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Miriam was testing her null hypothesis that the population mean of some data set is equal to 18 versus her alternative hypothesis is that the mean is less than 18 with a sample of seven observations. Her test statistic, I can never say that right, was t is equal to negative 1.9. Assume that the conditions for inference... | Using TI calculator for P-value from t statistic AP Statistics Khan Academy.mp3 |
What is the approximate p-value for Miriam's test? So pause this video and see if you can figure this out on your own. All right, well I always just like to remind ourselves what's going on here before I just go ahead and calculate the p-value. So there's some data set, some population here, and the null hypothesis is ... | Using TI calculator for P-value from t statistic AP Statistics Khan Academy.mp3 |
So there's some data set, some population here, and the null hypothesis is that the true mean is 18. The alternative is that it's less than 18. So to test that null hypothesis, Miriam takes a sample. Sample size is equal to seven. From that, she would calculate her sample mean and her sample standard deviation. And fro... | Using TI calculator for P-value from t statistic AP Statistics Khan Academy.mp3 |
Sample size is equal to seven. From that, she would calculate her sample mean and her sample standard deviation. And from that, she would calculate this t-statistic. The way she would do that, or if they didn't tell us ahead of time what that was, they would say, okay, well we would say the t-statistic is equal to her ... | Using TI calculator for P-value from t statistic AP Statistics Khan Academy.mp3 |
The way she would do that, or if they didn't tell us ahead of time what that was, they would say, okay, well we would say the t-statistic is equal to her sample mean minus the assumed mean from the null hypothesis, that's what we have over here, divided by, and this is a mouthful, our approximation of the standard erro... | Using TI calculator for P-value from t statistic AP Statistics Khan Academy.mp3 |
This is equal to negative 1.9. And so if we think about a t-distribution, I'll try to hand-draw a rough t-distribution really fast, and if this is the mean of the t-distribution, what we are curious about, because our alternative hypothesis is that the mean is less than 18, so what we care about is, well, what is the p... | Using TI calculator for P-value from t statistic AP Statistics Khan Academy.mp3 |
So it's this area right there. And so I'm gonna do this with a TI-84, at least an emulator of a TI-84, and all we have to do is we would go to second distribution and then I would use the t-cumulative distribution function. So let's go there, that's the number six right there, click Enter. And so my lower bound, yeah, ... | Using TI calculator for P-value from t statistic AP Statistics Khan Academy.mp3 |
And so my lower bound, yeah, I essentially want it to be negative infinity, and so we can just call that negative infinity, it's an approximation of negative infinity, very, very low number. Our upper bound would be negative 1.9, negative 1.9. And then our degrees of freedom, that's our sample size minus one. Our sampl... | Using TI calculator for P-value from t statistic AP Statistics Khan Academy.mp3 |
What we're going to do in this video is talk about type one errors and type two, type two errors. And this is in the context of significance testing. So just as a little bit of review, in order to do a significance test, we first come up with a null and an alternative hypothesis. And we'll do this on some population in... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
And we'll do this on some population in question. These will say some hypotheses about a true parameter for this population. And the null hypothesis tends to be kind of what was always assumed or the status quo, while the alternative hypothesis, hey, there's news here, there's something alternative here. And to test it... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
And to test it, and we're really testing the null hypothesis, we're gonna decide whether we want to reject or fail to reject the null hypothesis, we take a sample. We take a sample from this population. Using that sample, we calculate a statistic, we calculate a statistic that's trying to estimate the parameter in ques... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
And then using that statistic, we try to come up with the probability of getting that statistic, the probability of getting that statistic that we just calculated from that sample of a certain size, given, if we were to assume that our null hypothesis, if our null hypothesis is true. And if this probability, which is o... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
So this right over here, this is our p-value. This should be all we review, we introduce it in other videos. We have seen in other videos if our p-value is less than our significance level, then we reject, reject our null hypothesis. And if our p-value is greater than or equal to our significance level, alpha, then we ... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
And if our p-value is greater than or equal to our significance level, alpha, then we fail to reject, fail to reject our null hypothesis. And when we reject our null hypothesis, some people say that might suggest the alternative hypothesis. And the reason why this makes sense is if the probability of getting this stati... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
But we might be wrong in either of these scenarios, and that's where these errors come into play. Let's make a grid to make this clear. So there's the reality. Let me put reality up here. So the reality is there's two possible scenarios in reality. One is is that the null hypothesis is true, and the other is that the n... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
Let me put reality up here. So the reality is there's two possible scenarios in reality. One is is that the null hypothesis is true, and the other is that the null hypothesis is false. And then based on our significance test, there's two things that we might do. We might reject the null hypothesis, or we might fail to ... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
