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(d) Suppose it had previously been believed that when air void increased by 1 percent, the associated true average change in dielectric constant would be at least -0.055. 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. Ho: ₁-0.055 Ha:-0.055 O Ho: ₁-0.055 H:A-0.055 OH: A₁ = -0.055 H:A-0.055 OH:₁-0.055 H₂:₁ = -0.055 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value= State the conclusion in the problem context. O Reject Ho. There is insufficient evidence to contradict the prior belief. O Reject Ho. There is sufficient evidence to contradict the prior belief. O Fail to reject Ho. There is insufficient evidence to contradict the prior belief. O Fail to reject H. There is sufficient evidence to contradict the prior belief.

(d) Suppose it had previously been believed that when air void increased by 1 percent, the associated true average change in dielectric constant would be at least -0.055. 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. Ho: ₁-0.055 Ha:-0.055 O Ho: ₁-0.055 H:A-0.055 OH: A₁ = -0.055 H:A-0.055 OH:₁-0.055 H₂:₁ = -0.055 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value= State the conclusion in the problem context. O Reject Ho. There is insufficient evidence to contradict the prior belief. O Reject Ho. There is sufficient evidence to contradict the prior belief. O Fail to reject Ho. There is insufficient evidence to contradict the prior belief. O Fail to reject H. There is sufficient evidence to contradict the prior belief.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 32PPS
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(d) Suppose it had previously been believed that when air void increased by 1 percent, the associated true average change in dielectric constant would be at least -0.055. 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. Ho: P1-0.055 H:P <-0.055 Ho: P₁ = -0.055 H:A-0.055 OH: P₁= -0.055 H:A-0.055 ⒸHO: ₁-0.055 H: P, = -0.055 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value= State the conclusion in the problem context. O Reject Ho. There is insufficient evidence to contradict the prior belief. O Reject Ho. There is sufficient evidence to contradict the prior belief. O Fail to reject Ho. There is insufficient evidence to contradict the prior belief. O Fail to reject H. There is sufficient evidence to contradict the prior belief.
Transcribed Image Text:(d) Suppose it had previously been believed that when air void increased by 1 percent, the associated true average change in dielectric constant would be at least -0.055. 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. Ho: P1-0.055 H:P <-0.055 Ho: P₁ = -0.055 H:A-0.055 OH: P₁= -0.055 H:A-0.055 ⒸHO: ₁-0.055 H: P, = -0.055 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value= State the conclusion in the problem context. O Reject Ho. There is insufficient evidence to contradict the prior belief. O Reject Ho. There is sufficient evidence to contradict the prior belief. O Fail to reject Ho. There is insufficient evidence to contradict the prior belief. O Fail to reject H. There is sufficient evidence to contradict the prior belief.
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 Mixtures and Relationship with Density," was used to relate 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 The following R output is from a simple linear regression of y on x. Std. Error Estimate 4.858691 0.059768 -0.074676 0.009923 (Intercept) AirVoid Residual standard error: 0.03551 on 16 R-squared: 0.7797, F-statistic: 56.63 on 1 and 16 DF, Analysis of Variance Table Response: Dielectric. Df 1 Airvoid Residuals 16 Sum Sq 0.071422 0.20178 Mean Sq 0.071422 0.001261 t value. 81.283 -7.526 Pr (>|t|) <2e-16 1.21e-06 DF Multiple. Adjusted R-squared: 0.766 p-value: 1.214e-06 F value 56.635 Pr (>F) 1.214e-06
Transcribed Image Text: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 Mixtures and Relationship with Density," was used to relate 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 The following R output is from a simple linear regression of y on x. Std. Error Estimate 4.858691 0.059768 -0.074676 0.009923 (Intercept) AirVoid Residual standard error: 0.03551 on 16 R-squared: 0.7797, F-statistic: 56.63 on 1 and 16 DF, Analysis of Variance Table Response: Dielectric. Df 1 Airvoid Residuals 16 Sum Sq 0.071422 0.20178 Mean Sq 0.071422 0.001261 t value. 81.283 -7.526 Pr (>|t|) <2e-16 1.21e-06 DF Multiple. Adjusted R-squared: 0.766 p-value: 1.214e-06 F value 56.635 Pr (>F) 1.214e-06
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