Geissler collected data on the distributions of the sexes of children in families in Saxony during 1876–1885. The data below is the number of girls within the first 12 children of families with 13 children. 0 1 2 3 4 5 6 7 8 9 10 11 12 7 45 181 478 829 1112 1343 1033 670 286 104 24 3 The aim of this analysis is to estimate π, the probability of a girl birth. (a) How would you model the outcome of this experiment? Clearly state your statistical model. (b) Using your model, find the likelihood function and the log-likelihood function of π (given the data). (c) Find the maximum likelihood estimate ˆπ of π and its standard error.

A. Geissler collected data on the distributions of the sexes of children in families in Saxony during 1876–1885. The data below is the number of girls within the first 12 children of families with 13 children.

0 1 2 3 4 5 6 7 8 9 10 11 12
7 45 181 478 829 1112 1343 1033 670 286 104 24 3

The aim of this analysis is to estimate π, the probability of a girl birth.
(a) How would you model the outcome of this experiment? Clearly state your statistical
model.
(b) Using your model, find the likelihood function and the log-likelihood function of π (given
the data).
(c) Find the maximum likelihood estimate ˆπ of π and its standard error.
(d) Does your model use any assumptions that might open it to criticism? Include any
evidence of model inadequacy in a brief discussion.
(e) As stated above, these data are on families with 13 children and only the sex distribution
among the first 12 children is reported.
What may be the reason for omitting the information on the last child? Discuss briefly.