Polyester fiber ropes are increasingly being used as components of mooring lines for offshore structures in deep water. The authors of the paper “Quantifying the Residual Creep Life of Polyester Mooring Ropes” (Intl. J. of Offshore and Polar Exploration, 2005: 223–228) used the accompanying data as a basis for studying how time to failure (hr) depended on load (% of breaking load):
X | 77.7 | 77.8 | 77.9 | 77.8 | 85.5 | 85.5 |
y | 1 5.067 | 552.056 | 127.809 | 7.611 | .124 | .077 |
X | 89.2 | 89.3 | 73.1 | 85.5 | 89.2 | 85.5 |
y | .008 | .013 | 49.439 | .503 | .362 | 9.930 |
x | 89.2 | 85.5 | 89.2 | 82.3 | 82.0 | 82.3 |
y | .677 | 5.322 | .289 | 53.079 | 7.625 | 155.299 |
A linear regression of log(time) versus load was fit. The investigators were particularly interested in estimating the slope of the true regression line relating these variables. Investigate the quality of the fit, estimate the slope, and predict time to failure when load is 80, in a way that conveys information about reliability and precision
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Chapter 13 Solutions
Probability and Statistics for Engineering and the Sciences
- The depth of wetting of a soil is the depth to which water content will increase owing to extemal factors. The article "Discussion of Method for Evaluation of Depth of Wetting in Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of wetting beneath a structure and the age of the structure. The article presents measurements of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the following table. Age Depth 7.6 4 4.6 6.1 9.1 3 4.3 7.3 5.2 10.4 15.5 5.8 10.7 4 5.5 6.1 10.7 10.4 4.6 7.0 6.1 14 16.8 10 9.1 8.8 Compute the least-squares line for predicting depth of wetting (y) from age (x). b. Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point. Identify another point which can be classified as an outlier. Compute the least-squares line that results from deletion of the outlier,…arrow_forwardAs the population ages, there is increasing concern about accident-related injuries to the elderly. An article 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: 28, 34, 32, 27, 28, 32, 31, 35, 32, 28 OF: 19, 14, 21, 13, 12 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value =arrow_forwardSolve An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp.59-75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. Test that the average interior temperature is equal to 22.5°C using alpha (a) = 0.05. 1.)This problem is a test on what population parameter? a.Variance/ Standard Deviation b.Mean c.Population Proportion d.None of the above 2.)What is the null and alternative 3 points hypothesis? a.Ho / (theta = 22.5) , Ha: (0 # 22.5) b.Ho / (theta > 22.5) , Ha: (0 # 22.5) c.Ho / (theta < 22.5) , Ha: (theta >= 22.5) d.None of the above 3.)What are the Significance level 3 points and type of test? alpha = 0.05 two-tailed alpha = 0.95 two-tailed alpha = 0.95 one-tailed None of the above 4.)What standardized test statistic will…arrow_forward
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- As the population ages, there is increasing concern about accident-related injuries to the elderly. An article 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: 28, 35, 33, 27, 28, 32, 31, 35, 32, 25 OF: 17, 15, 21, 13, 12arrow_forwardNW 6.12 CORPORATE SUSTAINABILITY OF CPA FIRMS. Corporate sustainability refers to business practices designed CORSUS around social and environmental considerations. Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.23 (p. 59). Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992 senior managers at CPA firms. Higher point values indicate a higher level of support for sustainability. The accompanying StatCrunch printout gives a 99% confidence interval for the mean level of support for all senior managers at CPA firms. One sample T confidence interval: μ: Mean of variable 99% confidence interval results: Variable Sample Mean Std. Err. DF L. Limit U. Limit Support 67.75504 0.85314633 991 65.553241 69.95684 a. Locate the 99% confidence interval on the printout. b. Use the sample mean and standard deviation on the…arrow_forwardThe article "Earthmoving Productivity Estimation Using Linear Regression Techniques" (S. Smith, Journal of Construction Engineering and Management, 1999:133–141) presents the following linear model to predict earth-moving productivity (in m3 moved per hour): Productivity = - 297.877 + 84.787x, + 36.806x, + 151.680x, – 0.081x, – 110.517x5 - 0.267.x, – 0.016x,x, +0.107.x,x5 + 0.0009448x,x, – 0.244x;x, where X1 = number of trucks X2 = number of buckets per load X3 = bucket volume, in m³ X4 = haul length, in m X5 = match factor (ratio of hauling capacity to loading capacity) X6 = truck travel time, in s If the bucket volume increases by 1 m², while other independent variables are unchanged, can you determine the change in the predicted productivity? If so, determine it. If not, state what other information you would need to determine it. b. If the haul length increases by 1 m, can you determine the change in the predicted productivity? If so, determine it. If not, state what other…arrow_forward
- The article “‘Little Ice Age’ Proxy Glacier Mall Balance Records Reconstructed from Tree Rings in the Mt. Waddington Area, British Columbia Coast Mountains, Canada” (S. Larocque and D. Smith, The Holocene, 2005:748–757) evaluates the use of tree ring widths to estimate changes in the masses of glaciers. For the Sentinel glacier, the net mass balance (change in mass between the end of one summer and the end of the next summer) was measured for 23 years. During the same time period, the tree ring index for white bark pine trees was measured, and the sample correlation between net mass balance and tree ring index was r = −0.509. Can you conclude that the population correlation ρ differs from 0?arrow_forwardAn article in the journal Air and Waste (Update on Ozone Trends in California's South Coast Air Basin, Vol. 43, 1993) investigated the ozone levels in the South Coast Air Basin of California for the years 1976-1991. The author believes that the number of days the ozone levels exceeded 0.20 ppm (the response) depends on the seasonal meteorological index, which is the seasonal average 850-millibar Temperature (the predictor). The following table gives the data. Year Index 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 Days 91 105 106 108 88 91 58 82 81 65 61 48 61 43 33 36 16.7 17.1 18.2 18.1 17.2 18.2 16.0 17.2 18.0 17.2 16.9 17.1 18.2 17.3 17.5 16.6 (a) Construct a scatter diagram of the data. (b) Estimate the prediction equation. (c) Test for significance of regression. (d) Calculate the 95% CI and PI on for a seasonal meteorological index value of 17. Interpret these quantities.arrow_forwardThe article "Modeling of Urban Area Stop-and-Go Traffic Noise" (P. Pamanikabud and C. Tharasawatipipat, Journal of Transportation Engineering, 1999:152–159) presents measurements of traffic noise, in dBA, from 10 locations in Bangkok, Thailand. Measurements, presented in the following table, were made at each location, in both the acceleration and deceleration lanes. Location Acceleration Deceleration 78.1 78.6 78.1 80.0 3 79.6 79.3 4 81.0 79.1 78.7 78.2 78.1 78.0 78.6 78.6 78.5 78.8 78.4 78.0 10 79.6 78.4 Can you conclude that there is a difference in the mean noise levels between acceleration and deceleration lanes?arrow_forward
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