Question

Suppose we want to select a stratified random sample from a population and we have $5000 for data collection. The population has been divided into four strata, and we have decided to allocation 20% of the total sample size into stratum 1, 15% of the sample size into stratum 2, 35% of the sample size into stratum 3, and 30% of the sample size into stratum 4. The cost of sampling per unit is $6 for stratum 1, $4 for stratum 2, $5 for stratum 3, and $8 for stratum 4.

(a) Determine the sample sizes for the four strata as well as the total sample size.

(b) How much money is left in our budget?

Answer 1

Let n be the total sample size

Thus, sample sizes for the strata 1,2,3 and 4 are 0.2n, 0.15n, 0.35n and 0.30n respectively

Thus, total cost of sampling = 0.2n*$6 + 0.15n*$4 + 0.35n*$5 + 0.3n*$8

= $5.95n

Amount present for data collection = $5000

Thus, we should have $5000 ≥ $5.95n

-> n ≤ 5000/5.95

-> n ≤ 840.336

Thus, n = 840

(a) Sample size for strata 1 = 0.2*840 = 168

Sample size for strata 2 = 0.15*840 = 126

Sample size for strata 3 = 0.35*840 = 294

Sample size for strata 4 = 0.30*840 = 252

Total sample size = 840

(b) Money left in budget = $5000 - (168*$6 + 126*$4 + 294*$5 + 252*$8)

= $2