A university has 27 academic units ranging in size from 2 to 92 faculty members. A sample of 10 academic units were selected with probabilities proportional to size and with replacement, and within each sample academic unit an SRS of four (or fewer, if Mi < 4) members were selected. Note that academic unit 14 appears three times in the sample; each time it appears, a different subsample was collected. Find the estimated total number of publications, along with its standard error. Also, and its 95% confidence interval.

?

Academic Unit M; Yij 3,0,0,4 2,1,2,0 0,0,1,0 2,0,1,0 2,0 0,2,2,5 1,0,0,3 4,1,0,0 2,2,3,1 2,5,12,3 14 65 0.0805452 23 25 0.0309789 9. 48 0.0594796 14 65 0.0805452 16 2 0.0024783 6. 62 0.0768278 14 65 0.0805452 19 62 0.0768278 21 61 0.0755886 11 41 0.0508055