Math 6010 • Linear Models

1000 individuals were classified according to sex and to whether or
not they were color-blind, with the following results: male normal 442; female
normal 514; male color-blind 38; and female color-blind 6. According to a
genetic model, the four relative frequencies should be of the form
\(p/2\); \(p^2/2+p(1-p)\); \((1-p)/2\); and \((1-p)^2/2\), respectively. Suppose we want
to test whether the data fit the model.

\textbf{(a)} Find the maximum likelihood estimator \(\hat p\) of \(p\).

\textbf{(b)} Describe a size \(\alpha=0.10\) test of the null hypothesis that the
data fit the model, assuming that \(\hat p=0.913\). Specify the critical region as
precisely as possible, perhaps in terms of a quantile of a certain \(\chi^2\)
distribution.