*y*= dielectric constant to

*x*= air void (%) for 18 samples having 5% asphalt content.

y |
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 |
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 |

*y*on

*x*.

Estimate | Std. Error | t value | Pr(>|t|) | |
---|---|---|---|---|

(Intercept) | 4.858691 | 0.059768 | 81.283 | <2e-16 |

AirVoid | −0.074676 | 0.009923 | −7.526 | 1.21e-06 |

Residual standard error: 0.03551 on 16 DF Multiple | ||||

R-squared: 0.7797, | Adjusted R-squared: 0.766 | |||

F-statistic: 56.63 on 1 and 16 DF, | p-value: 1.214e-06 |

Response: Dielectric | |||||

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |
---|---|---|---|---|---|

Airvoid | 1 | 0.071422 | 0.071422 | 56.635 | 1.214e-06 |

Residuals | 16 | 0.20178 | 0.001261 |

*H*

_{0}: β

_{1}≠ 0

*H*

_{a}: β

_{1}= 0

*H*

_{0}: β

_{1}= 0

*H*

_{a}: β

_{1}> 0

*H*

_{0}: β

_{1}= 0

*H*

_{a}: β

_{1}< 0

*H*

_{0}: β

_{1}= 0

*H*

_{a}: β

_{1}≠ 0

*P*-value. (Round your test statistic to two decimal places and your

*P*-value to three decimal places.)

*t*=

*P*-value=

*H*

_{0}. There is a useful linear relationship between dielectric constant and air void percentage.Reject

*H*

_{0}. There is not a useful linear relationship between dielectric constant and air void percentage. Fail to reject

*H*

_{0}. There is not a useful linear relationship between dielectric constant and air void percentage.Fail to reject

*H*

_{0}. There is a useful linear relationship between dielectric constant and air void percentage.

*H*

_{0}: β

_{1}= −0.061

*H*

_{a}: β

_{1}> −0.061

*H*

_{0}: β

_{1}= −0.061

*H*

_{a}: β

_{1}< −0.061

*H*

_{0}: β

_{1}≠ −0.061

*H*

_{a}: β

_{1}= −0.061

*H*

_{0}: β

_{1}= −0.061

*H*

_{a}: β

_{1}≠ −0.061

*P*-value. (Round your test statistic to two decimal places and your

*P*-value to three decimal places.)

*t*=

*P*-value=

*H*

_{0}. There is insufficient evidence to contradict the prior belief.

*H*

_{0}. There is sufficient evidence to contradict the prior belief.

*H*

_{0}. There is insufficient evidence to contradict the prior belief.

*H*

_{0}. There is sufficient evidence to contradict the prior belief.

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