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AP.STATS:

DAT‑2 (EU)

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let's say that your school has a population of 80 students in it maybe it's not your whole school maybe it's just your grade so there's 80 students in your population and you want to get an estimate of the average height in your population and you think it's too hard for you to go and measure the height of all 80 students so you decide to find a simple or take a simple random sample you think it's reasonable for you to measure the heights of 30 of these students and so you want what you want to do is randomly sample 30 of the 80 students and take their average height and say well that's probably a that's probably a pretty good estimate for the population parameter for the average height of the entire population so once you decide to do this you say well how do I select those 30 students and how do I select it so that I feel good that it is actually random and there's several ways that you could approach this one way to do it is associate every person in your school with a piece of paper and put them all in a bowl and then pick them out so let's do that so let's say you this is alphabetically the first person in the school they're on a slip of paper then the next slip of paper gets the next person and you're going to go all the way down so you can have 80 pieces of paper they all should be the same size and then you throw them all you throw them all into a bowl of some kind and this seems like a very basic way of doing it but it's actually a pretty effective way of getting a simple of getting a simple random sample so I'll try to draw well it looks like a bit of a fishbowl or something all right so that's our Bowl and so all the pieces of paper go in there and then you get put a blindfold on someone and they can't feel what names are there and so they should pick out the first 30 without replacing them because you obviously don't want to pick the same you don't want to pick out the same name twice and those 30 names that you pick that would be your simple random sample and then you could measure their heights to estimate the average height for the population this would be a completely legitimate way of doing it other ways that you could do it if you have a computer or calculator you could use a random number generator and the random functions on computer programming languages are on your calculator they tend to be something you know someplace you'll see something like a math dot R and R and short for random you might see something like random you might see might see something like random without anything passed into it it might give you a number between 0 & 1 or 1 or 0 and 100 you have to be very careful on how you use this to make sure that you have an even chance of picking us of picking certain numbers but what you would do in this situation if you had access to some random number generator and it could even pick out a random number between 1 and 80 including 1 and 80 is you would maybe line up all the students names alphabetically and so the first student alphabetically assign the number zero one and you could just say one if you're using a random number generator but I'll I'll use two digits for it just because it'll be useful and consistent and in a little bit we'll use another technique where it's going to be nice to be consistent with our number of digits and so the next one zero two and you go all the way to 79 and all the way to 80 and then you use your random number generator to keep generating numbers from 1 to 80 and as long as though that you don't get repeats you pick the first 30 to be your actual random sample another related technique which is a little bit more old-school but it's definitely the way that it has been done in the past and even done now sometimes it's use a random digit table you still start with these number associations with each student in the class and then you use a randomly generated list of numbers and so let's say that's our randomly generated list of numbers and it keeps going well beyond this and you start at the beginning and you say ok we're interested in getting we're interested in getting 32 digit numbers from 1 to 80 including 1 and 80 so one technique that you could use as you start it right at the beginning and you could say all right this is randomly generated list of numbers so the first number here is 59 is 59 in one and eighty sure is as long as we can if this was a zebra one that would have worked if this was an eight zero that would have worked if this was a zero zero it wouldn't have worked if this was an eight one it wouldn't have worked but this would be our this right over here that would be our first name that we you could imagine this the same as picking that first name out of the Hat whoever's associated with number 59 now you would move on you get the next two digits the next two digits are 83 they don't fall into our range from 1 to 80 so we're not going to use it then you look at the next two digits so we get a 5 and a 9 well that fits in our range but we already picked 59 we already picked person 59 so we're not going to pick 59 again so we keep moving on then we get a 37 well that's in our range we haven't picked that yet we do that then we get 0/0 once again not in our range I think you see where this is going 91 not in our range 23 it's in our range and we haven't picked it yet so we're going to pick the 23 I think you see where this going we're going to keep going down this list in the way that I've just described until we get until we get 30 of these we've just gotten three we just have to keep on going and this isn't an exhaustive list of all of the different ways you can get random numbers but it starts to give you some techniques in your toolkit and you might say oh well why don't I just randomly come up with some numbers in my head and I would I would really suggest that you don't do that because humans are famously bad at being truly random at and you might want to do something like even use a something that you think is a random process but you realize later that it wasn't as random as you thought so that once again multiple techniques but these are some of the I would say best practices for actually generating a simple random sample

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