r/HomeworkHelp • u/hjalgid47 AP Student • Feb 02 '25
Social Studies—Pending OP Reply [AP Statistics: Assignment] Is it true that it is difficult to poll minorities in North America?
Hi, I would like to ask: Is it true that it is somewhat difficult to poll (contact and sample) minorites (Hispanics or Asians) in the USA? And that results based on such opinion polls are uncertain?
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u/Frodojj 👋 a fellow Redditor Feb 02 '25
The margin of error (MOE) of a binomial distribution (yes/no question) for a particular confidence level (based on Z, width W), percentage of yes responses (p, q=1-p), and sample size (n), and can found using:
MOE = W/2 = Z√(pq/n)
The maximum margin of error is when p=q=0.5. (Half are yes; half are no). For a 95% confidence interval distribution, Z = 1.96. (Two tailed, so split the 5% error into two for each side. 100%-2.5%=97.5%=0.975. Use statistical table A.1, whose values are derived by integrating the normal distribution's probability density function with mean μ=0, standard deviation σ=1, for the curious.)
In a poll of 1000 adults in the USA, assuming the sample is representative of the US demographics cira 2014 (source):
| race | count (n) | margin of error (W/2) |
|---|---|---|
| white | 651 | 3.84% |
| hispanic | 152 | 7.95% |
| black | 117 | 9.06% |
| Asian | 54 | 13.34% |
As you can see, because minorities represent smaller proportions of the population, they have a much higher margin of error. Now this assumes they respond with the same rate as their demographics. If there are antagonistic conditions that cause their counts to go down (such as fear of discrimination), then the margin of errors get even larger.
(P.S. I took statistics long ago. I didn't remember everything, so I had to look this up. It was fun deriving the graphic of the Pew Research Center's article that I linked to.)
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