Question

the human resource department at a certain company wants to conduct a survey regarding worker benefits. the department has an alphabetical list of all 3525 employees at the company and wants to conduct a systematic sample of size 40. (a) what is k? k = \square

Explanation:

Step1: Define k for systematic sampling

In systematic sampling, $k$ is calculated as the ratio of the population size $N$ to the sample size $n$, i.e., $k = \frac{N}{n}$.

Step2: Substitute given values

Here, $N=3525$ and $n=40$. Substitute into the formula:
$k = \frac{3525}{40}$

Step3: Calculate the value

Perform the division:
$k = 88.125$
Since we use the floor value for $k$ in systematic sampling (we round down to the nearest whole number to ensure we can select the required sample size), $k=88$.

Answer:

88