This exercise continues Exercise 9 in the Supplementary Exercises for Chapter 3. The

Chapter 6, Problem 9

(choose chapter or problem)

This exercise continues Exercise 9 in the Supplementary Exercises for Chapter 3. The article “Insights into Present-Day Crustal Motion in the Central Mediterranean Area from GPS Surveys” (M. Anzidei, P. Baldi, et al., Geophysical Journal International, 2001:98–100) reports measurements of the velocity of the earth’s crust in Zimmerwald, Switzerland. The component of velocity in a northerly direction was measured to be \(X=22.10\), and the component in an easterly direction was measured to be \(Y=14.30\), where the units are mm/year. The uncertainties in the measurements were given as \(\sigma_{X}=0.34\) and \(\sigma_{Y}=0.32\).

a. Compute the estimated velocity V of the earth’s crust, based on these measurements. Use the method of propagation of error to estimate its uncertainty.

b. Assuming the estimated velocity to be normally distributed, find the P-value for the hypothesis

\(H_{0}: \mu_{V} \leq 25\).

c. Assuming that the components of velocity in the northerly and easterly directions are independent and normally distributed, generate an appropriate simulated sample of values \(V^{*}\). Is it reasonable to assume that V is approximately normally distributed?

Equation Transcription:

Text Transcription:

X=22.10

Y=14.30

X=0.34

Y=0.32

H_0:{mu}V{</=}25

V^*