2. (-/12 Points] DETAILS DEVORESTAT9 12.E.034 MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER istorie Links ly Writing A statistical program is recommended. 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 Matures and Relationship with Density," was used to relate y - dielectric constant to war vold (M) for 18 samples having 5 asphalt content. y 4.55 4.49 4.50 447 4.47 4.45 4.40 4.34 443 443 4.42 4.40 4.33 444 4.40 4.26 4.32 4.34 * 4.35 4.79 5.57 5.20 5.07 5.79 5.36 6.40 5.66 5.90 649 5.70 6.49 6.37 6.51 7.88 6.74 7.08 or get textbo The following Routput is from a simple linear regression of yon rter dard ship Estimate StdKerr t value Pr(t) (Intercept) 4.858691 0.059760 81.283 P) Airvoid 1 0.071422 0.071422 56.635 1.214-06 Residuals 16 0.20178 0.001261 (a) Obtain the equation of the least squares line. (Enter your numerical values to six decimal places.) aper ons of source ya Interpret the slope of the equation of the least squares ine. According to the slope, a one-percentage-point increase in air void is associated with an estimated -- in dielectric constant of ---Select- (b) What percentage of observed variation in dielectric constant can be attributed to the approximate linear relationship betiveen dielectric constant and air vold? (Round your answer to two decimal places.) (c) Does there appear to be a useful linear relationship between dielectric constant and air vold? Carry out a test of appropriate hypotheses using a significance level of 0.01 State the appropriate null and alternative hypotheses. Hi-0 W, 8 + 0 Mo: 8,0 M: B. - 0 Hoi,oo Hi, co Mo:, -0 H; B, > 0 Find the test statistic value and find the value. (Round your test statistic to two decimal places and your P value to three decimal places.) t- R.value State the conclusion in the problem context. Reject H. There is a useful linear relationship between dielectric constant and air vold percentage. Reject Ho. There is not a useful linear relationship between dielectric constant and air void percentage. Fail to reject My. There is not a useful linear relationship between dielectric constant and air vold percentage. Fail to reject Ho. There is a useful linear relationship between dielectric constant and air vold percentage. (d) Suppose it had previously been believed that when air vold increased by 1 percent, the associated true average change in dielectric constant would be at least -0.056. Does the sample data contradict this belief? Carry out a test of appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. My: B. - -0.056 H, B, > -0.056 Ho: B. - -0.056 HB, -0.056 HO: B. - -0.056 HiB, P) Airvoid 1 0.071422 0.071422 56.635 1.214-06 Residuals 16 0.20178 0.001261 (a) Obtain the equation of the least squares line. (Enter your numerical values to six decimal places.) aper ons of source ya Interpret the slope of the equation of the least squares ine. According to the slope, a one-percentage-point increase in air void is associated with an estimated -- in dielectric constant of ---Select- (b) What percentage of observed variation in dielectric constant can be attributed to the approximate linear relationship betiveen dielectric constant and air vold? (Round your answer to two decimal places.) (c) Does there appear to be a useful linear relationship between dielectric constant and air vold? Carry out a test of appropriate hypotheses using a significance level of 0.01 State the appropriate null and alternative hypotheses. Hi-0 W, 8 + 0 Mo: 8,0 M: B. - 0 Hoi,oo Hi, co Mo:, -0 H; B, > 0 Find the test statistic value and find the value. (Round your test statistic to two decimal places and your P value to three decimal places.) t- R.value State the conclusion in the problem context. Reject H. There is a useful linear relationship between dielectric constant and air vold percentage. Reject Ho. There is not a useful linear relationship between dielectric constant and air void percentage. Fail to reject My. There is not a useful linear relationship between dielectric constant and air vold percentage. Fail to reject Ho. There is a useful linear relationship between dielectric constant and air vold percentage. (d) Suppose it had previously been believed that when air vold increased by 1 percent, the associated true average change in dielectric constant would be at least -0.056. Does the sample data contradict this belief? Carry out a test of appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. My: B. - -0.056 H, B, > -0.056 Ho: B. - -0.056 HB, -0.056 HO: B. - -0.056 HiB,