1. Sixteen independent measurements were made of the resistance of a resistor. The average was 52.37 Ω and the standard deviation was 0.12 Ω.
a. Estimate the resistance of this resistor, and find the uncertainty in the estimate. A single measurement is made of the resistance of another resistor.
b. This measurement is 61.42 Ω. What is the uncertainty in this measurement?
2. 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 that the components of velocity of the earth's crust in Zimmerwald, Switzerland, are 22.10 ± 0.34 mm/year in a northerly direction and 14.3 ± 0.32 mm/year in an easterly direction.
a. Estimate the velocity of the earth's crust, and find the uncertainty in the estimate.
b. Using your answer to part (a), estimate the number of years it will take for the crust to move 100 mm, and find the uncertainty in the estimate.
3. A piece of plywood is composed of five layers. The two outer layers are veneers with thickness 0.50 ± 0.02 mm, and the three inner layers each have thickness 6.25 ± 0.05 mm. Assume the thicknesses of the layers are independent. Estimate the thickness of the plywood and its uncertainty.
4. The article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142–148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.
