The following table gives stratification of all farms in a country by farm size and the acreage of corn (maize) in the sampled farms. Obtain the estimate of average acres of corn per farm in the population and its variance. Also obtain the variances of the estimates of population mean under proportional allocation and optimum allocation Hence for the same sample size of 21 farms.

Obtain the 95% confidence interval for the mean and efficiency of the given allocation and the proportional allocation with respect to the optimum allocation (Hint: the coast not considered).

Stratum No.	Farm size (acres)	No. of farms (Ni)	Acreage of corn in sampled farms (10 acres)	Standard deviation (10 acres) from a past survey) Si
1	0-40	12	3.5, 2.7, 1.1, 1.9	5.2
2	41-80	24	2.4, 6.9, 3.7, 2.8, 3.4, 2.6	3.7
3	81-120	19	1.0, 1.3, 2.9, 1.6, 3.4	6.5
4	121-160	13	1.0, 0.0, 2.3, 0.5	3.4
5	161-200	9	5.8, 4.9	2.7