 bring it down to 74 and then I'll copy that whole thing and paste it across to the hundred tests that we will make that would have an uneven coin so now we're going to paste all the way across so there's our table generation let's insert a table insert table and so now we have our random generator for the unfair coin so now let's select the whole thing and and make a static test copying the whole thing and put our cursor over here and we'll put it right here and right-click and I'm gonna paste one two three just the values I'm gonna select the headers and format the headers so I'm gonna make them home tab font group black white centered and wrapping the text I'll select all of the data now and let's make that our blue and bordered so we'll select the entire data set and we'll make that home tab font bordered and blue and then now when I do my count if it's heads it's gonna say I want you to say equals count if brackets and then I'm gonna take the whole thing I'm putting my cursor up one control shift up and then shift down now I'm gonna look up here to my formula bar comma if it's a one count it and that comes out to 21 and then I one way I can do the second bit if it's tails I'm just gonna say I know there's 75 of them so I can or 74 so I could just say this equals you know this count of 74 minus 21 that would be the easiest thing to do we could also come up with a with a formula to say count if it's not equal to you know one right and that would give it but but the easiest thing to do would be that and I'm gonna say then the totals and sum them up which of course should come out to 74 and then we can take our percent our percent heads versus the percent tails and then the percent total so the percent head this time was equal to 21 divided by 74 making that a percent home tab numbers percentifying tails is 51 over 74 and we'll say home tap numbers percentify font group underline the total percent then of course summing 2872 is number group percent 100 percent so there we have it if I copy this across it's copied all the way across for our 100 tests so now we've got that copied I will make this something funny happen here hold on us oh I can't I have an issue and that's because I used this 74 and that's not going to move that needs to be absolute so that's r i 7 1 that's our our i 75 so I'm gonna put my cursor in here f4 dollar sign before the letter dollar sign before the number and then copy that across and it should be good to go and then I'll select the whole bottom bit and make it that dark blue and white for our totals down here and so we'll make that home tab font group dark blue and white so now you can see of course if I looked at the percent heads then you're gonna say hey look that doesn't look right something looks leaning towards it looks like it's leaning towards the tails right so if I let's copy all of the heads and transpose our totals I'm just gonna say if I just look at my heads I would expect it to be around 5050 if I go up top and transpose it first I'm gonna right click just the values then I'm gonna copy that and put my cursor in vh right click paste it one pasted special transpose enter delete all of this stuff because we don't need it anymore and then I'm gonna insert a table insert table okay make it a percent home tab number percentifying it so there so there we have our numbers and then if I wanted to say this is what was expected expected and this is the difference difference expected would be 0.5 or 50 percent I'm gonna double click copying that down the difference is 28 minus 50 and so notice the differences are all you know going one way so now we have some evidence where we're saying hey look something doesn't look right according to these tests we have a preponderance of evidence to then reject the null assumption that it's a fair coin which if looked an infinite amount of times would come out to 5050 right in the total population I'm going to delete this now if I make a histogram of this data I'm going kind of quick because we're running long on time I can go to the insert charts histogram so here's a histogram of the unfair coin leaning towards tails and you can see the center of the graph it still looks like it's centered but you could see where the the labels are over here instead of around 50 percent so the center point is spreading out over here which is is not where we would expect the center to be whereas if I copy the the even coin and I copy the histogram we came from that and we copy that over here then let's paste that we can see that the center point is what we would is closer you know to what we would expect so so that's our uh this one still kind of shifting over to the right here a bit that's kind of interesting but you get the point here so you get so so so the idea is is that we would test it the total population is an infinite number of flips here when we compare it to like sampling that we might do in an election so an infinite number of flips which would be 5050 we took a sample which is a finite number of flips and here we've got a preponderance of evidence that certainly leads us to believe that something looks off here we're still a little bit shifted over to to to the right but we're nowhere we're nowhere near as skewed as obviously this one up top and again obviously because it's a random sample we can then get into questions of how close are we to the actual number given the samples which we'll talk more specifically about in future presentations