The article "Polyhedral Distortions in Tourmaline" (A. Eril, J. Hughes, et al., 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 0.33 0.36 0.36 0.36 0.54 0.58 0.56 0.66 0.64 0.64 0.66 0.67 0.74 0.58 0.74 0.78 0.79 0.86 0.97 0.97 1.11 1.03 110 1.06 1.13 1.08 114 117 Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (ie., equal to the true value), then y = x+ , where e is measurement error. a. b. Compute the least-squares line y= Show that if the calculated value is accurate, then the true coefficients are , = Oand e, Â, + Â,x- C. =1. d. Test the null hypotheses e,-0 and e, = 1. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain. e.
The article "Polyhedral Distortions in Tourmaline" (A. Eril, J. Hughes, et al., 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 0.33 0.36 0.36 0.36 0.54 0.58 0.56 0.66 0.64 0.64 0.66 0.67 0.74 0.58 0.74 0.78 0.79 0.86 0.97 0.97 1.11 1.03 110 1.06 1.13 1.08 114 117 Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (ie., equal to the true value), then y = x+ , where e is measurement error. a. b. Compute the least-squares line y= Show that if the calculated value is accurate, then the true coefficients are , = Oand e, Â, + Â,x- C. =1. d. Test the null hypotheses e,-0 and e, = 1. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain. e.
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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Transcribed Image Text:The article "Polyhedral Distortions in Tourmaline" (A. Eril, J. Hughes, et al., 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
0.33
0.36
0.36
0.36
0.54
0.58
0.56
0.66
0.64
0.64
0.66
0.67
0.74
0.58
0.74
0.78
0.79
0.86
0.97
0.97
1.11
1.03
110
1.06
1.13
1.08
114
117
Assume that the observed value y is an unbiased measurement of the true value. Show
that if the calculated value x is accurate (ie., equal to the true value), then y = x+ ,
where e is measurement error.
a.
b. Compute the least-squares line y=
Show that if the calculated value is accurate, then the true coefficients are , = Oand e,
Â, + Â,x-
C.
=1.
d. Test the null hypotheses e,-0 and e, = 1.
Is it plausible that the calculated value is accurate? Or can you conclude that it is not?
Explain.
e.
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