And then based on our significance test, there's two things that we might do. We might reject the null hypothesis, or we might fail to reject the null hypothesis. And so let's put a little grid here to think about the different combinations, the different scenarios here. So in a scenario where the null hypothesis is tr... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
So in a scenario where the null hypothesis is true, but we reject it, that feels like an error. We shouldn't reject something that is true, and that indeed is a type one error. Type one error. You shouldn't reject the null hypothesis if it was true. You should reject the null hypothesis if it was true. And you could ev... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
You shouldn't reject the null hypothesis if it was true. You should reject the null hypothesis if it was true. And you could even figure out what is the probability of getting a type one error? Well, that's gonna be your significance level. Because if your null hypothesis is true, let's say that your significance level... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
Well, that's gonna be your significance level. Because if your null hypothesis is true, let's say that your significance level is 5%. Well, 5% of the time, even if your null hypothesis is true, you're going to get a statistic that's going to make you reject the null hypothesis. So one way to think about the probability... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
So one way to think about the probability of a type one error is your significance level. Now, if your null hypothesis is true and you fail to reject it, well, that's good. This, we could write this as, this is a correct, correct conclusion. The good thing just happened to happen this time. Now, if your null hypothesis... | Introduction to Type I and Type II errors AP Statistics Khan Academy.mp3 |
Flavia wanted to estimate the mean age of the faculty members at her large university. She took an SRS, or simple random sample, of 20 of the approximately 700 faculty members, and each faculty member in the sample provided Flavia with their age. The data were skewed to the right with a sample mean of 38.75. She's cons... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
She's considering using her data to make a confidence interval to estimate the mean age of faculty members at her university. Which conditions for constructing a t-interval have been met? So pause this video and see if you can answer this on your own. Okay, now let's try to answer this together. So there's 700 faculty ... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
Okay, now let's try to answer this together. So there's 700 faculty members over here. She's trying to estimate the population mean, the mean age. She can't talk to all 700, so she takes a sample, a simple random sample of 20. So the n is equal to 20 here. From this 20, she calculates a sample mean of 38.75. Now ideall... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
She can't talk to all 700, so she takes a sample, a simple random sample of 20. So the n is equal to 20 here. From this 20, she calculates a sample mean of 38.75. Now ideally, she wants to construct a t-interval, a confidence interval using the t-statistic. And so that interval would look something like this. It would ... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
Now ideally, she wants to construct a t-interval, a confidence interval using the t-statistic. And so that interval would look something like this. It would be the sample mean, plus or minus the critical value, times the sample standard deviation divided by the square root of n. And we use a t-statistic like this, and ... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
Now in order for this to hold true, there's three conditions, just like what we saw when we thought about z-intervals. The first is, is that our sample is random. Well, they tell us that here, that she took a simple random sample of 20. And so we know that we are meeting that constraint, and that's actually choice A. T... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
And so we know that we are meeting that constraint, and that's actually choice A. The data is a random sample from the population of interest. So we can circle that in. So the next condition is the normal condition. Now the normal condition when we're doing a t-interval is a little bit more involved, because we do need... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
So the next condition is the normal condition. Now the normal condition when we're doing a t-interval is a little bit more involved, because we do need to assume that the sampling distribution of the sample means is roughly normal. Now there's a couple of ways that we can get there. Either our sample size is greater th... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
Either our sample size is greater than or equal to 30. The central limit theorem tells us that then our sampling distribution, regardless of what the distribution is in the population, that the sampling distribution actually would then be approximately normal. She didn't meet that constraint right over here. Here, her ... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
Here, her sample size is only 20. So, so far, this isn't looking good. Now that's not the only way to meet the normal condition. Another way to meet the normal condition, if we have a smaller sample size, smaller than 30, is one, if the original distribution of ages is normal. So original, distribution, normal. Or even... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
Another way to meet the normal condition, if we have a smaller sample size, smaller than 30, is one, if the original distribution of ages is normal. So original, distribution, normal. Or even if it's roughly symmetric around the mean. So approximately symmetric. But if you look at this, they tell us that it has a right... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
So approximately symmetric. But if you look at this, they tell us that it has a right skew. They say the data were skewed to the right with the sample mean of 38.75. So that tells us that the data set that we're getting in our sample is not symmetric. And the original distribution is unlikely to be normal. Think about ... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
