[SOUND] In this video, I'm going to show you the impact of sample size. Let's assume that we took a sample of 50. And the sample of 200 and a sample of 500 and for the sake of demonstration, I'm going to assume that all the samples gave us basically the same value for the mean. As well as their standard deviation. So what would change in our equation, and again remember that the equation for confidence interval is sample mean plus and minus the margin of error. And margin of error is your critical value times the standard error. So now we need to calculate the standard error. So standard errors are basically your sample standard deviation, which we are using as a point estimator for the population standard deviation divided by the square route of sample size. So in this case, it's 50. So this is the standard error for sample size of 50. And I can grab and pull this and you will calculate the rest for me automatically. Lets look at what happens to our t-distrubition when we have this. So once again we are saying that we are looking for the 95% confidence interval so here is my 95%. So this is 95% so everything to the left of this is .975. And im looking for this value t of alpha over two because .025 is set in here and that's alpha which is .05 divided by 2. So therefore, my t distribution is t.inverse and I'm going to give it the value of .975 and the degrees of freedom is n minus 1. And in this case, in this column, my n, Is 50 right here. So it's going to be 50 minus 1, so that's 49. And I'm going to actually write it as an equation so I can just copy it. So it's going to be this cell minus 1. And now, if I just grab this and pull it, I will get appropriate values. I am just going to show you for the sake of illustration how Z will change accordingly. So Z does not require the degrees of freedom. So I am going to use NORM.S.INV and I will say that everything to the left of it is .975. And clearly that's not going to change because there is independent of the sample size. So as you can see as my sample size has increased, these two values are becoming closer and closer. For 50 it's not as close as it is for 200 and for 200 it's not as close as it is for 500. So once again if you are not having access to a Spreadsheet you can always use 1.96 as a quick was of estimating what a t of alpha over two would have been. So what is that margin of error? Margin of error is always your standard error multiplied by the t value. Since I'm calculating it here, I'm going to use the accurate values. So again I can just grab this and it will calculate it for all of them. So if I click on this now, it's appropriately multiplying the standard error by the correct value of t of f over two. What you see is that margin of error has decreased as the sample size has gone up, our accuracy and our precision are going to go up. Why two folds, one is as you can see your critical value is decreasing from 50 to 200 to 500. It's getting smaller and smaller but also. So is your standard error, so both the standard error and t of alpha over two are decreasing. So as a result the margin of error is decreasing quite a bit, going from 50 your margin of error is plus or minus five, but at 500 your plus or minus 1.5. So let's see what happens to our confidence intervals. Our confidence intervals is going to be the mean of this sample minus its margin of error. That's its lower bound. And this one is equal to mean of the sample plus its margin of error. So again, if I grab these and just copy them it would repeat it for me, so this is again the mean for the sample of 200 minus the margin of error. And this is the same mean plus the margin of error, for 500, the sample mean minus the margin of error. Sample mean plus the margin of error. So now what has happened to our width? So at sample size of 50, the width of our interval is 10 degrees. That's quite a bit. At 500, the width of our sample Is three, add 200 the width of interval is five. So our sample size decreases the width of the confidence interval. So when we want to have high confidence levels, but also we want to e precise. Then the best way to achieve that is by increasing the sample size, because sample size reduces the margin of error.