Question

A scientific study assembled a cohort of 7541 families with exactly three biological children. More precisely, these are all the families of this size taken from a much larger number of families participating in a large-scale health survey. For these families, the researchers tabulated the sexes of the two oldest children: 1941 of the families had two girls, 2207 families had two boys, and 3393 families had one girl and one boy.

Are these data consistent with the genders of the two oldest children behaving like independent and identically distributed random trials? Carry out a chi-squared test to address this question. Give all your steps, and state as clearly as you can what hypotheses you are testing, and what you conclude. comment briefly on what you think about your findings, particularly in light of how this cohort was assembled.

Answer 1

The hypothesis being tested is:

H₀: The data is not consistent with the genders of the two oldest children behaving like independent and identically distributed random trials

H_a: The data is consistent with the genders of the two oldest children behaving like independent and identically distributed random trials

observed	expected	O - E	(O - E)² / E
1941	2513.667	-572.667	130.466
2207	2513.667	-306.667	37.413
3393	2513.667	879.333	307.609
7541	7541.000	0.000	475.488
475.49	chi-square
2	df
5.61E-104	p-value

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the data is consistent with the genders of the two oldest children behaving like independent and identically distributed random trials.