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 directionwas 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 σX = 0.34 and σY = 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 H0 :μV ≤ 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?