Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.3, Problem 42E
Verify that if each xi is multiplied by a positive constant c and each yi is multiplied by another positive constant d, the t statistic for testing H0: β1 = 0 versus Ha: β1 ≠ 0 is unchanged in value (the value of
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Some people don't gain weight even when they overeat. Perhaps fidgeting and other “nonexercise activity"
(NEA) explains why – the body might spontaneously increase nonexercise activity when fed more. Researchers
deliberately overfed 16 healthy young adults for 8 weeks. They measured fat gain (y, in kilograms) and increase
in energy use (NEA) (x, in calories), as an explanatory variable, from activity other than deliberated exercise –
fidgeting, daily living, and the like. Here are the data (sorted by NEA):
NEA increase
-94
-57
-29 135
143
151
245 355
620 690
Fat gain
4.2
3.0
3.7 2.7
3.2
3.6
2.4
1.3
2.3
1.1
Assume that the model Fat gain= Bo +B,NEA increase +ɛ is reasonable. Selected SAS output are given here.
0.73985 R-Square 0.6061
2.38750 Adj R-Sq 0.5780
Root MSE
Dependent Mean
Coeff Var
30.98860
Parameter Estimates
Variable
DF
Parameter Estimate
Standard Error
t Value
Pr > It|
Intercept
1
3.50512
0.30362
11.54
<.0001
1
-0.00344
0.00074141
-4.64
0.0004
nea
(a) Find the average fat…
A large national bank charges local companies for using its services. A bank official reported the results of a regression analysis designed to predict the bank's charges (y), measured in dollars per month, for services rendered to local companies. One independent variable used to predict the service charge to a company is the company's sales revenue (x), measured in Data for 21 companies who use the bank's services were used to fit the model
E(y) = β0 + β1x.
The results of the simple linear regression are provided below. = 2,700 + 20xInterpret the estimate of β0, the y-intercept of the line.
For every $1 million increase in sales revenue, we expect a service charge to increase $2,700.
All companies will be charged at least $2,700 by the bank.
There is no practical interpretation since a sales revenue of $0 is a nonsensical value.
About 95% of the observed service charges fall within $2,700 of the least squares line.
A study reports data on the effects of the drug tamoxifen on change in the level of cortisol-binding globulin (CBG) of patients during treatment. With age = x and ACBG = y, summary
values are n = 26, Ex, = 1615, E(x, - x) = 3756.96, Ey, = 281.9, E(y, - v) = 465.34, and Exy, = 16,720.
(a) Compute a 90% CI for the true correlation coefficient p. (Round your answers to four decimal places.)
(b) Test H: p = -0.5 versus H: p < -0.5 at level 0.05.
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 Reject Ho. There is evidence that p < -0.5.
O Fail to reject Ho: There is evidence that p < -0.5.
O Fail to reject H. There is no evidence that p < -0.5.
O Reject H.. There is no evidence that p < -0.5.
(c) In a regression analysis of y on x, what proportion of variation in change of cortisol-binding globulin level could be explained by…
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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