Which of the following applies to random sampling? Group of answer choices a) The sample may be larger than the population. b) Observations in the population can be selected for the sample only once. c) Smaller samples are less likely than larger samples. d) All observations in the population are equally likely to be selected into the sample.

d)

Explanation:

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. It also has the characteristic that a simple random sample is meant to be an unbiased representation of a group.

In a simple random sample, the sample is always smaller than the population (since it's a subset of it).

There are also two kinds of random sample, one with replacement (in which the same element is put back into the population and it can be taken for the sample again, thus is being selected more than once) and one without replacement (in which every element can only be selected once).

There is no really a standard size for each sample as long as it is smaller than the population, however, smaller samples can tend to reduce reliability and therefore can bias our experiment so they are not recommend. Also the idea of the sample is that we can generalize our observations into the general population and this can happen with larger samples.

Thus, the characteristics that apply to random sampling are:

d) All observations in the population are equally likely to be selected into the sample.