Which sampling method involves selecting households at random and including every person within those households?

Cluster sampling is the correct method because it involves selecting entire groups or clusters, such as households, at random. In this sampling technique, each selected household includes every individual within it, allowing researchers to collect data from a natural grouping as a whole. This method is particularly efficient when populations are spread out over a geographical area, as it reduces the costs and time associated with surveying individuals dispersed across a larger region.

Other methods, such as simple random sampling, involve selecting individuals randomly from the entire population without considering the groupings. Systematic sampling typically chooses individuals at regular intervals from a list, while stratified sampling involves dividing the population into subgroups and then sampling randomly from each subgroup rather than focusing on entire household units. Thus, cluster sampling effectively captures data from complete households, making it the appropriate choice in this scenario.