PROBABILITY & STATS FOR ENGINEERING &SCI
9th Edition
ISBN: 9781285099804
Author: DEVORE
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 13.3, Problem 35E
The article “The Respiration in Air and in Water of the Limpets Patella caerulea and Patella lusitanica” (Comp. Biochemistry and Physiology, 1975: 407–411) proposed a simple power model for the relationship between respiration rate y and temperature x for P. caerulea in air. However, a plot of ln(y) versus x exhibits a curved pattern. Fit the quadratic power model
x | 10 | 15 | 20 | 25 | 30 |
y | 37.1 | 70.1 | 109.7 | 177.2 | 222.6 |
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
In a study conducted at Dartmouth College, mice with a particular type of cancerous tumor were
treated with a chemotherapy drug called Cisplatin. If the volume of one of these tumors at the time
of treatment is Vo, then the volume of the tumor t days after treatment is modeled by the function
V(t) = = Vo(0.99e- + 0.01e0.239t).
-0.1216t
1. Set Vo = 3 and plot V(t) over the interval 0 ≤ t ≤ 16. Appropriately adjust the viewing
window to see the behavior of V(t) and sketch the graph below.
2. From the graph, estimate the time at which the volume of the tumor decreased to half its
original amount. There are two such times, record each to the nearest whole number.
3. With Vo = 3, write down the equation whose solution gives the time at which the tumor is
half its original volume. (Re)write the equation with zero in the right-hand side.
4. Using one of your answers from 2. as to and your equation from 3., apply two steps of Newton's
method to better approximate this time. (Round to 3 decimal…
An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafıne PSZ Powders" (1991, Vol. 74, pp. 1547-1553)
considered the microstructure of the ultrafıne powder of partially stabilized zirconia as a function of temperature. The data are shown
below:
x= Temperature (°C) 1100 1200 1300 1100 1500 1200 1300
y = Porosity (%)
30.8
11.4 7.7
19.2
6
13.5
3.6
(a) Fit the simple linear regression model using the method of least squares. Find the least squares estimates of the intercept and slope
in the simple linear regression model. Find an estimate of o.
i
(Round your answer to 3 decimal places.)
(Round your answer to 5 decimal places.)
6 =
i
(Round your answer to 2 decimal places.)
(b) Estimate the mean porosity for a temperature of 1447 °C.
ŷ =
(Round your answer to 2 decimal places.)
Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as
determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and
y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t
x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651
y
334 342 355
363
365 372 381
400
392
412 420
Here is regression output from Minitab:
Predictor
Constant
absorb
S = 3.60498
Coef
321.878
156.711
SOURCE
Regression
Residual Error
Total
R-Sq= 98.5%
DF
SE Coef
2.483
6.464
1
9
10
SS
7639.0
117.0
7756..0
T
129.64
24.24
P
0.000
0.000.
R-Sq (adj) 98.3%
MS
7639.0
13.0
F
587.81
(a) Does the simple linear regression model appear to be appropriate?…
Chapter 13 Solutions
PROBABILITY & STATS FOR ENGINEERING &SCI
Ch. 13.1 - Suppose the variables x = commuting distance and y...Ch. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - As the air temperature drops, river water becomes...Ch. 13.1 - The accompanying scatterplot is based on data...Ch. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Consider the following four (x, y) data sets; the...Ch. 13.1 - a. Show that i=1nei=0 when the eis are the...
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - If there is at least one x value at which more...Ch. 13.2 - No tortilla chip aficionado likes soggy chips, so...Ch. 13.2 - Polyester fiber ropes are increasingly being used...Ch. 13.2 - The following data on mass rate of burning x and...Ch. 13.2 - Failures in aircraft gas turbine engines due to...Ch. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Mineral mining is one of the most important...Ch. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Kyphosis refers to severe forward flexion of the...Ch. 13.2 - Prob. 25ECh. 13.3 - The following data on y 5 glucose concentration...Ch. 13.3 - The viscosity (y) of an oil was measured by a cone...Ch. 13.3 - Prob. 29ECh. 13.3 - The accompanying data was extracted from the...Ch. 13.3 - The accompanying data on y 5 energy output (W) and...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The following data resulted from an experiment to...Ch. 13.3 - The article The Respiration in Air and in Water of...Ch. 13.4 - Cardiorespiratory fitness is widely recognized as...Ch. 13.4 - A trucking company considered a multiple...Ch. 13.4 - Let y = wear life of a bearing, x1 = oil...Ch. 13.4 - Let y = sales at a fast-food outlet (1000s of ),...Ch. 13.4 - The article cited in Exercise 49 of Chapter 7 gave...Ch. 13.4 - The article A Study of Factors Affecting the Human...Ch. 13.4 - An investigation of a die-casting process resulted...Ch. 13.4 - Prob. 43ECh. 13.4 - The accompanying Minitab regression output is...Ch. 13.4 - The article Analysis of the Modeling Methodologies...Ch. 13.4 - A regression analysis carried out to relate y =...Ch. 13.4 - Efficient design of certain types of municipal...Ch. 13.4 - An experiment to investigate the effects of a new...Ch. 13.4 - Prob. 49ECh. 13.4 - Prob. 50ECh. 13.4 - The article Optimization of Surface Roughness in...Ch. 13.4 - Utilization of sucrose as a carbon source for the...Ch. 13.4 - Prob. 53ECh. 13.4 - Prob. 54ECh. 13.5 - The article The Influence of Honing Process...Ch. 13.5 - Prob. 