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# The article “Polyhedral Distortions in Tourmaline” (A. ## Problem 18SE Chapter 7

Statistics for Engineers and Scientists | 4th Edition

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Problem 18SE

The article “Polyhedral Distortions in Tourmaline” (A. Ertl, J. Hughes, et at., The Canadian Mineralogist, 2002: 153-162) presents a model for calculating bond-length distortion in vanadium-bearing tourmaline. To check the accuracy of the model, several calculated values (x) were compared with directly observed values (y). The results (read from a graph) are presented in the following table.

 Observed Value Calculated Value Observed Value Calculated Value 0.33 0.36 0.74 0.78 0.36 0.36 0.79 0.86 0.54 0.58 0.97 0.97 0.56 0.64 1.03 1.11 0.66 0.64 1.10 1.06 0.66 0.67 1.13 1.08 0.74 0.58 1.14 1.17

a. Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (i.e., equal to the true value), then y = x + ε, where ε is measurement error.

b. Compute the least-squares line c. Show that if the calculated value is accurate, then the true coefficients are β0= 0 and β1= 1.

d. Test the null hypotheses β0 = 0 and β1= 1.

e. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain.

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##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 18SE from 7 chapter was answered, more than 252 students have viewed the full step-by-step answer. This full solution covers the following key subjects: calculated, observed, true, accurate, show. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “The article “Polyhedral Distortions in Tourmaline” (A. Ertl, J. Hughes, et at., The Canadian Mineralogist, 2002: 153-162) presents a model for calculating bond-length distortion in vanadium-bearing tourmaline. To check the accuracy of the model, several calculated values (x) were compared with directly observed values (y). The results (read from a graph) are presented in the following table.Observed ValueCalculated ValueObserved ValueCalculated Value0.330.360.740.780.360.360.790.860.540.580.970.970.560.641.031.110.660.641.101.060.660.671.131.080.740.581.141.17a. Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (i.e., equal to the true value), then y = x + ?, where ? is measurement error.________________b. Compute the least-squares line ________________c. Show that if the calculated value is accurate, then the true coefficients are ?0= 0 and ?1= 1.________________d. Test the null hypotheses ?0 = 0 and ?1= 1.________________e. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain.” is broken down into a number of easy to follow steps, and 152 words. The full step-by-step solution to problem: 18SE from chapter: 7 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 7 - Problem 18se