# Probability questions

73% of the US population is white
12% of the US population is black

Given a sample size of 1,620 commercials, and ignoring potential variables such as television viewer demographics and self-selection, what are the chances that, drawing a random sample from the population: 952 commercials are white only, 53 are black only, and 465 consist of both blacks and whites? How do I determine if such numbers are statistically significant?
Thanks much.

If you're curious as to why I'm asking, I'm taking a Poli Sci 4000 level class and have to give a presentation on racial bias in the media. I see what appear, on the surface, to be flaws in the author's arguments (such as claiming racial discrimination because 58.8% of commercials are all white and only 3.3% are all black, yet dismissing that 28.7% consist of both black and white bringing cumulative totals to 32% of commercials having blacks and 87.5% of commercials having whites...overlap takes it over 100%).

If my questions above aren't the best way to counter/support the author's claims, what statistical calculation would be?

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You don't have nearly enough data to draw any conclusions like these. For instance, how many people are in the average commercial? What percentage of commercials feature only one person? Plus, in order to be statistically significant, you would need to have an objective measure of what the percentage of commercials containing white only/black only/mixed/etc. should be based on "nondiscriminatory" commercial numbers.

In other words, good luck applying rigorous analysis to such soft science.

You don't have nearly enough data to draw any conclusions like these. For instance, how many people are in the average commercial? What percentage of commercials feature only one person? Plus, in order to be statistically significant, you would need to have an objective measure of what the percentage of commercials containing white only/black only/mixed/etc. should be based on "nondiscriminatory" commercial numbers.

In other words, good luck applying rigorous analysis to such soft science.

1. Very true, so hypothetically I will say 5 people in the average commercial.

2. Isn't that what I'm trying to figure out? What the % breakdown should be if it were based on chance and how that compares to the actual breakdown? Once you have the first set of numbers, can't you say"It should be 34%, but it is 58%; the odds of that happening purely by chance are..."?

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1. Very true, so hypothetically I will say 5 people in the average commercial.

That's still not enough information. You need to know the distribution of numbers of people in each commercial, not just the mean.

Ok, if there are 5 people in the average commercial, then 3.3% of commercials containing only black people is 1300 times more than is expected. See what I mean? By the time you're done making simplifying assumptions, the statistical analysis will tell you more about your assumptions than it will about anything else.

By the way, your calculation of over 100% does not take into account that there are commercials with both whites and blacks. You can't sum probabilities like that. For instance, the probability of getting at least one heads in three tosses of a coin is not 3/2.

I wasn't attempting to sum probabilities. When I mentioned the cumulative totals and how they added up to over 100%, I was simply summing the real #s to explain why I had a problem with the author's contentions.

518/1620 (32%) of commercials had at least one black
1417/1620 (87.5%) of commercials had at least one white

Thanks for the help though. You can see why I stay far away from math related fields and that the stereotype that lawyers (including future lawyers) suck at math is true.