(10 marks) A scientific study assembled a cohort of 7541 families with exactly three biologicalchildren. More precisely, these are all the families of this size taken from a muchlarger 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 hadtwo girls, 2207 families had two boys, and 3393 families had one girl and one boy.

(a) Are these data consistent with the genders of the two oldest children behaving likeindependent and identically distributed random trials? Carry out a chi-squared testto address this question. Give all your steps, and state as clearly as you can what hypothesesyou are testing, and what you conclude.

(b) Now stepping back a bit, comment briefly on what you think about your findings in(a), particularly in light of how this cohort was assembled.