# Margin of error and confidence level relationship trust

### Confidence intervals and margin of error (video) | Khan Academy

Trust me. It works, okay?" So a sample of just 1, people gives you a margin So you can think of the margin of error at the 95 percent confidence interval as. Pollsters disclose a margin of error so that consumers can have an or minus 3 percentage points at the 95% confidence level means that if. Trust declines, not so good, . 'we have to Confidence level is how likely the value will fall within your Upper interval = mean + margin of error = x̄+ zσ x̄.

And we are pollsters. And we're interested in figuring out, well, what's the likelihood that candidate A wins this election? Well, ideally, we would go to the entire population of likely voters right over here, let's say there'slikely voters, and we would ask every one of the them, who do you support?

And from that, we would be able to get the population proportion, which would be, this is the proportion that support, support candidate A. But it might not be realistic. In fact, it definitely will not be realistic to ask, well, allpeople. So instead, we do the thing that we tend to do in statistics is, is that we sample this population, and we calculate a statistic from that sample in order to estimate this parameter. So let's say we take a sample right over here. So this sample size, let's say n equals And we calculate the sample proportion that support candidate A.

So out of thelet's say that 54 say that they're going to support candidate A. So the sample proportion here is 0. And just to appreciate that we're not always going to get 0.

Maybe in that one, we got 0. And we already have the tools in statistics to think about this, the distribution of the possible sample proportions we could get.

## Confidence intervals and margin of error

We've talked about it when we thought about sampling distributions. So you could have the sampling distribution of the sample proportions, of the sample proportions, proportions. And it's going, this distribution's going to be specific to what our sample size is, for n is equal to And so we can describe the possible sample proportions we could get and their likelihoods with this sampling distribution.

So let me do that. So it would look something like this.

Also, if we make the assumption that the true proportion isn't too close to zero or not too close to one, then we can say that, well, look, this sampling distribution is roughly going to be normal. So we'll have a normal, this kind of bell curve shape. And we know a lot about the sampling distribution of the sample proportions. We know already, for example, and if this is foreign to you, I encourage you to watch the videos on this on Khan Academy, that the mean of this sampling distribution is going to be the actual population proportion.

And we also know what the standard deviation of this is going to be. Along with the confidence level, the sample design for a survey, and in particular its sample sizedetermines the magnitude of the margin of error. A larger sample size produces a smaller margin of error, all else remaining equal.

### survey - How are margins of error related to confidence Intervals? - Cross Validated

If the exact confidence intervals are used, then the margin of error takes into account both sampling error and non-sampling error. If an approximate confidence interval is used for example, by assuming the distribution is normal and then modeling the confidence interval accordinglythen the margin of error may only take random sampling error into account.

It does not represent other potential sources of error or bias such as a non-representative sample-design, poorly phrased questionspeople lying or refusing to respond, the exclusion of people who could not be contacted, or miscounts and miscalculations. Concept[ edit ] An example from the U. The size of the sample was 1, Basic concept[ edit ] Polls basically involve taking a sample from a certain population. In the case of the Newsweek poll, the population of interest is the population of people who will vote.

But how can we distinguish real change from statistical noise? As with the difference between two candidates, the margin of error for the difference between two polls may be larger than you think.

But taking into account sampling variability, the margin of error for that 3-point shift is plus or minus 8 percentage points. This is not to say such large shifts are likely to have actually occurred or that no change has occurredbut rather that we cannot reliably distinguish real change from noise based on just these two surveys. The level of observed change from one poll to the next would need to be quite large in order for us to say with confidence that a change in the horse-race margin is due to more than sampling variability.

Even when we do see large swings in support from one poll to the next, one should exercise caution in accepting them at face value. Some of these might be quite far from the truth. Yet often these outlier polls end up receiving a great deal of attention because they imply a big change in the state of the race and tell a dramatic story.

A result that is inconsistent with other polling is not necessarily wrong, but real changes in the state of a campaign should show up in other surveys as well. The amount of precision that can be expected for comparisons between two polls will depend on the details of the specific polls being compared. In practice, almost any two polls on their own will prove insufficient for reliably measuring a change in the horse race.

As a general rule, looking at trends and patterns that emerge from a number of different polls can provide more confidence than looking at only one or two. Generally, the reported margin of error for a poll applies to estimates that use the whole sample e.

But polls often report on subgroups, such as young people, white men or Hispanics.