Confidence Intervals

00:01 Hi again. In the previous lesson we learned about point estimators, but as you can guess, they are not very reliable.

00:10 Imagine visiting 5% of the restaurants in London and saying that the average meal is worth £22.50.

00:18 You may be close, but chances are that the true value isn't really 20 to 50, but somewhere around it.

00:26 It's much safer to say that the average meal in London is somewhere between 20 and £25, isn't it? In this way, you have created a confidence interval around your point estimate of 20 to 50. A confidence interval is a much more accurate representation of reality.

00:45 However, there is still some uncertainty left, which we measure in levels of confidence. So getting back to our example, you may say that you are 95% confident that the population parameter lies between 20 and 25 quit.

01:01 Keep in mind that you can never be 100% confident unless you go through the entire population.

01:08 And there is, of course, a 5% chance that the actual population parameter is outside of the 20 to £25 range.

01:17 We'll observe that if the sample we have considered deviates significantly from the entire population.

01:25 All right. There is one more ingredient needed.

01:28 The level of confidence.

01:30 It is denoted by one minus alpha and is called the confidence level of the interval. Alpha is a value between zero and one. For example, if we want to be 95% confident that the parameter is inside the interval, alpha is 5%.

01:49 If we want to higher confidence level of, say, 99% alpha will be 1%.

01:57 Don't worry. We will discuss this in more detail in our next video.

02:02 Oh, you can't wait until the next lesson.

02:04 Okay, then.

02:05 Here it is. The formula for all confidence intervals is.

02:10 From the point estimate minus the reliability factor times the standard error to the point estimate plus the reliability factor.

02:20 Times the standard error.

02:24 We know what the point estimate is.

02:26 Values like X bar and SW bar, right? We also know what the standard error is.

02:34 What about the reliability factor? We'll have to introduce it in our next lesson.

02:40 Thanks for watching.