Question

4. A HR specialist is especially interested in two traits of workers: whether they are diligent (or lazy) and whether they are creative (or not). We assume that the two traits are independent, and that the probabilities that a worker is diligent and lazy are each equal toWe assume that the probability that a worker is creative is equal to p, where pE (0,1) is unknown. A group of workers were asked to take a test; the results are summarized in the table below: Type of worker Diligent Lazy and not creative and creative not creative N3=20 Diligent Lazy and and creative Number of workers Assumed probabilities N2 30 (1-p) N4= 40 (1-p) N1=10 Find the formula for the MLE of p (depending on Ni, N2, N3, N4): .and the value of the estimator for the above sample: .. Using the chi-squared test (and the estimate from the previous point), verify whe ther the assumed probability scheme is valid for a significance level 0.05. The value of the appropriate test statistic is equal to nul hypothesis the statistic has a distribution with degrees of freedom and a critical value equal to TO REJECT (underline the appropriate) the nul hypothesis .., under the so we REJECT /HAVE NO GROUNDS

Answer 1

imterun ed in tno trai ta : 4. HR ai apiaty neative (er nst) dilig int (or le ay in derendent arR ThE di ligent FECID },(1) Creative & rentek in Agromp PYonkes gsMCA l5 Fake a ten- hwey & Creanre Di lbgort Pi Uigent CenHre TYpe Mt0reive nut CHeanive N42A0 N/7 10 NL30 1/2 C4) (1)

4 porulariona mae ench he We cam aume treated as g8uys are mdependen, o il an be dibbiruted. heme ae A on ul ti nom lenging h each he 4. there me prrauili es fer :: (M,Ks,N, N4) - .. N 3 NN2 N3 N4 N 2-TNN4 (A4) N, N2 N3 N 4 C + hey ikeli herd is fror K2 N4 fhaimum N N2 7 ( 1-4) Likelinsod etimaten N2+NA 70 (N2 N/4) (NTN2 NNA) (NINg)(1) N, N2+N3 N MLE N,+Nt N +NA MAi ng valnes In the 9iren Case 10 t 20 MLE l0+ 30+ 20 + A0

Freviems Fatm and eshmates fms chi-A quanad toMG Uing te ane t iralid for a Nhethem the wam ed ptd Lity (ymaticane lerel dr5 , The tohewid ya hunts fugueney LNpected Unden Nun 1he tten Mniic A2 (too) AM test Mar T 14h- Prinimatrly We 6-37 , fo20;カ240 / & du (0)05 n 15 (9) 35 2ten-arariaic We cempati the A 2 fi 202 a2 3.5 2 302 0 35 t5 15 104 9619-100 ithe mpuRd ralue the b19t - (Am) f2-tet MaMirc

The Citi can ralme is ual t N K-9 2 Campated mpurad 2 7.82. ーデA·7619 ぐ72 w eridene la'stn WRe assrumed patnris he prbalei ity theme AM The value apphop t ale ten Maiic hypPmeria i enual l4.7619 under the nnt dishibntin hitw 4-13 PhR ten Aevhitnc has and a Crih ca ralue eanal l dtgrus frtdem har no 7.82 Fhe amM hypotmeri6