56ECh. 13.5 - In the accompanying table, we give the smallest...Ch. 13.5 - Prob. 58ECh. 13.5 - Prob. 59ECh. 13.5 - Pillar stability is a most important factor to...Ch. 13.5 - Prob. 61ECh. 13.5 - Prob. 62ECh. 13.5 - Prob. 63ECh. 13.5 - Prob. 64ECh. 13 - Curing concrete is known to be vulnerable to shock...Ch. 13 - Prob. 66SECh. 13 - The article Validation of the Rockport Fitness...Ch. 13 - Feature recognition from surface models of...Ch. 13 - Air pressure (psi) and temperature (F) were...Ch. 13 - An aeronautical engineering student carried out an...Ch. 13 - An ammonia bath is the one most widely used for...Ch. 13 - The article An Experimental Study of Resistance...Ch. 13 - The accompanying data on x = frequency (MHz) and y...Ch. 13 - Prob. 74SECh. 13 - Prob. 75SECh. 13 - The article Chemithermomechanical Pulp from Mixed...Ch. 13 - Prob. 77SECh. 13 - Prob. 78SECh. 13 - Prob. 79SECh. 13 - Prob. 80SECh. 13 - Prob. 81SECh. 13 - Prob. 82SECh. 13 - Prob. 83SE
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
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardThe following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.arrow_forward
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardThe population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?arrow_forwardWrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".† x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total SE Coef 2.483 6.464 R-Sq = 98.5% DF 1 9 10 SS 7639.0 117.0 7756.0 T 129.64 24.24 0.000 0.000 R-Sq (adj) = 98.3% MS 7639.0 13.0 F P 587.81 (a) Does the simple linear regression model appear to be…arrow_forward
- Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t 半 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Coef SE Coef P Constant 321.878 2.483 129.64 0.000 absorb 156.711 6.464 24.24 0.000 S = 3.60498 R-Sq = 98.5% R-Są (adj) - 98.3% SOURCE DF MS F P Regression 1 7639.0 7639.0 587.81 0.000 Residual Error 9 117.0 13.0 Total 10 7756.0 (a) Does the simple linear regression model appear to be…arrow_forwardGiven the data below about the Axial Strain(%) vs Deviator Stress: Axial Strain 1 3 (%), x Deviator Stress 27.227 44.92 59.776 (kPa), y What is the equation form Using Lagrange Interpolation? oy 13.6135(x)(x-2)(x-3) - 22.46(x)(x-1)(x-3) + 9.96267(x)(x-1)(x-2) oy 13.6135(x-1)(x-2)(x-3) - 22.46(x)(x-1)(x-3) + 9.96267(x)(x-1)((x-2) oy 13.6135(x)(x-2)(x-3) + 22.46(x)(x-1)(x-3) - 9.96267(x)(x-1)(x-2) %3D oy 13.6135(x-1)(x-2)(x-3) + 22.46(x)(x-1)(x-3) - 9.96267(x)(x-1)(x-2) っ2f? 2.arrow_forwardNeed help on part D! How does lateral acceleration—side forces experienced in turns that are largely under driver control—affect nausea as perceived by bus passengers? An article reported data on x = motion sickness dose (calculated in accordance with a British standard for evaluating similar motion at sea) and y = reported nausea (%). Relevant summary quantities are n = 17, xi = 223.9 , yi = 196 , xi2 = 3056.65 , xiyi = 2759.6 , yi2 = 2976 . Values of dose in the sample ranged from 6.0 to 17.6. (a) Assuming that the simple linear regression model is valid for relating these two variables (this is supported by the raw data), calculate and interpret an estimate of the slope parameter that conveys information about the precision and reliability of estimation. (Calculate a 95% CI. Round your answers to three decimal places.) , (b) Does it appear that there is a…arrow_forward
- Please solve part d and e only. The body mass index (BMI) of a person is defined to be the person’s body mass divided by the square of the person’s height. The article “Influences of Parameter Uncertainties within the ICRP 66 Respiratory Tract Model: Particle Deposition” (W. Bolch, E. Farfan, et al., Health Physics, 2001:378–394) states that body mass index (in kg/m2) in men aged 25–34 is lognormally distributed with parameters μ = 3.215 and σ = 0.157. a.Find the mean and standard deviation BMI for men aged 25–34. b.Find the standard deviation of BMI for men aged 25–34. c.Find the median BMI for men aged 25–34. d.What proportion of men aged 25–34 have a BMI less than 20? e.Find the 80th percentile of BMI for men aged 25–34.arrow_forwardb) Data was collected on 344 corporate executives to find out the effect of MBA degree and work experience on their salary. The following model was estimated: Y = 2.3501 + 3.6306D11 – 2.6354 D2i + 0.8527 X¡ + 1.634 (D, * X)i (2.1805) (- 3.457) (1.263) (7.605) (2.98) R? = 0.8968 Y: Annual Income in Lakhs of Rupees Di and D2 are MBA and gender dummies respectively X: Work experience in years DI = 1 if one has MBA degree = 0 otherwise D2 = 1 for a female executive = 0 for a male executive i. Write the regression equations for female MBA executives and male MBA executives separately. ii. Find the mean income level for the reference category and interpret it. iii. Test the statistical significance of differential intercept coefficient between female MBA executives and Male MBA executives at 5% level of significance. iv. Interpret the coefficient of D,*Xi.arrow_forwardThe relationship between carbon dioxide emissions and fuel efficiency of a certain car can be modeled by the least-squares regression equation ln(yˆ)=7−0.045x, where x represents the fuel efficiency, in miles per gallon, and yˆrepresents the predicted carbon dioxide emissions, in grams per mile. Which of the following is closest to the predicted carbon dioxide emissions, in grams per mile, for a car of this type with a fuel efficiency of 20 miles per gallon? 1.8 6.1 446 2,697 1,250,000arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY