Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 13, Problem 83SE
a.
To determine
Estimate the model parameters.
b.
To determine
Interpret the
Test for model utility.
c.
To determine
Identify whether the two predictors give useful information about wear life of film lubricants.
d.
To determine
Predict the wear life of film lubricants when the speed is 50 rpm and load is 5 in 1,000’s of hour in a way that it conveys precision and reliability.
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In an experiment to determine factors related to weld toughness, the Charpy V-notch impact
toughness in ft - 1b (v) was measured for 22 welds at 0°Č, along with the lateral expansion
at the notch in % (x,), and the brittle fracture surface in % (x2). The data are presented in the
following table.
X1
X2
y
32
20.0
28
39
23.0
28
20
12.8
32
21
16.0
29
25
10.2
31
20
11.6
28
32
17.6
25
29
17.8
28
27
16.0
29
43
26.2
27
22
9.6
32
22
15.2
32
18
8.8
43
32
20.4
24
22
12.2
36
25
14.6
36
25
10.4
29
20
11.6
30
20
12.6
31
24
16.2
36
18
9.2
34
28
16.8
30
a. Fit the model y = Bo + B1 X1 + ɛ. For each coefficient, test the null hypothesis that it is
equal to 0.
b. Fit the model y = Bo + B, xz + ɛ. For each coefficient, test the null hypothesis that it is
equal to 0.
c. Fit the model y = Bo + B1 X1 + Bzx2 + ɛ. For each coefficient, test the null hypothesis
that it is equal to 0.
d. Which of the models in parts (a) through (c) is the best of the three? Why do you think
%3D
+ E.
so?
Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA,
which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y = the extent of mist droplets
having diameters smaller than 10 µm (mg/m³):
90 177 180 354 365 442 964
y 0.38 0.60 0.47 0.66 0.62 0.69 0.91
(a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy?
shows a reasonable linear relationship.
O No, a scatter plot does not show a reasonable linear relationship.
(b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.)
(c) The investigators were particularly interested in…
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm2 for the
modified mortar (m = 42) and y = 16.86 kgf/cm for the unmodified mortar (n = 30). Let µ1 and Hz be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions
are both normal.
(a) Assuming that o1 = 1.6 and o2 = 1.3, test Ho: µ1 - 42 = 0 versus H3: µ1 – 42 > 0 at level 0.01.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z =
P-value =
State the conclusion in the problem context.
Fail to reject Ho: The data does not suggest that the difference in average tension bond strengths exceeds from 0.
o Reject Ho: The data does not suggest that the difference in average tension bond…
Chapter 13 Solutions
Probability and Statistics for Engineering and the Sciences
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
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- 17.7 Butterfly wings. Researchers studied the morphological attributes of monarch butterflies (Danaus plexippus), a species that undertakes large seasonal migrations over North America. They measured the forewing weight (in milligrams, mg) of a sample of 92 monarch butterflies, all of which had been reared in captivity in identical conditions.° Figure 17.4 shows the output from the statistical software JMP. (The data are also available in the Large.Butterfly the data file if you wish to practice working with your own software.) Estimate with 95% confidence the mean forewing weight of monarch butterflies reared in captivity. Follow the four- step process as illustrated in Example 17.2. 4 STEP そMP FWweight 30 25 20 15 10 11 12 13 14 15 8 9 10 Summary Statistics Mean 11.795652 Std Dev 1.1759413 Std Err Mean 0.1226004 Upper 95% Mean Lower 95% Mean 1 FIGURE 17.4 Software output (JMP) for the forewing weight of monarch 12.039183 11.552122 92 N. butterflies. Countarrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.13 kgf/cm? for the modified mortar (m = 42) and y = 16.85 kgf/cm2 for the unmodified mortar (n = 32). Let u, and u, be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o, = 1.6 and o, = 1.3, test Ho: 4, - H, = 0 versus H: u, - µ, > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) z = 3.80 P-value = 0.0001 State the conclusion in the problem context. O Fail to reject H,. The data suggests that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho: The data does not suggest that the difference in average…arrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.19 kgf/cm? for the modified mortar (m = 42) and y = 16.85 kgf/cm? for the unmodified mortar (n = 30). Let u, and u, be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. Assuming that o, = 1.6 and o, = 1.3, test Hn: 4, - H, = 0 versus H: u, - u, > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value = Compute the probability of a type II error for the test of part (a) when 4 - Hz = 1. (Round your answer to four decimal places.) Suppose the investigator decided to use a level 0.05 test and vwished B = 0.10 when u, - uz = 1. If m = 42, what value of n…arrow_forward
