Hey, everyone. So in this video, we're going to take a look at confidence intervals. Now, the formal definition of a confidence interval is that it's a specific interval estimate of a parameter determined by using data obtained from a sample. In simplistic terms, a confidence interval is basically us being confident, hence the name "confidence," that the mean lies within a given range. So, for example, if we say we're dealing with a 95% confidence interval, that means we are 95% confident the mean lies within a given interval.

So if we take a look here at the formula for a confidence interval, we're going to say confidence interval is equal to 𝛾 plus or minus tsn. Here, t is the Student's t-statistic, s is our standard deviation, n is our number of measurements, and again, our average or mean is ̅𝛾.

With the confidence interval formula, we have our Student's t statistical table. This is used in our understanding of confidence interval in the comparative data from different experiments. Let's look at the parts of this table to get a better understanding of it. Here, we have first our degrees of freedom, which range from 1 all the way to infinity. Here, infinity means we're dealing with a large amount of measurements, something greater than 120. When we say degrees of freedom, degrees of freedom are equal to your measurements n minus 1. For example, if we have 10 measurements, the degrees of freedom would be 10 minus one, which is equal to 9. So, we'd be right here.

Then we could talk about our confidence level in terms of our measurements, ranging from 50% confidence all the way to 99.9% confident. Of course, we can never be 100% confident because there's going to be a little bit of uncertainty with all of our measurements, but we can get all the way up to 99.9. So, let's say we wanted to look at the 95% confidence interval, we'd look at 95% here and we're at 9 for the degrees of freedom since we're dealing with 10 measurements and they both would meet here. So, our t value would be 2.262.

Just remember, a confidence interval is a way of us giving confidence to our mean or average residing within a particular range, plus or minus.