Question

Q4). Suppose that you are drawing a sample of random observations yyy2y, from a population that is normally distributed with a mean- u and variance 2. Derive the two-sided likelihood ratio test for testing Ho : μ Ho versus H! : μ where μ. μο. 123. (5 points)

Answer 1

Solahanuppase th yau une ehwinga sample of ranalem nemmelly dichbule with meun anelNamanca 6 L, then IT て20 u nale th DLE of l andl 62 is given by olvine fatloving ://dikerhooel equallons gives2 62 Thus maxinum ielihael fanchen o1e whale perzi melkm space is given bj-

2S2 s- ナーで No uR dekmmine LE of nomal parrameler ovem para me under unknown tre- Space--under-ho is enou ie Ho Value of The-only ovem hole parameken space is giuen b o 62 then-maximum dikelihood-function - ove man L ( ulol 62 ) S- ven by _ HO Nou)-- usi 9 e ef m).ersople、 でnler.

2. Now ronsider ー substitute value of Joz İn equaHon③ So2 2 Square-oe-bath Sides- a e get

s2 /(n-1) use this nelation in equatonthen 2 t2. _deads to usuedーーtuoーーAided students t distobulfen ith () degrees of fredem