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.
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 |
(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.
The test statistic is . (Round your answer to 3 decimal places, if needed.)
Using the appropriate statistical table, the p-value
Based on the p-value, the null hypothesis. This data sufficient evidence to conclude that the slope is 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.
The test statistic is . (Round your answer to 3 decimal places, if needed.)
Using the appropriate statistical table, the p-value range is .
Based on the p-value, the null hypothesis. This data sufficient evidence to conclude that the slope is ? -0.064.
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