Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 5.1, Problem 11E
Find a second-order formula for approximating
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Answer questions 8.3.3 and 8.3.4 respectively
8.3.4 .WP An article in Medicine and Science in Sports and
Exercise [“Electrostimulation Training Effects on the Physical Performance of Ice Hockey Players” (2005, Vol. 37, pp.
455–460)] considered the use of electromyostimulation (EMS) as
a method to train healthy skeletal muscle. EMS sessions consisted of 30 contractions (4-second duration, 85 Hz) and were carried
out three times per week for 3 weeks on 17 ice hockey players.
The 10-meter skating performance test showed a standard deviation of 0.09 seconds. Construct a 95% confidence interval of the
standard deviation of the skating performance test.
8.6.7 Consider the tire-testing data in Exercise 8.2.3. Compute a 95% tolerance interval on the life of the tires that has confidence level 95%. Compare the length of the tolerance interval with the length of the 95% CI on the population mean. Which interval is shorter? Discuss the difference in interpretation of these two intervals.
8.6.2 Consider the natural frequency of beams described in
Exercise 8.2.8. Compute a 90% prediction interval on the
diameter of the natural frequency of the next beam of this type
that will be tested. Compare the length of the prediction interval
with the length of the 90% CI on the population mean.
8.6.3 Consider the television tube brightness test described in
Exercise 8.2.7. Compute a 99% prediction interval on the brightness of the next tube tested. Compare the length of the prediction
interval with the length of the 99% CI on the population mean.
Chapter 5 Solutions
Numerical Analysis
Ch. 5.1 - Use the two-point forward-difference formula to...Ch. 5.1 - Use the three-point centered-difference formula to...Ch. 5.1 - Use the two-point forward-difference formula to...Ch. 5.1 - Carry out the steps of Exercise 3, using the...Ch. 5.1 - Use the three-point centered-difference formula...Ch. 5.1 - Use the three-point centered-difference formula...Ch. 5.1 - Develop a formula for a two-point...Ch. 5.1 - Prove the second-order formula for the first...Ch. 5.1 - Develop a second-order formula for the first...Ch. 5.1 - Find the error term and order formula for the...
Ch. 5.1 - Find a second-order formula for approximating by...Ch. 5.1 - (a) Compute the two-point forward-difference...Ch. 5.1 - Develop a second-order method for approximating ...Ch. 5.1 - Extrapolate the formula developed in Exercise...Ch. 5.1 - Develop a first-order method for approximating ...Ch. 5.1 - Apply extrapolation to the formula developed in...Ch. 5.1 - Develop a second-order method for approximating ...Ch. 5.1 - Find, an upper bound for the error of the machine...Ch. 5.1 - Prove the second-order formula for the third...Ch. 5.1 - Prove the second-order formula for the third...Ch. 5.1 - Prob. 21ECh. 5.1 - This exercise justifies the beam equations (2.33)...Ch. 5.1 - Use Taylor expansions to prove that (5.16) is a...Ch. 5.1 - Prob. 24ECh. 5.1 - Investigate the reason for the name extrapolation....Ch. 5.1 - Make a table of the error of the three-point...Ch. 5.1 - Make a table and plot of the error of the...Ch. 5.1 - Make a table and plot of the error of the...Ch. 5.1 - Prob. 4CPCh. 5.1 - Prob. 5CPCh. 5.2 - Apply the composite Trapezoid Rule with , , and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, , and 4...Ch. 5.2 - Apply the composite Simpson’s Rule with, 2, and 4...Ch. 5.2 - Apply the composite Simpson’s Rule with, 2, and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, 2, and 4...Ch. 5.2 - Apply the Composite Midpoint Rule with, 2, and 4...Ch. 5.2 - Prob. 7ECh. 5.2 - Apply the open Newton-Cotes Rule (5.28) to...Ch. 5.2 - Apply Simpson’s Rule approximation to, and show...Ch. 5.2 - Integrate Newton’s divided-difference...Ch. 5.2 - Find the degree of precision of the following...Ch. 5.2 - Prob. 12ECh. 5.2 - Develop a composite version of the rule (5.28),...Ch. 5.2 - Prove the Composite Midpoint Rule (5.27).
Ch. 5.2 - Find the degree of precision of the degree four...Ch. 5.2 - Use the fact that the error term of Boole’s Rule...Ch. 5.2 - Prob. 17ECh. 5.2 - Prob. 1CPCh. 5.2 - Prob. 2CPCh. 5.2 - Prob. 3CPCh. 5.2 - Prob. 4CPCh. 5.2 - Prob. 5CPCh. 5.2 - Prob. 6CPCh. 5.2 - Apply the Composite Midpoint Rule to the improper...Ch. 5.2 - The arc length of the curve defined by from to ...Ch. 5.2 - Prob. 9CPCh. 5.2 - Prob. 10CPCh. 5.3 - Apply Romberg Integration to find for the...Ch. 5.3 - Apply Romberg Integration to find for the...Ch. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prove formula (5.31).
