A systematic sample is a sampling type where, the population units are listed in a certain order, the first unit is randomly chosen from the first k number of units and then the subsequent units are selected in intervals of k. To calculate k, in case you know the population size, you have to divide the population size by the sample size (usually established based on previous information. Remember k is always a whole number.

a) k= pob/n= 4247/40= 106.175 ≅ 106

b) From the 106 individuals you have to randomly select the first unit. Then starting from it the next 39 individuals surveyed will be the +k

Using a random number calculator I've chosen the first individual to be surveyed as number 57 after that you have to add k= 106 to know wich are the next individuals to be sampled:

1) 57 11) 1117 21) 2177 31) 3237

2) 57 + 106= 163 12) 1223 22) 2283 32) 3343

3) 269 13) 1329 23) 2389 33) 3449

4) 375 14) 1435 24) 2495 34) 3555

5) 481 15) 1541 25) 2601 35) 3661

6) 587 16) 1647 26) 2707 36) 3767

7) 693 17) 1753 27) 2813 37) 3873

8) 799 18) 1859 28) 2919 38) 3979

9) 905 19) 1965 29) 3025 39) 4085

10) 1011 20) 2071 30) 3131 40) 4191

I hope it helps!

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