So that tells us that the data set that we're getting in our sample is not symmetric. And the original distribution is unlikely to be normal. Think about it. It's not going to be, you're likely to have people who are, you could have faculty members who are 30 years older than this, 68 and 3 quarters, but you're very un... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
It's not going to be, you're likely to have people who are, you could have faculty members who are 30 years older than this, 68 and 3 quarters, but you're very unlikely to have faculty members who are 30 years younger than this. And that's actually what's causing that skew to the right. So this one does not meet the no... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
We can't feel good that our sampling distribution of the sample means is going to be normal. So I'm not gonna fill that one in. Choice C, individual observations can be considered independent. So there's two ways to meet this constraint. One is, is if we sample with replacement. Every faculty member we look at after as... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
So there's two ways to meet this constraint. One is, is if we sample with replacement. Every faculty member we look at after asking them their age, we say, hey, go back into the pool and we might pick them again until we get our sample of 20. It does not look like she did that. It doesn't look like she sampled with rep... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
It does not look like she did that. It doesn't look like she sampled with replacement. And so even if you're sampling without replacement, the 10% rule says that, look, as long as this is less than 10% or less than or equal to 10% of the population, then we're good. And the 10% of this population is 70. 70 is 10% of 70... | Conditions for valid t intervals Confidence intervals AP Statistics Khan Academy.mp3 |
We're told that a board game has players roll two three-sided dice. These exist, and actually I looked it up, they do exist and they're actually fascinating. And subtract the numbers showing on the faces. The game only looks at non-negative differences. For example, if a player rolls a one and a three, the difference i... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
The game only looks at non-negative differences. For example, if a player rolls a one and a three, the difference is two. Let D represent the difference in a given roll. Construct the theoretical probability distribution of D. So pause this video and see if you can have a go at that before we work through it together. ... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
Construct the theoretical probability distribution of D. So pause this video and see if you can have a go at that before we work through it together. All right, now let's work through it together. So let's just think about all of the scenarios for the two die. So let me draw a little table here. So let me do it like th... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
So let me draw a little table here. So let me do it like that. And let me do it like this. And then let me put a little divider right over here. And for this top, this is going to be die one, and then this is going to be die two. Die one can take on one, two, or three. And die two could be one, two, or three. | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
And then let me put a little divider right over here. And for this top, this is going to be die one, and then this is going to be die two. Die one can take on one, two, or three. And die two could be one, two, or three. And so let me finish making this a bit of a table here. And what we wanna do is look at the differen... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
And die two could be one, two, or three. And so let me finish making this a bit of a table here. And what we wanna do is look at the difference, but the non-negative difference. So we'll always subtract the lower die from the higher die. So what's the difference here? Well, this is going to be zero if I roll a one and ... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
So we'll always subtract the lower die from the higher die. So what's the difference here? Well, this is going to be zero if I roll a one and a one. Now, what if I roll a two and a one? Well, here the difference is going to be two minus one, which is one. Here the difference is three minus one, which is two. Now, what ... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
Now, what if I roll a two and a one? Well, here the difference is going to be two minus one, which is one. Here the difference is three minus one, which is two. Now, what about right over here? Well, here the higher die is two, the lower one is one right over here. So two minus one is one, two minus two is zero. And no... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
Now, what about right over here? Well, here the higher die is two, the lower one is one right over here. So two minus one is one, two minus two is zero. And now this is going to be the higher roll. Die one is gonna have the higher roll in this scenario. Three minus two is one. And then right over here, three minus one ... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
And now this is going to be the higher roll. Die one is gonna have the higher roll in this scenario. Three minus two is one. And then right over here, three minus one is two. Now, if die one rolls a two, die two rolls a three. Die three is higher, three minus two is one. And then three minus three is zero. | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
And then right over here, three minus one is two. Now, if die one rolls a two, die two rolls a three. Die three is higher, three minus two is one. And then three minus three is zero. So we've come up with all of the scenarios, and we can see that we're either gonna end up with a zero or one or a two when we look at the... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
