Sampling techniques

3. A factory produces the face masks in it 50 production line. A sample of 10 production line was selected by using simple random sampling without replacement method. The number of workers and the productions of face marks (in hundred cartons) is shown in Table 2. Table 2 Production line A B C D E F G H Number of workers 20 30 35 40 60 40 45 40 50 30 Number of face masks 10 15 produced (in '00 catons) 20 25 40 30 30 30 40 20 (a) Estimate the average face masks (in hundred cartons) produced per worker and its standard error. [7 marks] ( b ) Estimate the mean face masks (in hundred cartons) produce per production line and obtain 90% confidence interval of the mean face masks (in hundred cartons). Estimate the relative efficiency of the ratio estimator with respect to the sample mean. [8 marks]