. The management of a certain company interviewed five employees E1 , E2 , E3 , E4 and E5 with a view to promoting them to the next job group. After the interview, the management presented the results as follows: S1 , F2, F3 ,S4 and F5 , where F and S stand for ‘Failure’ and ‘Pass” of the respective candidates. The subscripts are the respective candidates.
(i) Prepare the sampling distribution for proportion of candidates who passed the interview, where sampling is done without replacement and samples of size n=2 are taken.
(ii) Using your answer to (i), determine the standard error of the sample proportions.