The given statement is: "Using a systematic sample guarantees that members of each group within a population will be sampled."
To determine whether this statement is true or false, let's first understand what a systematic sample is. In systematic sampling, we select every k-th item from a population list, starting from a randomly chosen point. However, this method does not ensure that members from each subgroup (or stratum) within the population are sampled, as it simply follows a fixed interval pattern.
On the other hand, a stratified sample involves dividing the population into distinct subgroups (strata) and then taking a sample from each of those groups. This approach guarantees that every group within the population is represented in the sample.
Given this explanation, it’s clear that systematic sampling does not guarantee that members of each group will be sampled, whereas stratified sampling does.
Therefore, the correct answer to the statement is:
B. False. Using a stratified sample guarantees that members of each group within a population will be sampled.
