a company alphabetically lists of all 6425 employees and wants to conduct a systematic sample of size 60.(a) What is k?k=107(b) Determine the individuals who will be administered the survey. Randomly select a number from 1 to k. Suppose that we randomly select 13. Starting with the first individual selected, the individuals in the survey will be 13, 120, 227…, 6326
I understand how to do everything except the last part how they get 6326.
just keep adding k=107 to each term. (6326-13)/107 = 59
To determine the individuals who will be administered the survey, you start with the first individual selected (which is 13) and then add the value of k to this individual to get the next individual in the survey. You continue this process until you have selected the desired number of individuals.
In this case, k is given as 107. Starting with the first individual (13), you would add 107 to get the next individual. So, 13 + 107 = 120.
For the following individuals, you would add 107 to the previous individual to get the next individual:
120 + 107 = 227
227 + 107 = 334
334 + 107 = 441
441 + 107 = 548
548 + 107 = 655
Since there are only 6425 employees, you need to adjust the value of the last individual in the survey. The last individual actually goes beyond the total number of employees, so you need to subtract the excess number from 107.
In this case, 655 is beyond the number of employees (which is 6425). So, you subtract the excess from 107:
655 - (655 - 6425) = 6325
Therefore, the last individual in the survey would be 6325.