Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 7.2, Problem 8E
The following table presents shear strengths (in kN/mm) and weld diameters (in mm) for a sample of spot welds.
Diameter | Strength |
4.2 | 51 |
4.4 | 54 |
4.6 | 69 |
4.8 | 81 |
5.0 | 75 |
5.2 | 79 |
5.4 | 89 |
5.6 | 101 |
5.8 | 98 |
6.0 | 102 |
- a. Construct a
scatterplot of strength (y) versus diameter (x). Verify that a linear model is appropriate. - b. Compute the least-squares line for predicting strength from diameter.
- c. Compute the fitted value and the residual for each point.
- d. If the diameter is increased by 0.3 mm, by how much would you predict the strength to increase or decrease?
- e. Predict the strength for a diameter of 5.5 mm.
- f. Can the least-squares line be used to predict the strength for a diameter of 8 mm? If so, predict the strength. If not, explain why not.
- g. For what diameter would you predict a strength of 95 kN/mm?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: 329.2 409.5 311.0 326.5 316.8 349.8 309.7
6: 425.1 347.2 361.0 404.5 331.0 348.9 381.7
8: 389.4 366.2 351.0 357.1 409.9 367.3 382.0
10: 341.7 452.9 461.4 433.1 410.6 384.2 362.6
12: 414.4 441.8 419.9 410.7 473.4 441.2 465.8
USE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
O Ho: M₁ = H₂ = 13 = H4 = 1₂
H₂: all five μ's are unequal
O Ho: My H₂ H3 ‡ M4 # M5
H₂: at least two μ's are equal
O Ho: My # H₂ H3 # H4 # H5
H₂: all five us are equal
=
=
o Hỏi khi là không = 3 = Mà khô
H₂: at least two μ's are unequal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Sum of
Squares
Source
Treatments
Error…
A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: 321.2 409.5 311.0 326.5 316.8 349.8 309.7
6: 439.1 347.2 361.0 404.5 331.0 348.9 381.7
8: 390.4 366.2 351.0 357.1 409.9 367.3 382.0
10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6
12: 402.4 441.8 419.9 410.7 473.4 441.2 465.8
USE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
○ Ho: H₁ = H₂ = H3 = H4=H5
Ha: all five u's are unequal
O Ho: H₁ H₂ H3 H4 H5
Ha: all five μ's are equal
Ho H₁ = ₂ = 3 = H4 = 5
H₂: at least two μ's are unequal
Ho: H₁ H₂ H3 H4 H5
Ha: at least two μ's are equal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Mean
Degrees of Sum of
freedom Squares Squares
Source
Treatments…
A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: 333.2 409.5 311.0 326.5 316.8 349.8 309.7
6: 433.1 347.2 361.0 404.5 331.0 348.9 381.7
8: 382.4 366.2 351.0 357.1 409.9 367.3 382.0
10: 350.7 452.9 461.4 433.1 410.6 384.2 362.6
12: 413.4 441.8 419.9 410.7 473.4 441.2 465.8
LUSE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
O Hoi Hy #fly #Hz" Ha #Hs
H: all five μ's are equal
O Hoi H₂H₂ = H3 = HaHs
H: at least two μ's are unequal
O Hoi H₂ = H₂ = H₂ "HaHs
H: all five μ's are unequal
O Hoi H₂ #4₂ # Hz*H4 *H5
H: at least two μ's are equal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Degrees of Sum of Mean
freedom Squares Squares
Error
Total…
Chapter 7 Solutions
Statistics for Engineers and Scientists
Ch. 7.1 - Compute the correlation coefficient for the...Ch. 7.1 - For each of the following data sets, explain why...Ch. 7.1 - For each of the following scatterplots, state...Ch. 7.1 - True or false, and explain briefly: a. If the...Ch. 7.1 - In a study of ground motion caused by earthquakes,...Ch. 7.1 - A chemical engineer is studying the effect of...Ch. 7.1 - Another chemical engineer is studying the same...Ch. 7.1 - Tire pressure (in kPa) was measured for the right...Ch. 7.1 - Prob. 10ECh. 7.1 - The article Drift in Posturography Systems...
Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - A scatterplot contains four points: (2, 2), (1,...Ch. 7.2 - Each month for several months, the average...Ch. 7.2 - In a study of the relationship between the Brinell...Ch. 7.2 - A least-squares line is fit to a set of points. If...Ch. 7.2 - Prob. 4ECh. 7.2 - In Galtons height data (Figure 7.1, in Section...Ch. 7.2 - In a study relating the degree of warping, in mm....Ch. 7.2 - Moisture content in percent by volume (x) and...Ch. 7.2 - The following table presents shear strengths (in...Ch. 7.2 - Structural engineers use wireless sensor networks...Ch. 7.2 - The article Effect of Environmental Factors on...Ch. 7.2 - An agricultural scientist planted alfalfa on...Ch. 7.2 - Curing times in days (x) and compressive strengths...Ch. 7.2 - Prob. 13ECh. 7.2 - An engineer wants to predict the value for y when...Ch. 7.2 - A simple random sample of 100 men aged 2534...Ch. 7.2 - Prob. 16ECh. 7.3 - A chemical reaction is run 12 times, and the...Ch. 7.3 - Structural engineers use wireless sensor networks...Ch. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - The coefficient of absorption (COA) for a clay...Ch. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Three engineers are independently estimating the...Ch. 7.3 - In the skin permeability example (Example 7.17)...Ch. 7.3 - Prob. 12ECh. 7.3 - In a study of copper bars, the relationship...Ch. 7.3 - Prob. 14ECh. 7.3 - In the following MINITAB output, some of the...Ch. 7.3 - Prob. 16ECh. 7.3 - In order to increase the production of gas wells,...Ch. 7.4 - The following output (from MINITAB) is for the...Ch. 7.4 - The processing of raw coal involves washing, in...Ch. 7.4 - To determine the effect of temperature on the...Ch. 7.4 - The depth of wetting of a soil is the depth to...Ch. 7.4 - Good forecasting and control of preconstruction...Ch. 7.4 - The article Drift in Posturography Systems...Ch. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - A windmill is used to generate direct current....Ch. 7.4 - Two radon detectors were placed in different...Ch. 7.4 - Prob. 11ECh. 7.4 - The article The Selection of Yeast Strains for the...Ch. 7.4 - Prob. 13ECh. 7.4 - The article Characteristics and Trends of River...Ch. 7.4 - Prob. 15ECh. 7.4 - The article Mechanistic-Empirical Design of...Ch. 7.4 - An engineer wants to determine the spring constant...Ch. 7 - The BeerLambert law relates the absorbance A of a...Ch. 7 - Prob. 2SECh. 7 - Prob. 3SECh. 7 - Refer to Exercise 3. a. Plot the residuals versus...Ch. 7 - Prob. 5SECh. 7 - The article Experimental Measurement of Radiative...Ch. 7 - Prob. 7SECh. 7 - Prob. 8SECh. 7 - Prob. 9SECh. 7 - Prob. 10SECh. 7 - The article Estimating Population Abundance in...Ch. 7 - A materials scientist is experimenting with a new...Ch. 7 - Monitoring the yield of a particular chemical...Ch. 7 - Prob. 14SECh. 7 - Refer to Exercise 14. Someone wants to compute a...Ch. 7 - Prob. 16SECh. 7 - Prob. 17SECh. 7 - Prob. 18SECh. 7 - Prob. 19SECh. 7 - Use Equation (7.34) (page 545) to show that 1=1.Ch. 7 - Use Equation (7.35) (page 545) to show that 0=0.Ch. 7 - Prob. 22SECh. 7 - Use Equation (7.35) (page 545) to derive the...
Additional Math Textbook Solutions
Find more solutions based on key concepts
AVX Home Entertainment, Inc., recently began a “no-hassles” return policy. A sample of 500 customers who recent...
EBK STATISTICAL TECHNIQUES IN BUSINESS
In Exercises 9-20, use the data in the following table, which lists drive-thru order accuracy at popular fast f...
Essentials of Statistics (6th Edition)
Four different beverages are sold at a fast-food restaurant: soft drinks, tea, coffee, and bottled water. a. Ex...
Basic Business Statistics, Student Value Edition
Testing Hypotheses. In Exercises 13-24, assume that a simple random sample has been selected and test the given...
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
31. Putting It Together: A Tornado Model Is the width of a tornado related to the amount of distance for which ...
Statistics: Informed Decisions Using Data (5th Edition)
Ten equally qualified marketing assistants are candidates for promotion to associate buyer; seven are men and t...
