likelihood principle and pvalues

Exercise 4.1 (ii-\"3'11? Likelihood principle and pvalues (50%)). (Background) Suppose that, in a social media \"FaceLook\Example 5.3 (www Proportional likelihood). 1. Let X ~ Bin(4, 0), where e e (0, 1). Suppose X = x is realized. Then the likelihood of 0 is L(0 | x) = fo(x) = 0" (1 - 0)1-1(x =0, ...,4). In particular, if a = 3, then L(0 | 3) = 3 03(1 - 0) 4-3 xx 03(1 - 0). (5.2) 2. Let N ~ 3 + NB(3, 1 - 0), where o e (0, 1). Suppose N =n is realized. Then the likelihood of 0 is L(0 | n) = fo(n) = (3_103(1 -0)"-31(n = 3,4, ...). In particular, if n = 4, then L(0 | 4) = (3103(1-0)1-3 xx03(1 -0). (5.3)Remark 4.1 (Hints fer Exercise 4.1). 1. 0 Example 5.3 is related. 0 pvalue is the probability that the data are at least as extreme (in the direction of H1) as the actually realized observations under H0. We reject H 0 at 5% level if the pvalue is less than 5%