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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2009 • Question 9

Question

Math 6010 • Linear Models Spring 2009 • Question 9

According to a genetic model the proportions of individuals having the four blood types should be given by O: \(q^2\); A: \(p^2+2pq\); B: \(r^2+2qr\); AB: \(2pr\). Here \(p>0\), \(q>0\), \(r>0\), and \(p+q+r=1\), but the three parameters are unknown. We observe \(n_O\), \(n_A\), \(n_B\), \(n_{AB}\) individuals of the four blood types in a random sample of size \(n\). Describe a goodness-of-fit test of size \(\alpha \) of the stated hypothesis.

Raw LaTeX

According to a genetic model the proportions of individuals having
the four blood types should be given by O: \(q^2\); A: \(p^2+2pq\); B: \(r^2+2qr\);
AB: \(2pr\). Here \(p>0\), \(q>0\), \(r>0\), and \(p+q+r=1\), but the three parameters
are unknown. We observe \(n_O\), \(n_A\), \(n_B\), \(n_{AB}\) individuals of the four
blood types in a random sample of size \(n\). Describe a goodness-of-fit test of
size \(\alpha\) of the stated hypothesis.

Topic Tags

F-Tests and t-Tests Uniform Integrability and Truncation Methods