Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 9.2, Problem 28E
As the population ages, there is increasing concern about accident-related injuries to the elderly. The article “Age and Gender Differences in Single-Step Recovery from a Forward Fall” (J. of Gerontology, 1999: M44–M50) reported on an experiment in which the maximum lean angle—the farthest a subject is able to lean and still recover in one step—was determined for both a sample of younger females (21–29 years) and a sample of older females (67–81 years). The following observations are consistent with summary data given in the article:
| YF: | 29. | 34, | 33. | 27, | 28, 32, 31, 34, 32, 27 |
| OF: | 18, | 15, | 23, | 13, | 12 |
Does the data suggest that true average maximum lean angle for older females is more than 10 degrees smaller than it is for younger females? State and test the relevant hypotheses at significance level .10.
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A researcher hypothesizes that in a certain country the net annual growth of private sector purchases of government bonds, B, is positively related to the nominal rate of interest on the bonds, NI, and negatively related to the rate of inflation Π:
Bt = a0 + a1NIt + a2Π t + ut
Note that it may be hypothesized that B depends on the real rate of interest on bonds, R, where R = NI – Π.
Using a sample of 56 annual observations, s/he estimates the following equations:
(1) Bt = 0.43 + 0.90NIt - 0.97Πt R21 = 0.962, SSR1 = 2.20, QRESET(F1,52) = 16.6
(3.58) (8.80) (-1.05)
(2) Bt = 0.44 + 0.94Rt R22 = 0.960, SSR2 = 2.22, QRESET(F1,53) = 0.9
(9.70) (16.7)
(3) Bt = 0.44 + 1.14NIt SSR3 = 9.20, QRESET(F1,53) = 59.9
(8.84) (36.1)
(4) NIt = 0.08 + 0.94Πt R24 = 0.997, SSR4 = 0.18, QRESET(F1,53) = 1.4…
A study is made for a particular allergy medication in order to determine the length of relief it provides Y (in hours) in relation to the dosage of medication X (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off.
Patient
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10
Dosage (x)
Relief Hours (y)
3 3.5 4 5 6 6.5 7 8 8.5 9
9.1 5.5 12.3 9.2 14.2 16.8 22.0 18.3 24.5 22.7
(i) Draw a scatter diagram.
(ii) Calculate the product moment correlation coefficient and comment on your answer.
(iii) Construct the least squares regression line.
The article “Withdrawal Strength of Threaded Nails” (D. Rammer, S. Winistorfer, and D. Bender, Journal of Structural Engineering 2001:442–449) describes an experiment comparing the ultimate withdrawal strengths (in N/mm) for several types of nails. For an annularly threaded nail with shank diameter 3.76 mm driven into spruce-pine-fir lumber, the ultimate withdrawal strength was modeled as lognormal with μ = 3.82 and σ = 0.219. For a helically threaded nail under the same conditions, the strength was modeled as lognormal with μ = 3.47 and σ = 0.272. a) What is the mean withdrawal strength for annularly threaded nails? b) What is the mean withdrawal strength for helically threaded nails? c) For which type of nail is it more probable that the withdrawal strength will be greater than 50 N/mm? d) What is the probability that a helically threaded nail will have a greater withdrawal strength than the median for annularly threaded nails? e) An experiment is performed in which withdrawal…
Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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