Chapter 2, Problem 4P

The glucose concentrations in a patient with mildly elevated glucose levels were determined by a spectrophotometric analytical method and were recorded in mg/L as follows: 799, 745, 750, 774, 777, 800, 758 and the true value is 792.  (a) Calculate the standard deviation (b) Calculate the relative error in ppm

Estimate the absolute standard deviation (or uncertainty) for the results of the following calculations. Round each result so that it contains only  significant digits. The numbers in parentheses are absolute standard deviations. Show  your solution and express the final answer and its  corresponding uncertainty. a)  y= 2.998(±0.002)   - 3.98 (±0.15) + 9.035 (±0.002) = 8.0531 b)  y= 39.2(±0.3) x 3.054 (±0.022) x 10^ -2 = 1.197   c)   y= [198(±6)   - 89 (±3)] / 1335 (±2) + 64 (±7)]  = 7.791 x 10^-2

In replicate analyses, the carbohydrate content of a glycoprotein (a protein with sugars attached to it) is found to be 12.6, 11.9, 13.0, 12.7, and 12.5 g of carbohydrate per 100 g of protein. (a) Find the mean of the measurements. (b) Find the standard deviation (s). (c) Find the 90% confidence intervals for the carbohydrate content. (d) If the mean and s are unchanged, but there are 10 measurements (N=10) instead of 5, what would be the confidence interval? (e) How does increasing the number of replicate measurements affect the reliability of measurements? Explain your answer. (Hint: better precision gives smaller confidence intervals)