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. Th following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relations with Density," was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt conte x 4.35 4.75 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 7.14 y 4.55 4.49 4.50 4.47 4.48 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.35|4.44 4.40 4.26 4.32 4.34 (a) Determine the slope and intercept of the estimated regression line. (Round your answers to 5 decimal places, if needed.) slope:
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. Th following data, kindly provided by the authors of the article "Dielectric Modeling of Asphalt Mixtures and Relations with Density," was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt conte x 4.35 4.75 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 7.14 y 4.55 4.49 4.50 4.47 4.48 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.35|4.44 4.40 4.26 4.32 4.34 (a) Determine the slope and intercept of the estimated regression line. (Round your answers to 5 decimal places, if needed.) slope:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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," was used to relate y = dielectric constant to x = air void (%) for 18 samples having 5% asphalt content.
x 4.35 4.75 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 7.14
y 4.55 4.49 4.50 4.47 4.48 4.45 4.40 4.34 4.43 4.43 4.42 4.40 4.35 4.44 4.40 4.26 4.32 4.34
(a) Determine the slope and intercept of the estimated regression line. (Round your answers to 5 decimal places, if
needed.)
slope:
intercept:
Interpret the slope.
According to the slope, a one-percentage-point increase in air void is associated with an estimated increase + in
dielectric constant of 0
(b) Does there appear to be a useful linear relationship between dielectric constant and air void? Carry out a test of
appropriate hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses.
O Họ: B1 + 0 vs. HA: B1 = 0
O Ho: B1 = 0 vs. H4: B1 > 0
O Ho: B1 = 0 vs. HẠ: B1 < 0
O Họ: B1 = 0 vs. HA: B1 ± 0
The test statistic is
(Round your answer to 3 decimal places, if needed.)
Transcribed Image Text:The test statistic is
(Round your answer to 3 decimal places, if needed.)
Using the appropriate statistical table, the p-value range is (0.002, 0.01) +
Based on the p-value, reject
+ the null hypothesis. This data provides
• sufficient evidence to
conclude that the slope is less than
zero.
(c) Suppose it had previously been believed that when air void increased by 1 percent, the associated true average
change in dielectric constant would be less than -0.064. Does the sample data support this belief? Carry out a test of
appropriate hypotheses using a significance level of 0.05. State the appropriate null and alternative hypotheses.
O Ho: B1 = -0.064 vs. H4: B1 + -0.064
O Ho: B1 + -0.064 vs. HA: B1 = -0.064
O Ho: B1 < -0.064 vs. Ha: B1 > -0.064
O Ho: B1 2 -0.064 vs. HA: B1 < -0.064
The test statistic is
(Round your answer to 3 decimal places, if needed.)
Using the appropriate statistical table, the p-value range is (0.01, 0.025)
Based on the p-value, fail to reject + the null hypothesis. This data does not provide +
sufficient evidence to
conclude that the slope is less than
+ -0.064.
Check
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