Question

13. The table below presents the numbers of employees, by age group, who wer e promoted, or not promoted, in sample drawn from a certain industry for the past ear Under 40 Years 38(38.01) 77(76.99) Over 40 Years 41(83.01) 83(83.01) Promoted Not Promoted "Expected frequencies are in parenthesis. You are to do the test of homogeneity with the null hypothesis, Ho: The age of employees have the same effect on promotion. a) Find the degree of freedom. .01 level. b) Find the critical value at the d c) Compute the test statistic, x d) Do you reject Ho at & 01 e) What conclusion can you make?

Answer 1

$(a)~df=(2-1)(2-1)=1\\ (b)~Critical~value=\chi^2_{0.01,1}=6.6349\\ (c)~Value~of~\chi^2=(38-38.01)^2/38.01&plus;(41-40.99)^2/83.01&plus;(77-76.99)^2/76.99&plus;(83-83.01)^2/83.01= 0.000006\\ Note:~Expected~frequency~of~cell`(1,2)~should~be~40.99~instead~of~83.01.\\ (d)~No~since~Value~of~\chi^2<Critical~value.\\ (e)~There~is~an~evidence~to~conclude~that~the~age~of~employees~have~the~same~effect\\ on~promotion.$