And then three minus three is zero. So we've come up with all of the scenarios, and we can see that we're either gonna end up with a zero or one or a two when we look at the positive difference. So there's a scenario of getting a zero, a one, or a two. Those are the different differences that we could actually get. And... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
Those are the different differences that we could actually get. And so let's think about the probability of each of them. What's the probability that the difference is zero? Well, we can see that one, two, three of the nine equally likely outcomes result in a difference of zero. So it's gonna be three out of nine or 1 ... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
Well, we can see that one, two, three of the nine equally likely outcomes result in a difference of zero. So it's gonna be three out of nine or 1 3rd. What about a difference of, let me use blue, one? Well, we could see there are one, two, three, four of the nine scenarios have that. So there is a 4 9th probability. An... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
Well, we could see there are one, two, three, four of the nine scenarios have that. So there is a 4 9th probability. And then last but not least, a difference of two. Well, there's two out of the nine scenarios that have that. So there is a 2 9th probability right over there. And we're done. We've constructed the theor... | Theoretical probability distribution example tables Probability & combinatorics.mp3 |
So let's say we define some random variable, let's call it x, and let's call it the number of rolls until we get a one. One. So what's the probability that x is equal to one? Pause this video and think about it. All right, the probability that x is equal to one means that it only takes us one roll to get a one. Well, t... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
Pause this video and think about it. All right, the probability that x is equal to one means that it only takes us one roll to get a one. Well, that's going to be a 1 1⁶ probability. Well, what's the probability that x is equal to two? Well, that means that on the first roll, we get something other than a one, so that ... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
Well, what's the probability that x is equal to two? Well, that means that on the first roll, we get something other than a one, so that is going to be 5 6. And then on the second roll, we get a one, so that has a 1 6th probability. And we could keep going. What's the probability that x is equal to three? Pause the vid... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
And we could keep going. What's the probability that x is equal to three? Pause the video and think about that. Well, that means we miss on the first two, so we have a 5 6th chance of getting something other than a one on the first two rolls. So we could say that's 5 6th times 5 6th, so we could write 5 6th squared. An... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
Well, that means we miss on the first two, so we have a 5 6th chance of getting something other than a one on the first two rolls. So we could say that's 5 6th times 5 6th, so we could write 5 6th squared. And then on the third roll, we have the 1 6th chance of getting the one, so times 1 6th. And I think you see a pat... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
And I think you see a pattern here, and you might recognize what type of random variable this is. This is a geometric variable. Now, how do we know that? Well, each trial or each roll is either a success or a failure. Every time we roll, we either get a one or we don't. We have the same probability of success of rollin... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
Well, each trial or each roll is either a success or a failure. Every time we roll, we either get a one or we don't. We have the same probability of success of rolling a one each trial. These are independent trials. And that there's no set number of trials. It could take us an arbitrary number of trials to get the firs... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
These are independent trials. And that there's no set number of trials. It could take us an arbitrary number of trials to get the first success. So that's what tells us that we're dealing with the geometric random variable. Now, one question is, is what is going to be the mean of this geometric random variable? Well, w... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
So that's what tells us that we're dealing with the geometric random variable. Now, one question is, is what is going to be the mean of this geometric random variable? Well, we prove it in another video where we talk about the expected value of a geometric random variable. We're really talking about the mean of a geome... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
We're really talking about the mean of a geometric random variable. And it is a little bit intuitive. If you were to just guess, what is the mean of a geometric random variable where the chance of success on each roll is one sixth, you might say, well, maybe on average, it takes you about six tries. And you would be co... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
And you would be correct. The mean of a geometric random variable is one over the probability of success on each trial. So in this situation, the mean is going to be one over, the probability of success in each trial is one over six. So it's equal to six. So one way to think about it is, on average, you would have six ... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
So it's equal to six. So one way to think about it is, on average, you would have six trials until you get a one. Now, another question is, what's a measure of the spread of a geometric random variable? And we don't prove this in another video. Maybe I'll do it eventually. That the standard deviation of a geometric ran... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
And we don't prove this in another video. Maybe I'll do it eventually. That the standard deviation of a geometric random variable is the mean times the square root of one minus P, or you could just write this as a square root of one minus P over P. Now, in this situation, what would this be? Well, the standard deviatio... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
