determining characteristics of pavement. The propagation of electromagnetic waves through
Electromagnetic technologies offer effective nondestructive sensing techniques for determining characteristics of pavement. The propagation of electromagnetic waves through the
material depends on its dielectric properties. The following data, kindly provided by the authors
of the article “Dielectric Modeling of Asphalt Mixtures and Relationship with Density” (J. of
Transp. Engr., 2011: 104–111), was used to relate y = dielectric constant to x = air void (%) for
18 samples having 5% asphalt content:
y <- c(4.55, 4.49, 4.50, 4.47, 4.47, 4.45, 4.40, 4.34, 4.43, 4.43, 4.42, 4.40, 4.33, 4.44, 4.40, 4.26, 4.32, 4.34)
x <- c(4.35, 4.79, 5.57, 5.20, 5.07, 5.79, 5.36, 6.40, 5.66, 5.90, 6.49, 5.70, 6.49, 6.37, 6.51, 7.88, 6.74, 7.08)
(a) Obtain the equation of the least squares line and interpret its slope.
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(b) What proportion of observed variation in dielectric constant can be attributed to the approximate linear relationship between dielectric constant and air void.
(c) Does there appear to be a useful linear relationship between dielectric constant and air void?
State and test the appropriate hypotheses.
(d) Suppose it had previously been believed that when air void increased by 1 percent, the
associated true average change in dielectric constant would be at least -0.05. Does the sample
data contradict this belief? Carry out a test of appropriate hypotheses using a significance
level of .01
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