Final answer:
In cluster sampling, the true statements are that sampling units are groups of items, and it's used when random sampling is not cost-effective. The correct answer is B: 1, 2, and 4 only.
Step-by-step explanation:
When using cluster sampling, the correct statements among the given options are:
Sampling units are groups of items. This is the basic premise of cluster sampling, as the population is divided into groups (clusters), and then some clusters are chosen at random for sampling.
The auditor uses cluster sampling when random sampling is not cost-effective. Because assessing every individual unit in a population can be time-consuming and expensive, selecting clusters can reduce these costs since only a subset of groups needs to be examined.
However, the statement that sample items within clusters need not be assigned random numbers is false because in cluster sampling, the clusters are randomly chosen, ensuring each element in the population has an equal chance of being included in the sample.
Moreover, the assertion that the auditor selects every nth item after a random start refers to systematic sampling, not cluster sampling. In cluster sampling, the entirety of chosen clusters is assessed, not every nth item.
Therefore, the combinations of true statements for cluster sampling are 1 and 4. The answer to the student's question is option B: 1, 2, and 4 only.