Well, the standard deviation of this random variable, this geometric random variable, it's going to be the square root of one minus one sixth, all of that over one sixth. So this is going to be equal to the square root of five sixths over one sixth, which is equal to six times the square root of five sixths. And this i... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
We'll take the square root of that and then multiply that times six, gets us to about 5.5. So approximately equal to 5.5. And what's interesting about a geometric random variable, obviously the lowest value here in this case is one, two, three, it can go higher and higher, but it can go arbitrary. You could get really ... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
You could get really unlucky and it might take you a thousand rolls in order to get that one. It could take you a million rolls, very low probability, but it could take you a million rolls in order to get that one. And so another thing to realize about a geometric random variable's distribution, it tends to look someth... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
And so you have a very long tail to the right of your mean, and this is classic right skew. And so all geometric random variables distributions are right skewed. They have a long tail of values, an infinitely long tail of values they can take to the right. Now, one last question. Instead of dealing with a six-sided die... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
Now, one last question. Instead of dealing with a six-sided die, what would be the situation if we were dealing with a 12-sided die? What would then be the mean of our random variable? And what would be the standard deviation of our random variable? Pause this video and think about that. Well, the mean would be one ove... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
And what would be the standard deviation of our random variable? Pause this video and think about that. Well, the mean would be one over 112, because you have a probability of 112 every time of getting a one. We're assuming we're playing the same game now with a 12-sided die. So one over 112 would be 12. So on average,... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
We're assuming we're playing the same game now with a 12-sided die. So one over 112 would be 12. So on average, it would take 12 rolls to get that first one. And then our standard deviation is going to be, essentially, this times the square root of one minus 112. Let me write it this way. It's one minus 112 over one ov... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
And then our standard deviation is going to be, essentially, this times the square root of one minus 112. Let me write it this way. It's one minus 112 over one over 12, which is the same thing as 12 times the square root of 11 twelfths. 11 divided by 12 is equal to, take the square root and then multiply that times 12,... | Geometric distribution mean and standard deviation AP Statistics Khan Academy.mp3 |
Let's say that we run a school, and in that school there is a population of students right over here. That is our population. And we want to get a sense of how these students feel about the quality of math instruction at this school. So we construct a survey, and we just need to decide who are we going to get to actual... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
So we construct a survey, and we just need to decide who are we going to get to actually answer this survey. One option is to just go to every member of the population, but let's just say it's a really large school. Let's say we're a college, and there's 10,000 people in the college. We say, well, we can't just talk to... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
We say, well, we can't just talk to everyone. So instead we say, let's sample this population to get an indication of how the entire school feels. So we are going to sample it. We're going to sample that population. Now, in order to avoid having bias in our response, in order for it to have the best chance of it being ... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
We're going to sample that population. Now, in order to avoid having bias in our response, in order for it to have the best chance of it being indicative of the entire population, we want our sample to be random. So our sample could either be random, random, or not random, not random. And it might seem at first pretty ... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And it might seem at first pretty straightforward to do a random sample, but when you actually get down to it, it's not always as straightforward as you would think. So one type of random sample is just a simple random sample. So simple, simple, random, random sample. And this is saying, all right, let me maybe assign ... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And this is saying, all right, let me maybe assign a number to every person in the school. Maybe they already have a student ID number. And I'm just going to get a computer, a random number generator, to generate the 100 people, the 100 students. So let's say there's a sample of 100 students that I'm going to apply the... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
So let's say there's a sample of 100 students that I'm going to apply the survey to. So that would be a simple random sample. We are just going into this whole population and randomly, let me just draw this. So this is the population. We are just randomly picking people out. And we know it's random because a random num... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
So this is the population. We are just randomly picking people out. And we know it's random because a random number generator, or we have a string of numbers or something like that, that is allowing us to pick these students. Now that's pretty good. It's unlikely that you're going to have bias from this sample. But the... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
