(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 -0.057. 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.O H.: B, = -0.057H.: A, > -0.057O H,: B, = -0.057H: B, = -0.057O H: B, = -0.057H: B, < -0.057O H: B, = -0.057H: 8, -0.057Compute 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.)P-value =State the conclusion in the problem context.O Reject H. There is insufficient evidence to contradict the prior belief.O Reject H. There is sufficient evidence to contradict the prior belief.O Fail to reject H. 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,"t was used to relate y = dielectric constant tox = 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 4.34x 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 7.08The following R output is from a simple linear regression of y on x.t value81.283EstimateStd. ErrorPr (>It|)4.858691(Intercept)AirVoid0.059768<2e-16-0.0746760.009923-7.5261.21e-06Residual standard error: 0.03551 on 16 DF MultipleAdjusted R-squared: 0.76Ep-value: 1.214e-06R-squared: 0.7797,F-statistic: 56.63 on 1 and 16 DF,Analysis of Variance TableResponse: DielectricDfSum SqMean SqF valuePr (>F)Airvoid10.0714220.07142256.6351.214e-06Residuals160.201780.001261

Answered: Image /qna-images/answer/033f8337-0634-4bf2-b98b-acbe2e19dc6f.jpg

Answered: (d) Suppose it had previously been…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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widely used as dielectrics and coolants in electrical systems in the past. They were found to be a major environmental contaminant in the 1960s. In a study, the mean PCB content at each of thirteen sites was reported for the years 1982 and 1996 (from “The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data”, Journal of Great Lakes Research 24 (1): 12-31, 1998). The data are below.Site:12345678910111213198261.4864.4745.5059.7058.8175.9671.5738.0630.5139.7029.7866.8963.93199613.9918.2611.2810.0221.0017.3628.207.3012.809.4112.6316.8322.74(a) Which test would be more appropriate in this case: a t-test for the difference between two population means, or a paired t-test? Why?(b) Do the data provide sufficient evidence to support the claim that the mean PCB level has decreased in the region? Be sure to check all assumptions, write the null and alternative hypotheses, calculate the appropriate test statistic, calculate the p-value,…
16
Question 7 > You wish to test the following claim (Ha) at a significance level of a = 0.05. H.: 41 Ha: µ1 7 42 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you have reason to believe that the variances of the two populations are equal. You obtain a sample of size nį = 14 with a mean of M1 first population. You obtain a sample of size n2 of SD2 = 7.4 from the second population. = 67.8 and a standard deviation of SD1 19 with a mean of M2 15.5 from the 61.7 and a standard deviation In the answer box below insert 2.0395 as the critical value for this test. (Report answer accurate to three decimal places.) critical value What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = %3D The test statistic is... O in the critical region O not in the critical region

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