 a random box generation that's doing 10 samples of however many samples down that we want to do. And we can then start to use this to apply our statistical tools to see if it gives us results that basically we would expect. Now once I have a random generating tool like this, I can then copy the entire thing because this has formulas in it and paste it static, meaning only the numbers. So these are simply hard coded numbers for all those random generations. So now if I go to the bottom of this, summing up our results, this is for Candidate A where we're asking Excel to look at this series of numbers in this column, which represents the poll that we took, which is going to give us results of either them being for Candidate A or not for Candidate A. The formula looking like this, we're going to say equals count the items in this column if this is the range, there's the criteria range, this column. And then the next criteria comma is if it's less than or equal to 60. Now because we have to put this less than or equal to and those are kind of like text, we have to put the quotations around that. And then we have to connect it to the 60 with an and so it looks a little bit complex, but not too bad once you do it a few times. And therefore, we're looking at this column, and it's counting all of the numbers that are equal to 60 or below 60. And then we can do the same thing if it's not a so if it's not a we're looking at this column, it's this formula, look at that range, Excel please, comma, and this time just take greater than not equal to but everything that's above 60. And that's going to give us this number. This number then is a double check, or this number is our total adding those two out. So 102 plus 48. That means that we did this 150 times in other words, if I count all of these rows that would come up to 150. So then I can take my percentage and I can say what's the percentage of times that we had a four candidate a versus against that would be 102 divided by the total of 150. 68% of the time for candidate a and the other being 48 divided by the total of 150, 32% of the time not. So again, we would expect that we had the starting point a priori that we said that it should be 60 40 if we did this infinite amount of times because or if we have the data for the entire population. We said that the population data was 60% for candidate a. So if I did this again, we did the same thing here again. And this comes out to 6535 this one 57. So this one's below 43. This one comes out to 5743 524867 and 33 and so on. So here's our series of results for us doing this multiple times. Now I'm going to take this column of numbers. I'm just going to take the ones that are for candidate a which the percent for candidate a and put it in the format of a column, which we can do it Excel by basically transposing. And it's a pretty simple procedure if you want to watch this practice problem or do it as well with us in Excel. So then we can say I'm going to then list it this way. So now we've got column a and these are the samples. So how many samples did we take 10? And these are the results that we got that were the percent for column a. And so we can compare that then to what was expected or what is the actual number which we said that we knew a priori beforehand. We knew it was already 60 and we created a test that you would think that if we did the test on infinite a number of times because it would come out to 60% because we took the test to take a random draw between one and a hundred and we took everything that was between below 60 and below. So so in any case the difference is 8, 5, 3, and then you can see the difference is kind of above and below. If I was to take the average of of these this column it comes out to around 61 which is pretty close to what to the actual of 60. Okay so so if we were to we can we could run this experiment with Excel just given the fact that it's a pretty simple thing to run. This is kind of blurry because I copied a whole bunch of columns here. We ran the same kind of thing one through 100 but you can do it basically a whole bunch of times not an infinite amount of times but a whole lot of times in Excel. So it's interesting to try to to run this same test which you can build very easily and analyze your results and see how much closer you get to kind of the actual this is just basically the sample running this I just copied the same formula all the way through and we did it you know a whole bunch of times. So this is a huge random number generator or relatively huge you know and then I just copied that and then here's the actual results which I just gave us a few of them so now you've got sample one two three same thing