Ch. 5.3 - Prove formula (5.35).
Ch. 5.3 - Use Romberg Integration approximation to...Ch. 5.3 - Use Romberg Integration to approximate the...Ch. 5.3 - (a) Test the order of the second column of Romberg...Ch. 5.4 - Apply Adaptive Quadrature by hand, using the...Ch. 5.4 - Apply Adaptive Quadrature by hand, using Simpson’s...Ch. 5.4 - Prob. 3ECh. 5.4 - Develop an Adaptive Quadrature method for rule...Ch. 5.4 - Use Adaptive Trapezoid Quadrature to approximate...Ch. 5.4 - Modify the MATLAB code for Adaptive Trapezoid Rule...Ch. 5.4 - Carry out the steps of Computer Problem 1 for...Ch. 5.4 - Carry out the steps of Computer Problem 1 for the...Ch. 5.4 - Carry out the steps of Computer Problem 1 for the...Ch. 5.4 - Use Adaptive Trapezoid Quadrature to approximate...Ch. 5.4 - Carry out the steps of Problem 6, using Adaptive...Ch. 5.4 - The probability within standard deviations of the...Ch. 5.4 - Write a MATLAB function called myerf.m that uses...Ch. 5.5 - Approximate the integrals, using Gaussian...Ch. 5.5 - Prob. 2ECh. 5.5 - Approximate the integrals in Exercise 1, using ...Ch. 5.5 - Change variables, using the substitution (5.46) to...Ch. 5.5 - Approximate the integrals in Exercise 4, using ...Ch. 5.5 - Approximate the integrals, using Gaussian...Ch. 5.5 - Prob. 7ECh. 5.5 - Find the Legendre polynomials up to degree 3 and...Ch. 5.5 - Prob. 9ECh. 5.5 - Verify the coefficients and in Table 5.1 for...Ch. 5.5 - Write a MATLAB function that uses Adaptive...Ch. 5.5 - Write a program that, for any input between 0 and...Ch. 5.5 - Equipartition the path of Figure 5.6 into ...Ch. 5.5 - Prob. 4SACh. 5.5 - Prob. 5SACh. 5.5 - Prob. 6SACh. 5.5 - Write a program that traverses the path according...
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- Answer question S8 stepwisearrow_forwardAnswer questions 8.2.11 and 8.2.12 respectivelyarrow_forward8.4.2 An article in Knee Surgery, Sports Traumatology, Arthroscopy [“Arthroscopic Meniscal Repair with an Absorbable Screw: Results and Surgical Technique” (2005, Vol. 13, pp. 273–279)] showed that only 25 out of 37 tears (67.6%) located between 3 and 6 mm from the meniscus rim were healed. a. Calculate a two-sided 95% confidence interval on the proportion of such tears that will heal. b. Calculate a 95% lower confidence bound on the proportion of such tears that will heal. 8.4.3 An article in the Journal of the American Statistical Association [“Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling” (1990, Vol. 85, pp. 972–985)] measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats. a. Calculate a 95% two-sided confidence interval on the true proportion of rats that would show underweight from the experiment. b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95%…arrow_forward
- 8.4.8 Use the data from Exercise 8.4.2 to compute the two-sided Agresti-Coull CI on the proportion of tears that heal. Compare and discuss the relationship of this interval to the one computed in Exercise 8.4.2.arrow_forwardAnswer questions 8.3.7 and 8.4.1 respectivelyarrow_forwardDon't do 14. Please solve 19arrow_forward
- 8.4.7 Use the data from Exercise 8.4.5 to compute the two-sided Agresti-Coull CI on the proportion of digits read correctly. Compare and discuss the relationship of this interval to the one computed in Exercise 8.4.5.arrow_forward8.6.5 Consider the fuel rod enrichment data described in Exercise 8.2.11. Compute a 90% prediction interval on the enrichment of the next rod tested. Compare the length of the prediction interval with the length of the 99% CI on the population mean.arrow_forward8.4.4 The Arizona Department of Transportation wishes to survey state residents to determine what proportion of the population would like to increase statewide highway speed limits from 65 mph to 75 mph. How many residents does the department need to survey if it wants to be at least 99% confident that the sample proportion is within 0.05 of the true proportion? 8.4.5 The U.S. Postal Service (USPS) has used optical character recognition (OCR) since the mid-1960s. In 1983, USPS began deploying the technology to major post offices throughout the country (www.britannica.com). Suppose that in a random sample of 500 handwritten zip code digits, 466 were read correctly. a. Construct a 95% confidence interval for the true proportion of correct digits that can be automatically read. b. What sample size is needed to reduce the margin of error to 1%? c. How would the answer to part (b) change if you had to assume that the machine read only one-half of the digits correctly?arrow_forward
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