2009-75.md

course	course_year	question_number	tags	title	year
Statistics	IB	75	IB 2009 Statistics	Paper 3, Section $\mathbf{I}$, H	2009

In a demographic study, researchers gather data on the gender of children in families with more than two children. For each of the four possible outcomes $G G, G B, B G, B B$ of the first two children in the family, they find 50 families which started with that pair, and record the gender of the third child of the family. This produces the following table of counts:

First two children Third child $B$ Third child $G$

$\begin{array}{ccc}G G & 16 & 34 \ G B & 28 & 22 \ B G & 25 & 25 \ B B & 31 & 19\end{array}$

In view of this, is the hypothesis that the gender of the third child is independent of the genders of the first two children rejected at the $5 %$ level?

[Hint: the $95 %$ point of a $\chi_{3}^{2}$ distribution is $7.8147$, and the $95 %$ point of a $\chi_{4}^{2}$ distribution is $9.4877 .]$