. Let Y1 . . . , Yn denote a random sample from the binomial distribution Bino(m, ?), where ? is an unknown parameter.

(c) Consider testing the hypothesis that the parameter / is equal to a particular value: Ho : 7 =0.5 versus H1 : 7 / 0.5. Write down the test statistics corresponding to each of the following hypothesis testing methods and also evaluate them under the assumption that n = 20 and the observed value of the MLE is * = 0.6: i. likelihood ratio test ii. score test iii. Wald test iv. approximate Wald test