If strata are heterogeneous then stratified sampling schemes provides estimates with greater precision.
By generating 10 uniform random variate U (0, 1) estimate the integral
Recognizing this function as probability density function of N (0, 1), compare the value of with
.
Three varieties A, B and C of wheat are shown in five plots each of the following fields per acre as obtained:
| Plots | A | B | C |
| 1 | 8 | 7 | 12 |
| 2 | 10 | 5 | 9 |
| 3 | 7 | 10 | 13 |
| 4 | 14 | 9 | 12 |
| 5 | 11 | 9 | 14 |
In SRSWOR, the possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nn .
Three varieties A, B and C of wheat are shown in five plots each of the following fields per acre as obtained:
| Plots | A | B | C |
| 1 | 8 | 7 | 12 |
| 2 | 10 | 5 | 9 |
| 3 | 7 | 10 | 13 |
| 4 | 14 | 9 | 12 |
| 5 | 11 | 9 | 14 |
To determine the yield rate of wheat in a district of Punjab, 6 groups were constructed of 6 plots each. The data is given in the following table:
| Plot No. | Group 1 | Group 2 | Group 3 | Group 4 | Group 5 | Group 6 |
| 1 | 8 | 6 | 18 | 13 | 17 | 12 |
| 2 | 13 | 5 | 8 | 7 | 15 | 15 |
| 3 | 11 | 16 | 6 | 13 | 10 | 11 |
| 4 | 26 | 5 | 10 | 6 | 21 | 17 |
| 5 | 13 | 16 | 16 | 7 | 20 | 8 |
| 6 | 31 | 5 | 20 | 2 | 25 | 10 |
If strata are heterogeneous then stratified sampling schemes provides estimates with greater precision.
A manufacturer wishes to determine the effectiveness of four types of machines (A, B, C and D) in the production of bolts. To accumulate this, the numbers of defective bolts produced for each of two shifts in the results are shown in the following table:
| Machine | First shift | Second Shif | ||||||||
| M | T | W | Th | F | M | T | W | Th | F | |
| A | 6 | 4 | 5 | 5 | 4 | 5 | 7 | 4 | 6 | 8 |
| B | 10 | 8 | 7 | 7 | 9 | 7 | 9 | 12 | 8 | 8 |
| C | 7 | 5 | 6 | 5 | 9 | 9 | 7 | 5 | 4 | 6 |
| D | 8 | 4 | 6 | 5 | 5 | 5 | 7 | 9 | 7 | 10 |