During last years budget crunch several deserving employees

During last year’s budget crunch, several deserving employees of the Bureau of Procedures (BP) were denied promotions. This year, an unusual number of BP employees retired. The bureau chief suspects that the denial of promotions resulted in increased retirements. Of the 115 employees denied promotion, 32 retired. Of the 58 employees promoted, 9 retired. Present a contingency table, and analyze this information.

Solution

in brackets we have given the expected values

we can use the chi square test and decide the chi square statitic value = summation of ((O-E)²)/E =

and check the chi square table value at say (2-1)(2-1) one degree of freedom

and if the statistic value is greater than table value reject our hypothesis that there is no significant change.