ABSTRACT

Another “natural” example where N<30 is, for example, the analysis of the degree of acidity of old paper in an archive. Performing N≥30 chemical lab tests would be too costly!

About one-sided tests

In all arguments given above we used two-sided tests for the mean . This means that we investigated whether or not is in one of the tails of the normal distribution, hence whether or not Z (see formulae 3.1 or 3.2) is in one of the tails of the standard normal distribution. In exceptional cases we can exclude one of the tails since the situation it describes cannot occur. For example, if one knows for sure that an average article in chemistry cannot have fewer co-authors than an average article in mathematics one could only check whether or not the average number of co-authors of chemistry articles is larger than the number for mathematics articles. The same applies for “natural things”, for example public libraries have more circulations than university libraries, scientific libraries have more outgoing interlibrary requests than public libraries and so on. Beyond the library, examples are heights of men and women, temperatures in different seasons of the year, and so on.