The Normal Law and Applications: Sample Size, Confidence Intervals, Tests

Abstract

Many histograms evoke the shape of a bell. The histogram of the variable “diastolic blood pressure” in Practical Work no. 2 of Sect. 13.6 is a good example. There is a theorem in the theory of probabilities that explains this observation; it is called the “central limit theorem”. As said before, we do not assume knowledge of probability theory in this book, so we describe only the intuitive meaning of the theorem. It says that under certain technical assumptions a random variable which can be thought of as the sum of a large number of components acting more or less independently of each other, will follow approximately a “normal law”, to be defined presently. An early application of the normal law around 1800 was to describe the distribution of errors in repeated independent measurements of the same quantity in astronomy and geodesy.

This lesson presents the fundamental ideas of inferential statistics. It deals with data that stem from either of two sources: – repeated observations that are essentially being done independently of each other under the same conditions; − a sample survey . It is confined to techniques based on the normal law; this permits the use of simple numerical methods.