Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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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
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1) Write the null hypothesis and the alternative hypothesis (for the factor).
2) Find the ANOVA table. (round to five decimal places).
3) What is your decision about the null hypothesis, consider ?.
4) If your decision in part (4) was reject , perform Tukey test to determine which pairwise means are…
The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of
steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens.
TOST
4200
3600
3750
3650
4050
2795
RBOT
370
340
375
310
350
205
TOST
4870
4500
3450
2700
3750
3275
RBOT
400
375
285
225
345
290
(a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.)
The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens.
TOST
4200
3600
3750
3650
4050
2770
RBOT
370
345
375
315
350
205
TOST
4870
4525
3450
2700
3750
3325
RBOT
400
380
285
220
345
290
(a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.)
r =
Carry out a test of hypotheses to decide whether RBOT Time and TOST time are linearly related. (Use
? = 0.05.)
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t
=
P-value
=
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
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