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 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. H0: β1 = -0.064 vs. HA: β1 ≠ -0.064 H0: β1 ≠ -0.064 vs. HA: β1 = -0.064 H0: β1 ≤ -0.064 vs. HA: β1 > -0.064 H0: β1 ≥ -0.064 vs. HA: β1 < -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 . Based on the p-value, the null hypothesis. This data sufficient evidence to conclude that the slope is -0.064
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 |
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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