Introductory Combinatorics
5th Edition
ISBN: 9780134689616
Author: Brualdi, Richard A.
Publisher: Pearson,
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Chapter 1, Problem 16E
To determine
To show: The result of replacing every integer
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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 1 Solutions
Introductory Combinatorics
Ch. 1 - Prob. 1ECh. 1 - Prob. 2ECh. 1 - Imagine a prison consisting of 64 cells arranged...Ch. 1 - Verify that there is no magic square of order 2.
Ch. 1 - Use de la Loubère’s method to construct a magic...Ch. 1 - 12. Use de la Loubère’s method to construct a...Ch. 1 - Construct a magic square of order 6.
Ch. 1 - Show that the result of replacing every integer a...Ch. 1 - Let n be a positive integer divisible by 4, say n...Ch. 1 - Show that there is no magic cube of order 2.
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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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