 hypothesis which is 50-50 if it was fair but if it's not fair I would have to prove that it's not fair how can we simulate that well one way we could say let's use my random generation tool and say that if it's a one it's a heads and if it's anything other than a one it's going to be tails so we could use the same kind of concept but then go to three and so now we're going to apply everything that's one a heads everything that's not a one a tail do the same number generation tools but now we get from one to three right and then we can copy this whole random generator tool over to to get the hard-coded numbers and so here's our hard-coded number outcomes and again the numbers are a little bit messed up here for the for the number of flips but I think this comes out to actually 70 74 flips so and it might come out to 75 so I think this 74 is a little bit so what happened here is is here I took the number of heads which means that I'm going to say count if there's a one and it took all the heads now this one I actually cheated a little bit and I didn't catch the fact that my numbers were not properly calculated here because this is well actually this is one this one's populated properly one two so this one looks right so the other one had some funny business going on so I think this one is right but I still kind of shortcutted it by saying that well if there's 21 heads and I flipped it 74 times then the two and the three are going to be the what are the rest are populated and I'm assuming those are tails so I just took 74 minus minus 21 gives us the 53 so that the 53 and the 21 add up to 74 which I'm saying is the total number of flips now notice that it would be better if I actually did another count if function to count this column if it came out to be three or two because then I get it kind of a double check on my total which I like to do as an accountant but but but that takes a little bit more complex of a formula because then I have to say if it's not only a one but a one or a two right so I kind of shortcutted it here because if it's not a one I could have said I could also said you know if it's not a one then put something here right if it isn't this thing then put something here right but in any case that adds up to 74 and then I can take my 21 over 74 that gives us 28.37 percent and the other one is 53 over 74 so again and so that's 72 now again you would expect it to come out 50-50 so if I just look at heads and I was to look at these results if I flipped a coin multiple times and I came out with results of it came out 28 heads 26 heads 36 heads 42 heads notice that none of these results are above 50 percent that is quite unusual if it was a a fair coin right so so so this would this would give us a preponderance of evidence to say the null hypothesis does not look proper here because although I'm looking at a sample it seems quite unlikely that this is going to be the case right so so then if I was to look at our results this way I transposed all the heads in a column and now we're going to compare it to the 50 percent that we would expect and the first one it's off by 22 so heads are too low by 22 it's too low by 24 by 14 so notice it's always too low right that it's not always the same number but but that's given us pretty good evidence that we're like okay this thing looks like it's weighted towards tails because because we would we would expect then that it would be that that it that you know it wouldn't so it didn't always come out tails right but but and this is the common thing that's going to happen we're going to get the expectation which is the null hypothesis what we would expect to happen if it were fair and then test it out and see if there's a difference to to to from the actual data to what you would think would be happening or to the entire population if it were in this case the entire population being as though we flipped a fair coin infinite amount of times and would have then a 50-50 split so here's a here's a histogram for the heads in a not fair coin of the results that we took here and notice it's the results that are populating around 31 to 35 percent instead of around the 50 and you've got this this shape that looks like it's that's happening somewhat consistently right and the outliers around around that center point somewhat balanced versus this is the histogram we looked at in a fair situation where it's closer to the 50 percent and then you've got this kind of shape populating around it so that's the kind you know just the kind of concepts that would that we can theoretically think about uh here applying more of a of a mathematical concept because we kind of thought of infinity in this case which is a mathematically conceptual term for the entire population if we flipped an infinite amount of times and also how we can kind and and then the statistics is similar to a situation that we saw before in weight where where we don't have a theoretical concept we have actual population of weights of individuals versus a sample of that example population but that's a similar concept as the theoretical infinite flips versus the sample number of flips and we we can see how you can play with this stuff in excel pretty easily once you know some of these concepts which really helps you to understand it better if you can actually you know run tests in excel