[stocksthatgoup]

No way do 400 votes give you a 95% confidence in a poll! Let’s all go back to statistics 101

[scrabblehack]

pq/sqrt(n) = 0.5*0.5/20 = 0.0125
Two standard deviations (95%) would be +/- 0.025

The points of dispute would be:
(1) is the sample random?
(2) has the poll accurately gauged a likely voter?

[11th Commandment]

Even worse:....

Sample Size: 400 completed telephone interviews among a random sample of likely Republican primary voters living in South Carolina (287 self-reported Republicans and 113 self-reported independents and Democrats.

[John Valentine]

You can’t just quote the confidence level without also providing the range.
400 participants are more than enough for 95% within plus or minus 5%.