This document provides a comprehensive analysis of statistical exercises and confidence intervals, including the calculation of confidence intervals for proportions and averages, and the discussion of statistical errors and biases.
Extract
[...] Statistical Exercises For this exercise, we will apply the following formula in the three cases: Where - is the estimated proportion on the sample of size - is the proportion in the population - is a value of the normal law to define the 95% confidence interval In all cases we have . and so . and so and so To determine the 95% confidence interval of the average age, we proceed as follows: - Calculation of the average age (weighted by the number of individuals): where is the total workforce, the ages and their frequencies. [...]
[...] - Lake Michigan is a bit too deep for swimming: its average depth is 85 meters (the total depth can be much higher than 85 meters). The target is within the confidence interval but not necessarily at the center. We can define an infinity of confidence intervals, it all depends on the margin of error considered. A sampling bias is more problematic than a statistical error because it is systematic. We can reduce the statistical error by increasing the size of the sample, but not the bias. [...]
[...] We can define, for example, the following three statistical variables: - Number of men - Number of women - Number of individuals under 25 years It is easy to imagine a scientific study on the distribution of men and women by age group in large cities. Average production . 5ème décile = median = 8 Modes = 11 and 13 Total production = average" total effectives" . The median is located between the mean and the mode so the distribution is asymmetric. The mean is greater than the mode so the asymmetry is to the left. [...]
