How big is the active vocabulary that an average hunter gather tribe in Africa uses? Is it comparable to the size of Western civilisation?
Active vocabulary size is a very difficult thing to measure or estimate. Is it all the words ever used in a lifetime or words routinely used? How about homonyms and polysemous words? How about functional words and languages that don't have many?
Another problematic term is 'hunter gatherers'? Do you mean modern hunter gatherers or historical ones? Do you mean small "uncontacted" tribes or large seminomadic societies with mixed modes of subsistence and extensive use of imported technology (think Aleut using snowmobiles).
When people mention hunter gatherers they usually mean small far-away tribes with minimal external contact. However, these are quite likely not to be very representative of what might have been typical before the encroachment of technologically superior belligerent cultures into their habitats resulting in societies under stress whose language may be under all sorts of pressure.
However, despite all that. The actual vocabulary size of somebody in a small relatively isolated community is not likely to be that much smaller than somebody of similar socioeconomic status living in an industrial society. Remember, hunter gatherer lives are not particularly simple. They tend to have knowledge of large folk taxonomies of plants and animals that can go into the hundreds or thousands. They are also likely to have quite complex kin and clan terminology as well as names for various tools and their uses. They might also have an extensive meteorological vocabulary dealing with seasons, parts of day, etc. They will not lack vocabulary for abstract concepts either. In some such societies, people will also have to deal with taboos resulting in name changes as a result of death. And many of them are also likely to be multilingual due to various influences such as intermarriage or other types of contact.
There will also be some variation among individuals depending on their role in knowledge maintenance, etc.
Big enough for their needs.
The question is difficult to answer, because you want to compare two vague sizes, using a flexible measurement.
An average hunter gather tribe in Africa. This is not exactly an accurate size. What language do they speak? Vocabulary will of course vary between languages. Do you mean the active vocabulary of an individual, or for the entire language?
The size of Western civilization. Who is that, and what language do they speak? Is it for an individual or for the entirely language? What about loanwords?
Active vocabulary. Languages is believed to have the ability to describe everything. The number of words in an active vocabulary is therefore directly related to the number of different objects, events and so on, the language speakers are exposed to. One study showed that some dock workers in the UK some hundred years ago, had an active vocabulary down to as little as 300 words. Professors in Linguistics could possibly have as many as 120.000 words in their active vocabulary. Languages with many speakers will naturally have bigger vocabulary, since the more people, the more diversified they can be. But that would not necessarily mean that the active vocabulary of a single person in that language would be any bigger.
To sum up, yes I think size of active vocabulary between an African hunter, and an American businessman can be compared. When the businessman knows different economical terms, the hunter probably knows the name of more animals, insects and flowers than the other. And I think it possibly could be the same size as well, depending on how much their every-day-life varies from day to day.