Duvniask wrote:Anyone who deals in statistics should knows about null-hypotheses, which as a rule assume no significance*, and that they are usually rejected when probability is estimated to be lower than 5% from a normal distribution (in this case, the sampling distribution of exit polls, assuming they are randomized).
*In this case, assumes no significant difference between the poll and the election result.
Also, using basic rules of probability for independent events, we multiply the chances of the event occurring with itself by each time it did. So if the exit polls had a ≤5% chance of being off each time, and that happened 5 times, then the probability of that happening is 0.05
5 = 0.0000003125 or 0.00003125%. In other words, not freaking likely.
A poll with a margin of error of, say, 3% and a 95% confidence interval, will tell you that the true value is within 3% of the estimate with 95% probability.
Let's say a hypothetical poll estimated 45% support for Sanders, margin of error 3%. Then we'd be able to say there's a 95% probability of the true population value being +/- 3 percentage points from 45%. The 95% confidence interval would thus be [0.42; 0.48]. If the actual result was 35% Sanders, then something would be very wrong here, either with the poll or the results themselves, because there was only a 5% chance of the results being more than 3 percentage points off (in our hypothetical example they were 10 percentage points off).
Also, the margin of error is dependent on the sample size,
n, as it is calculated from multiplying the given critical value with the standard error (which contains the sample size). It is already taken into consideration. A smaller sample size will yield a larger standard error, which in turn yields a larger margin of error.