- Mist (airborne droplets or aerosols) is generated when metal-removing fluids are used in machining operations to cool and lubricate the tool and workpiece. Mist generation is a concern to OSHA, which has recently lowered substantially the workplace standard. An article gave the accompanying data on x = fluid-flow velocity for a 5% soluble oil (cm/sec) and y the extent of mist droplets having diameters smaller than 10 µm (mg/m³): 85 177 190 354 360 442 960 0.39 0.60 0.45 0.66 0.60 0.69 0.90 (a) The investigators performed a simple linear regression analysis to relate the two variables. Does a scatter plot of the data support this strategy? Yes, a scatter plot shows a reasonable linear relationship. No, a scatter plot does not show a reasonable linear relationship. (b) What proportion of observed variation in mist can be attributed to the simple linear regression relationship between velocity and mist? (Round your answer to three decimal places.) (c) The investigators were particularly…arrow_forwardEngineers at a large company are trying to investigate if there is any difference in the average wear of brand A, brand B or brand C tires for the company's new models. To help them arrive at a decision, an experiment is conducted using 11 of each brand. The tires are run until they wear out. The results ( in kilometres) are as follows: Brand A: xī = 37,900 S1 = 5100 Brand B: X2 = 39,800 S2 = 5900 Brand C: X3 =38,500 S3 = 5600arrow_forwardThe work produced by a constant temperature, pressure - volume thermodynamic process can be computed as (picture 1) where W is work, p is pressure, and V is volume. Use Simpson's rules to evaluate the work for the following data given in TABLE picture.arrow_forward
- An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsións have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm2 for the modified mortar (m = 42) and y = 16.88 kgf/cm2 for the unmodified mortar (n = 31). Let ₁ and ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: H₁ - H₂> 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…arrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm² for the modified mortar (m = 42) and y = 16.86 kgf/cm² for the unmodified mortar (n = 30). Let µ1 and uz be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o1 = 1.6 and o2 = 1.3, test Ho: H1 - 42 = 0 versus Ha: H1 - H2 > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = 3.854 P-value = 0.0001 State the conclusion in the problem context. Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. Reject Ho. The data does not suggest that the difference in average…arrow_forwardAn automotive engineer subjects a large number of brake pads to a stress test and measures the wear on each. She obtains Y the P-value for testing Ho: µ = 7.0 versus H1: µ#7.0. = 7.4 mm and or = 0.2 mm, Use this information to findarrow_forward
- 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.)arrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm² for the modified mortar (m = 42) and y = 16.85 kgf/cm² for the unmodified mortar (n = 32). Let μ₁ and ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that 0₁ = 1.6 and ₂ = 1.3, test Ho: M₁ M₂ = 0 versus Ha: M₁ M₂ > 0 at level 0.01. 1 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = 4.74 X P-value = State the conclusion in the problem context. Ⓒ Reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds…arrow_forwardIn rock blasting, the peak particle velocity (PPV) depends both on the distance from the blast and on the amount of charge. The article "Prediction of Particle Velocity Caused by Blasting for an Infrastructure Excavation Covering Granite Bedrock" (A. Kahriman, Mineral Resources Engineering, 2001:205-218) presents data on PPV, scaled distance (which is equal to the distance divided by the square root of the charge), and the amount of charge. The following table presents the values of PPV, scaled distance, and amount of charge for 15 blasts. Scaled Distance (m/kg0.5) PPV Amount of Charge (mm/s) (kg) 1.4 47.33 4.2 15.7 9.6 92.0 2.54 15.8 40.0 1.14 24.3 48.7 0.889 23.0 95.7 1.65 12.7 67.7 1.4 39.3 13.0 26.8 8.0 70.0 1.02 29.94 13.5 4.57 10.9 41.0 6.6 8.63 108.8 1.02 28.64 27.43 3.94 18.21 59.1 1.4 33.0 11.5 1.4 34.0 175.0 Fit the model In PPV = Bo + B1 In Scaled Distance + B2 In Charge + E. Compute the P- value for testing Ho : B¡ = 0 for Bo. B1, and Bz. b. The article claims that the…arrow_forward
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