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
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
- The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter a)The predicted y-hat value for a diameter of 201 is 864. Interpret this predicted value. b)what is the predicted strength of a weld with a diameter of 51?arrow_forwardA study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 323.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 423.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 393.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 418.4 441.8 419.9 410.7 473.4 441.2 465.8 Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: at least two ?i's are equalH0: ?1 = ?2 = ?3 = ?4 = ?5Ha: all five ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 = ?5Ha: at least two ?i's are unequalH0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: all five ?i's are equal Test the relevant hypotheses using analysis of variance with ? = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Source Degrees offreedom Sum…arrow_forwardThe following data is the pull strength of a wire bond in a semiconductor manufacturing process, wire length, and die height. Observation number Pull strength (Y) Wire length (X1) Die Height (X2) 1 9.95 2 50 2 24.45 8 110 3 31.75 11 120 4 35.00 10 550 5 25.02 8 295 6 16.86 4 200 7 14.38 2 375 8 9.60 2 52 9 24.35 9 100 10 27.50 8 300 a i) Fit a regression line using pull strength as Y and wire length as X. Use calculator to find the a and b to do so. ii) Find the coefficient of correlation in this regression model. Interpret its meaning. iii) Find the coefficient of determination in this regression model. Interpret its meaning. b) Now the esearcher wanted to include one more variable, Die Height, in the regression model. Thus he obtained the following Excel output using both wire length and die height as independent variables: SUMMARY OUTPUT Regression Statistics Multiple R 0.994525658 0.989081284 R Square Adjusted R Square Standard Error Observations 1.043637866 10 ANOVA MS F…arrow_forward
- A rocket engine was produced by combining an igniter with a propellant source. The “shearing force” of the weld was measured over time. Determine the relationship between two parameters with Regression.arrow_forwardA study considered the porosity of an ultrafine powder of partially stabilized zirconia as a function of temperature. The data generated from the study is recorded in the table below. Select the best description for the pattern of the scatter plot of the parameters.arrow_forwardThe accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?arrow_forward
- For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data: X 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y 74.5 71.1 58.2 48.8 74.2 73.3 68.4 59.5 58.0 48.4 USE SALT (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.) y = -30.0452 +.9696 X Check the degree of your polynomial. Interpret the slope. A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. O A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. O A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope. A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. (b)…arrow_forwardFor the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data: x 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y 74.6 71.1 57.5 48.4 74.0 72.9 68.3 59.8 57.6 48.0 (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)y = −32.6485+0.9943x Interpret the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. (b) Calculate the coefficient of…arrow_forwardFor the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data: x 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 y 75.4 71.3 58.1 48.5 74.1 73.7 67.7 59.5 58.0 48.6 (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)y = Interpret the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope.A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. (b) Calculate the coefficient of determination.…arrow_forward
- For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x cube strength (MPa) based on the following sample data: 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 74.7 70.7 58.0 49.2 74.3 73.0 68.3 59.5 57.3 48.9 (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.) %3D Interpret the slope. A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope. A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. (b) Calculate the coefficient of determination. (Round your answer to four…arrow_forwarda) Copy the numbers you were given for Weight and Pulse from your MyMathLab homework to this table: Weight (Ib) Pulse (bpm) 40 2006 19 150 400 43 1600 29 7t Make a scatter plot of the given points on the grid below. Be sure to label the x and y axes. hoqqu2 b) Looking at the scatterplot BEFORE you run your regression, how do you know that Power Regression will be appropriate for this data? c) Write the power regression equation in terms of x and y, where x is the independent variable, and y is the dependent variable: d) Use your regression equation to predict the heart rate of an animal that weighs 100 pounds. Show your work and give your answer in a complete sentence.arrow_forwardFor the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x= cube strength (MPa) based on the following sample data: 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 75.4 70.9 57.8 49.0 73.8 73.7 67.8 59.6 57.5 48.9 A USE SALT (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.) y= Interpret the slope. O A one MPa decrease in cube strength is associated with an increase in the predicted axcial strength equal to the slope. O A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. O A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope. O A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. (b) Calculate the coefficient of determination. (Round your…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 IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics 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:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction 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
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