leeds-Harrison, and K. Harrison, Water Research, 2002:291–299.) Treatment Rate of Removal 5.21 4.65 5.59 2.69 7.57 5.16 6.24 5.94 6.41 6.85 9.18 4.94 4.04 3.29 4.52 3.75 Construct an ANOVA table. You may give a range for the P-value. Can you conclude that the treatment methods differ in their rates of removal? a. b. ABCAEarrow_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 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, give the equation of the least squares regression line.arrow_forward
- A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design. (a) Define the parameter of interest. O μ = true average braking distance for the new design O p = true proportion of cars whose braking distances did not reduce O p = true proportion of cars whose braking distances reduced O μ = true average braking distance for the old design State the relevant hypotheses. Ho: μ = 120 H₂: μ = 120 O Ho: p = 120 Ha: p 120 ⒸHo: μ = 120 H₂: μ< 120 O Ho: p = 120 H₂: p = 120 ✔ (b) Suppose braking distance for the new system is normally distributed with = 13. Let X denote the sample average braking distance for a random sample of 36 observations. Which values of X are more contradictory to Ho than 117.2? O x ≥…arrow_forward5.1 Byers and Williams (Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons," Journal of Chemical and Engineering Data, 32, 349 – 354, 1987) studied the impact of temperature (the regressor) on the viscosity (the response) of toluene- tetralin blends. The following table gives the data for blends with a 0.4 molar fraction of toluene. Temperature (°C) Viscosity (mPa·s) 24.9 1.133 35.0 0.9772 44.9 0.8532 55.1 0.7550 65.2 0.6723 75.2 0.6021 85.2 0.5420 95.2 0.5074 c. Basic principles of physical chemistry suggest that the viscosity is an exponential function of the temperature. Repeat part b using the appropriate transformation based on this information.arrow_forward5.1 Byers and Williams (Viscosities of Binary and Ternary Mixtures of Polyaromatic Hydrocarbons," Journal of Chemical and Engineering Data, 32, 349 – 354, 1987) studied the impact of temperature (the regressor) on the viscosity (the response) of toluene- tetralin blends. The following table gives the data for blends with a 0.4 molar fraction of toluene. Temperature (°C) Viscosity (mPa·s) 1.133 24.9 35.0 0.9772 44.9 0.8532 55.1 0.7550 65.2 0.6723 75.2 0.6021 85.2 0.5420 95.2 0.5074 b. Fit the straight line model. Compute the summary statistics and the residual plots. What are your conclusions regarding model adequacy?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License