What is meant by a 95% confidence interval?

Question

Thank you in advance.

Answer 1

In statistics, you typically take samples to try and infer something about a population. For example, you randomly sample 50 men and calculate their average height to be 70 inches. 70 inches is an estimate (called a sample statistic) of the overall population average male height (called a population parameter). There will always be variation from sample to sample though. You could take another random sample and get an average of 71 inches. So how do you know how "good" your estimate is? That's where confidence intervals come in...

The typical confidence interval is:
Estimate +/- Margin of Error
or
[Estimate - Margin of Error , Estimate + Margin of Error]

This gives you two endpoints. It means that you can be XX% (XX = confidence level) confident that the TRUE POPULATION PARAMETER is between these two values. If your estimate came from a truly random sample, it's pretty powerful stuff - you can take a small sample (30-50) and make a solid conclusion about an ENTIRE POPULATION. This of course depends on having a truly RANDOM sample, which in practice is not always easy, but another issue altogether. :)

Back to the confidence interval, there are several types of estimates and parameters depending on the situation. Sample means are estimates for population means (height example), Sample proportions are estimates for population proportions (What % of people are voting Ron Paul next election), and so on. Regardless of what you're estimating, the confidence interval follows the same format:

Estimate +/- Margin of Error

Ideally, you'd like the Margin of Error to be small. It is calculated differently for the different things you want to estimate (means, proportions, ...), but usually depends on three things

- Confidence Level
- Sample standard deviation
- Sample Size

Confidence Level dictates how certain you want to be that your population parameter is within you confidence interval. Typical values are 90%, 95%, and 99%. These values are the best at giving you a good balance between high confidence, but as small margin of error as possible. You could even calculate a 99.99% confidence interval, but then the margin of error becomes too high to be useful.

Sample standard deviation describes the variation of your sample.

Sample Size is the only thing you have control over, the bigger the sample, the smaller the margin of error.


In summary, if you do a truly random sample, and calculate a 95% confidence interval to be E +/- ME, then you can be 95% confident that your true population parameter is between E - ME and E + ME.

For example, if you calculate a 95% confidence interval for the average male height to be 70 +/- 3, then you can be 95% confident that the TRUE POPULATION MALE HEIGHT is between 67 inches and 73 inches. There's a 5% chance that it's outside this range.

Answer 2

Define 95 Confidence Interval

Answer 3

95 Confidence Interval Definition

Answer 4

The interpretation of a confidence interval is a difficult thing to grasp for students taking a stats course. I will start with a simple example and show how that relates to the common interpretation of a 95% confidence interval for the true mean.

Suppose you have a bag with large number of marbles. All you know about this bag of marbles is that it contains either white or black marbles and that 95% of the marbles are black (therefore 5% are white). You reach into the bag and pull out a marble BUT DON'T LOOK AT ITS COLOR. Is the color black or white?

We don't know for sure. however, we do know that if we guessed "black" then we would be right 95% of the time. That is, if we repeated our experiment of pulling a marble from the bag (but not looking at its color) and guessed that it was black each time, then over the long run (ie after repeating this experiment many, many times) we would be right 95% of the time. We can never know if we are right for a given experiment (because we don't look at the color of the marble we chose), but we do know that the very nature of our experiment guarantees that 95% of the time, the marble we draw will be black.

Now, how does this relate to a 95% confidence interval for the mean? When we collect a sample and calculate our confidence interval, that is like drawing a marble from the bag. We don't know what the true value for the mean is so we don't know if it falls within the interval or not (that is, in the marble experiment, we don't look at the color of the marble we chose). However, we do know that the procedure we used to construct the confidence interval guarantees that in the long run, if we were to repeat our sampling procedure over and over again, 95% of the confidence intervals we constructed would contain the true mean. Whether or not the one particular confidence interval we did calculate actually contains the true mean is unknown, just like the color of our marble we chose is unknown to us, but we do know that we have a 95% chance that our interval does contain the true mean.

One last remark, and this is very important, the above description does NOT mean there is a 95% probability that the true mean is within the confidencen interval. The population mean is not a random variable. Either it is or it is not contained within the interval. For the marble example, either the chosen marble is black or white, there is no other possibilities.

Math (and Stats) Rule!

Answer 5

This Site Might Help You.

RE:
What is meant by a 95% confidence interval?
Thank you in advance.

Answer 6

It means that an estimate that you make for some quantity has a 95% change of being within some interval [a,b].

Answer 7

It means that there is a 95% chance that results are significant. It is usually used in conjunction with the Normal Probability Distribution Curve as many data sets can be regarded as being part of a normal distribution curve.

95% is one of the two main confidence levels - the other is 99%.

Answer 8

In this situation, 95 out of 100 times, the predicted outcome is going to be correct.

Answer 9

This means that there is only a 5 % chance that the outcome is due to chance alone.