Concept explainers
The article “A Model of Pedestrians’ Waiting Times for Street Crossings at Signalized Intersections” (Transportation Research, 2013: 17–28) suggested that under some circumstances the distribution of waiting time X could be modeled with the following
a. Graph f (x; θ, 80) for the three cases θ = 4, 1, and .5 (these graphs appear in the cited article) and comment on their shapes.
b. Obtain the cumulative distribution
c. Obtain an expression for the
d. For the case θ = 4, τ = 80, calculate P(50 ≤ X ≤ 70) without at this point doing any additional
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Chapter 4 Solutions
Probability and Statistics for Engineering and the Sciences
- An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: ... x = Temperature (°C) | 1100 1200 1300 1100 1500 1200 1300 y = Porosity (%) 30.8 19.2 6 13.5 11.4 7.7 3.6 Find the least squares estimate of the slope. Input answers up to 5 decimal places. Slope = Blank 1 Blank 1 Add your answerarrow_forwardSuppose you are interested in the percentage of students who had burrito for lunch in your statistics class. There are a total of 120 students in your class. Instead of asking each student whether they had burrito for lunch, you randomly picked 36 students from the class and found that 11 students had burrito for lunch. Calculate a single value to estimate the parameter of interestarrow_forwardAssume you fit a logistic regression for binary Y [i.e., replace EY in linear regression by log(EY/(1- EY))=log(odds)]. Instructor claims: beta for the main effect is log(OR), and beta for interaction effect is log(ROR), where ROR denotes the ratio of the odds ratio. Explain your agreement or disagreement.arrow_forward
- The following table presents measurements of mean noise levels in dBA (y), roadway width in m (x1), and mean speed in km/h (x2), for 10 locations in Bangkok, Thailand, as reported in the article "Modeling of Urban Area Stop-and-Go Traffic Noise" (P. Pamanikabud and C. Tharasawatipipat, Journal of Transportation Engineering, 1999:152–159). y X1 X2 78.1 6.0 30.61 78.1 10.0 36.55 79.6 12.0 36.22 81.0 6.0 38.73 78.7 6.5 29.07 78.1 12.0 28.26 78.6 6.5 30.28 78.5 6.5 30.25 78.4 9.0 29.03 79.6 6.5 33.17 Construct a good linear model to predict mean noise levels using roadway width, mean speed, or both, as predictors. Provide the standard deviations of the coefficient estimates and the P-values for testing that they are different from 0. Explain how you chose your model.arrow_forwardAn article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: ... x = Temperature (°C) | 1100 1200 1300 1100 1500 1200 1300 y - Porosity (%) 30.8 19.2 6 13.5 11.4 7.7 3.6 Find an estimate of o2 Input answers up to two decimal places. o2= Blank 1arrow_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_forward
- 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, 34, 32, 27, 28, 32, 31, 35, 32, 28 OF: 19, 14, 21, 13, 12 Does the data suggest that true average maximum lean angle for older females (OF) is more than 10 degrees smaller than it is for younger females (YF)? State and test the relevant hypotheses at significance level 0.10. (Use ?1 for younger females and ?2 for older females.) H0: ?1 − ?2 = 10Ha: ?1 − ?2 > 10H0: ?1 − ?2 = 10Ha: ?1 − ?2 < 10 H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0 Calculate the test statistic and determine the P-value. (Round your test…arrow_forwardIf our data were a perfect fit to our regression model, such that y; = ŷ;, we would expect | to be in the CI on p.arrow_forwardAn article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: x = Temperature (°C)|1100 1200 1300 1100 1500 1200 1300 y = Porosity (%) 30.8 19.2 6 13.5 11.4 7.7 3.6 Find an estimate of o?arrow_forward
- An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: ... Temperature (°C) 1100 1200 1300 1100 1500 1200 1300 y - Porosity (%) 30.8 19.2 6 13.5 11.4 7.7 3.6 Find an estimate of o2 Input answers up to two decimal places. o2= Blank 1arrow_forward3. The mean hourly wage W (in dollars) of chemists in the United States from 2000 through 2014 can be modelled by W = 0.903t + 26.08, 0 sts 14 where t represents the year, t = 0 corresponding to 2000. (a) Based from the model, when was the mean hourly wage at least $30, but not more than $32? (b) Use the model to predict when the mean hourly wage will exceed $45 (Larson, 2018).arrow_forwardFind the median for each of the following pdfs: frV)=(0+1)y®, Osys1 for 0>0arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage