At a large university a simple random sample of five female professors is selected and a simple random sample of 10 male professors is selected. The two samples are combined to give an overall sample of 15 professors. The overall sample is a A. simple random sample. B. biased due to imbalance. C. a stratified sample. D. All of the above

D. All of the above

Step-by-step explanation:

Samples may be classified as:

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this problem:

Two random samples are selected and combined. The combination is a random sample. So A. is correct.

They are not balanced. More male professors than female are chosen. So B. is correct.

The teachers are divided into groups (male and female). And some members of each group are selected. So C. is correct.

So the correct answer is:

D. All of the above