In a city, all 5,000 households are classified into three strata according to household income (low / medium / high). We draw a stratified sample of 200 households for which we observe the variable yi, defined as the value of food expenditure for household i. Here is the data:

Stratum 1

Households with low income

N1 = 3000; n1 = 120; y1 = $ 200; s1 = $ 50

Stratum 2

Households with an average income

N2 = 1000; n2 = 40; y2 = $ 400; s2 = $ 80

Stratum 3

Households with high income

N3 = 1000; n3 = 40; y3 = $ 800; s3 = $ 60

Estimate the total food expenditure of 5,000 households.

Determine the margin of error in the estimate of total food expenditure for 5,000 households.

The sample size 200 is a preliminary sample intended to prepare a new, larger, stratified sampling of size 1000. Determine the number of households to be sampled in stratum 2 according to the optimal allocation of a sample of size 1000. Note : use the corrected standard deviation of the sample income.

The sample size 200 is a preliminary sample intended to prepare a new, larger, stratified sampling of size 1000. Determine the number of households to be sampled in stratum 3 according to the proportional allocation of a sample size 1000.