### Video Transcript

Karl Pearson tossed a coin 24,000 times and recorded 12,000 12 heads with 24,000 tosses. What is the point calculate ? so the bespeak estimate for this that we would use would be phosphorus prime equals 12,000 well divided by 24,000 which is 0.5005 What about the standard erroneousness of proportion ? then to find that we have to use the formula the square root of P Prime Times Q Prime, which is one minus T prime divided by and so that would be the square root of 0.5005 times in Q prime is one subtraction 10.5005 Sometimes you might see that he starting Q star divided by 24,000. No, decidedly calculate that in the calculator and you get 0.3 And that ‘s the standard error of proportion. Let ‘s calculate the 95 % confidence time interval. The inaugural thing we have to do is find Z you ‘re looking for. You would do Alfa Z is Alfa divided by two. So our Alfa is one minus 10.95 which is 0.5 divided by two means you would get 0.0 to 5. So that is the value will be 1.96 You ‘ll start to see after calculating these confidence intervals a batch that you start to remember some of these Z values. indeed 1.96 tens of standard error of proportion that we fair found, which was the square root of 0.5005 times one minus 10.5005 divided by 24,000 which would be 1.96 times 0.3 which is peer to 0.6 so immediately we do 0.0 point 5005 subtraction 50050.6 and 0.5005 plus 0.6 and we get 0.4945 and 0.506 So my 95 % assurance and thrills anywhere between 49.45 % toe 50.65 %. If you like to express it as percents, so I can do it. My own random experiment if I did n’t want to toss the mint 24,000 times and criminal record head does that could take a actually long clock. so one way to do a random experiment is in your calculator. And to do it in your kayak litter of you would do the random into your serve and to found to find that I went to math and I scrolled complete to PRB. You will see random integer in that number. indeed then, in my catheter, I put zero and one where zero can represent sales and one can represent heads. And I was a type 999. That ‘s the most issue of trials that the calculator will do for you. 01999 and then it takes a few seconds. Your results come up. Your results are like a long list of zeros and ones basically is tossing the head the coins for you and recording heads or tails. then, um, then I want to find this some of the head. thus if the heads were one, then to find the some of the heads, like how maney heads were their entire on score of all the ones, or I could n’t take the some because if I added up all of them, then the some would be the act of times that ahead showed up and that I when I do that in my results, I get 503 out of 999 now. These results condemned for for each person because it does n’t different random affair every unmarried time. But when I do, When I did it on the calculator, I got 503 of the 999 which was very close to about hats of 5/3 out of 9 99 is about 50 0.4 %. I even tried a second time in the moment prison term I did it. I got 483 heads and again, I merely let the heads represent the one and I summed so tilt at a 999 which is approximately 48.3 %. As you can see, the chances of getting heads is gets closer and closer to 50 % each time, and if continued this overall, we would see that we get about 50 %

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