According to the Hardy-Weinberg formula, the number of flies of certain types resulting from certain crossings should be in the proportions q2:2pq:p2 (that is q squared:2pq:p squared), where p+q=1.

If an experiment gave the frequencies n1=55 n2=70, n3=25 (that is n1, n2, n3 all in subscripts), would the results be compatible with this formula at alpha=0.05 (approximately) if:

(i) q=0.5? ;

(ii) q is estimated from the data by using the maximum likelihood estimator (n1+(n2/2))/(n1+n2+n3)?

(b) Prove that the estimator given in part (a): (ii) is the MLE of q based on the multinomial distribution.