Question

what if X<42, what's the answer of these four question?

5. Assume that X is following a normal distribution with mean y and variance o?. We want to test: Ho :u = 40 versus H:ll = 45. based on a sample of size n. Consider the following decision rule: if X > 42, claim that H = 45, otherwise claim that u = 40. Suppose n = 30 and o2 = 50. (a) What is the critical region of the test? Ã > 42 (b) What is a, probability of type I error of the test? 0.0607 (c) What is the power of the test? Interpret your answer. 0.9899 (d) Find n and c such that a = 0.01 and B = 0.05. c= 42.93, n = 32

Answer 1

Sony X~ N(4202) se ll=40 we reject null a Mo: M= 40 vs M M = 45 Given that If x>42 then 4:45 otherwise u=40 critical region is the region in which hypothesis an ! L e s HF?? Hence critical region for this given poblem is W: X>42. da pl Type - I edo 7 p[reject- no (ho is Houe] & P[x G w/Ho] sip [x>42/40] = a = PS X-40 Tom 1.50/30 42-40 150130 {i var (8) compete 3) 2= P(2 7 2 ) : 2 MN (011) cond] 150/30 1- Plzs 1.55] lap (1.55) & () in the God. f Biti --|-0-9394; filom 2-table- = 2: 0.0606 WWW

@ the Racer & the test (6-8) - P[Rejecting Holteis false? H oe 5 P[Rejecting Holu, is folue) than any .=P [6> 42.1 Hos Ksus] s precio n M.: 48 ) artinya illa 14tshme bring the 50/3 faoi th="p| 2 » +230) 149 1 [edita HP[zz-9:32] *1.0(-2.3223- 7 = 1-0.00017 from the 2-table 0.9898 0.9898 je ( sov Power & the test <0-9898 interpretation Buser is the poobablity of making a Greet decision i.e. Power is the probablity of rejecting the null hypothesis when it's es false So there is a 98.98% of chance that the hull hypothesis Mo:d1:40 will be rejected on this

@ Find n and a such that en and C 2-0.01 and 3-0.05 ) -) 2 =P[ ž>c/40) = o.ol pl X-My Gr 1 Mo: M:40] = 0.01 val() Vol o A >> pe zone 4097 => P[ze et on D30:916 → P125 telepon J = 0.99 => $ (55) 2017 0.99 C-yo = 2.33 al from 2-table 5016 lyre B=PL The Terror] =P[zie w lhe] Cine 0.05 = P(x < < / M: Meus] { witte Wix Ec spl za c-45 D 1E 1 Boln 1 WZ C-45 => 0.05 = 5010 lu) :- 1.64 = C-4S i folom 2-table on

to be foons 31 (1) , we have 6-45 - 164 C-VO9:33 DFS 233 C -45 *233 = -164C+164640 =) 3976 = 164*40 +45 233 > =166** 40 745* # 233 0196 397 5) 03 42.93452s 642.93 .si By putting the value to c in tem C-40 ob- soln 233M ) → 293 +1.33 > 50 - 993, 35 so DP 7. 1550 * 123332 (2934 22 N = 31.6188 Ris integer =) :32