A work sampling study was performed on 18 social workers in a county government office. The social workers handle three types of cases: A, single parents; B, foster parents; and C, juvenile delinquents. The purpose of the work sampling study was to determine estimates of the average time per case for each case type. In addition to the three case types, two additional activity categories were included in the study: D, traveling between cases; and E, other (miscellaneous) activities. The study was carried out over three weeks' period (three 5- workdays weeks, i.e. fifteen 8-hour days). Observations were taken at random times ten (10) times each day for 15 days. Each social worker was provided with a cell phone so they could be contacted if they were not in the office building. There were 23 worker-days of absences resulting loss of their observations. Results of the study are presented in the two tables below: Category of activity A B D E # cases completed 400 700 300 Day #obs. A#obs.B #obs. C#obs. D#obs. E 1 47 42 34 13 2 43 30 40 27 10 34 51 32 28 33 16 4 49 31 41 31 18 5 50 32 34 38 16 6 50 31 31 30 18 7 45 32 33 29 21 8 51 38 50 35 6 9 49 33 38 36 14 10 54 39 33 40 14 11 44 27 34 33 12 12 48 32 38 33 19 13 28 29 28 18 37 49 14 37 43 43 8 15 43 32 41 28 16 a. What is the mean time per case for each of the three types of cases? (18 points) b. Construct a 95% confidence interval for the mean time per case for each of the three types of cases. (84 points)