This approach can be applied to test whether a discrete data set of \(n\) values is a random sample from any distribution.
Example
The following table gives the number of male children among the first 12 children in 6,115 families of size 13, taken from hospital records in 19th century Saxony. (The 13th child has been ignored to avoid the possible distortion of families stopping when a desired sex is reached.)
Males | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Frequency | 3 | 24 | 104 | 286 | 670 | 1033 | 1343 | 1112 | 829 | 478 | 181 | 45 | 7 |
Assuming independence and that each child has the same probability of being male, \(\pi\), this would be a random sample from a \(\BinomDistn(n=12, \; \pi)\) distribution.
Is there evidence that the probability of a birth being male differs from family to family?
(Solved in full version)