Let k denote the number of successes observed in a sequence of n independent Bernoulli trials, where p = P(success). 

(a) Show that the critical region of the likelihood ratio test of H₀: p = 1/2 versus H₁: p = 1/2 can be written in the form

(b) Use the symmetry of the graph of 

to show that the critical region can be written in the form 

where c is a constant determined by α.

Transcribed Image Text:

** k. ln(k) + (n - k). In(n-k) ≥ 2*