error and uncertainty
Here is another question I'm having a hard time with:
Suppose you have a relationship between the average temperature in a region and the isotopic ratio of an element found in an organism: T = a*delta where delta is the isotopic ratio measured and "a" is the constant of proportionality. Your measurements of delta have uncertainty sigma_del = 0.2 and "a" = 4.3 C.
1)From a single measurement of delta, what is your uncertainty in T?
2) How many independent measurements of delta would you need to obtain an estimate of T with an uncertainty sigma_T_avg = 0.1 C?
For #1, my reasoning is that the uncertainty will range from:
(single measurement-0.2)*4.3 to (single measurement+0.2)*4.3?
For #2, I believe the formula for the standard deviation of the mean (aka standard error or standard error of the mean comes into play), where sigma_x_avg = sigma_x / sqrt (sample number) ?
Thank you very much for your time.