Systematic Sample To predict the outcome of a county election, a newspaper obtains a list of all 945,035 registered voters in the county and wants to conduct a systematic sample.


Determine k if the sample size is 130.

Verified step by step guidance

1. Understand that in systematic sampling, you select every k-th individual from the population list to form your sample.
2. Identify the population size (N) and the desired sample size (n). Here, N = 945,035 and n = 130.
3. Calculate the sampling interval k using the formula: \[k = \frac{N}{n}\]
4. Substitute the values into the formula: \[k = \frac{945,035}{130}\]
5. Interpret the value of k as the step size to select every k-th voter from the list to get a sample of size 130.

Key Concepts

Systematic Sampling

Systematic sampling is a method where you select every k-th individual from a list after choosing a random starting point. It is used to ensure a spread-out sample across the population, making it easier and quicker than simple random sampling while maintaining representativeness.

Sample Size (n)

Sample size refers to the number of individuals or observations selected from the population for analysis. It affects the accuracy and reliability of the results; in this question, the sample size is given as 130, which determines how frequently individuals are selected in the systematic sample.

Sampling Interval (k)

The sampling interval k is the fixed step size used in systematic sampling, calculated by dividing the population size (N) by the sample size (n). It indicates that every k-th individual on the list is chosen, ensuring the sample is evenly distributed across the population.