Question

1. Let X1,.. X, be a random sample from -0x re 0= 01, where Find a most powerful test of size a for Ho 01>>0. 00 against H 0

Answer 1

het x, xz, ... to be a random sample from the population with palf Pola- o²x e ox axo, oro Clearly xoG(2, t) Exib (an, to) (sino Xi's are icd) :: 20 xi nG (an, 2) ie X (an). Now Likely hood function is h = o forne) = on os nin o é ini Û xi I- nero ro= 2100) = 60 do sada ni h = 2101) = on s a ne Most powerful test of size & Seo testing Ho: 0.00 vs H : O= 0, Core is given by the where c is a where e is a constant such that is Now that c n (orouver les obres Go - 3 (00-01) zac' [d' = Contac] (60-OD & xi 7 logel → Sme sb [ ba logo, 60-0140] Now Poo xi sb]=a P [200 exc 5266] =d. -> p [ x 5.2006) = x (xou ] —0 Now X² table we can find you to such that P[ x x xhan, -d] =+ where 20%u x ryn) .::P[X < Xani-uled © from ① and ② 200 b= 10 m, na 7 b= x² Ho : 0=00 . Most porestal test of sige & ed for testing is H1:0= 0 (01700) is. Reject to į xi = Xan - and accept to otherwise