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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:

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 38E
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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: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.)
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
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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