An Introduction to Mathematical Statistics

Abstract

According to a common belief, the birth of a girl or of a boy are equiprobable events. Let us adopt this as the initial hypothesis, and check how it fits some available data. For example, in the period 1871–1900 there were n = 2, 644, 757 babies born in Switzerland including m = 1, 359, 671 boys and n − m = 1, 285, 086 girls.* How well does this data agree with our hypothesis that the probability of a boy’s birth is 0.5? By calling the last event a ‘success’, let us discuss the data in the framework of n = 2, 644, 757 Bernoulli trials, with unknown success probability p; the corresponding frequency is

$$\frac{m}{n} = \frac{{1,359,671}}{{2,644,757}} = 0.5141. $$