Now that's pretty good. It's unlikely that you're going to have bias from this sample. But there is some probability that just by chance, your random number generator just happened to select maybe a disproportionate number of boys over girls, or a disproportionate number of freshmen, or a disproportionate number of eng... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And that's a possibility. So even though you're taking a simple random sample and it's truly random, once again, it's some probability that's not indicative of the entire population. And so to mitigate that, there are other techniques at our disposal. One technique is a stratified sample. Stratified. And so this is the... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
One technique is a stratified sample. Stratified. And so this is the idea of taking our entire population and essentially stratifying it. So let's say we take that same population, we take that same population, I'll draw it as a square here just for convenience, and we're gonna stratify it by, let's say we're concerned... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
So let's say we take that same population, we take that same population, I'll draw it as a square here just for convenience, and we're gonna stratify it by, let's say we're concerned that we get an appropriate sample of freshmen, sophomores, juniors, and seniors. So we'll stratify it by freshmen, sophomores, juniors, a... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
So these are the stratifications. This is freshmen, sophomore, juniors, and seniors. And instead of just sampling 100 out of the entire pool, we sample 25 from each of these. So just like that. And so that makes sure that you are getting indicative responses from at least all of the different age groups or levels withi... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
So just like that. And so that makes sure that you are getting indicative responses from at least all of the different age groups or levels within your university. Now there might be another issue where you say, well, I'm actually more concerned that we have accurate representation of males and females in the school. A... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And there is some probability, if I do 100 random people, it's very likely that it's close to 50-50, but there's some chance just due to randomness that it's disproportionately male or disproportionately female. And that's even possible in the stratified case. And so what you might say is, well, you know what I'm gonna... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
I'm going to, there's a technique called a clustered sample. Let me write this right over here. Clustered, a clustered sample. And what we do is we sample groups. Each of those groups, we feel confident, has a good balance of male, females. So for example, we might, instead of sampling individuals from the entire popul... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And what we do is we sample groups. Each of those groups, we feel confident, has a good balance of male, females. So for example, we might, instead of sampling individuals from the entire population, we might say, look, you know, on Tuesdays and Thursdays, and this, well, even there, as you can tell, this is not a triv... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
We'll, let's just say that we can split our, let's say we can split our population into groups. Maybe these are classrooms. And each of these classrooms have an even distribution of males and females, or pretty close to even distributions. And so what we do is we sample the actual classrooms. So that's why it's called ... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And so what we do is we sample the actual classrooms. So that's why it's called cluster, or cluster technique, or clustered random sample, because we're going to randomly sample our classrooms, each of which have a close, or maybe an exact balance of males and females. So we know that we're gonna get good representatio... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
We are sampling from the clusters, but then we're gonna survey every single person in each of these clusters, every single person in one of these classrooms. So once again, these are all forms of random surveys, or random samples. You have the simple random sample, you can stratify, or you can cluster, and then randoml... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
Now, if these are all random samples, what are the non-random things like? Well, one case of non-random, you could have a voluntary, voluntary survey, or voluntary sample. This might just be, you tell every student at the school, hey, here's a web address, if you're interested, come and fill out this survey. And that's... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And that's likely to introduce bias, because you might have, maybe, the students who really like the math instruction at their school, more likely to fill it out. Maybe the students who really don't like it, more likely to fill it out. Maybe it's just the kids who have more time, more likely to fill it out. So this has... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
So this has a good chance of introducing bias. The students who fill out the survey might be just more skewed one way or the other, because they volunteered for it. Another non-random sample would be called a, a, you're introducing bias because of convenience, is a term that's often used. And this might say, well, let'... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And this might say, well, let's just sample the hundred first students who show up in school. And that's just convenient for me, because I didn't have to do these random numbers, or do the stratification, or doing any of this clustering. But you can understand how this also would introduce bias. Because the first hundr... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
Because the first hundred students who show up at school, maybe those are the most diligent students, maybe they all take an early math class that has a very good instructor, or they're all happy about it. Or it might go the other way. The instructor there isn't the best one, and so it might introduce bias the other wa... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
So if you let people volunteer, or you just say, oh, let me go to the first N students, or you say, hey, let me just talk to all the students who happen to be in front of me right now. They might be in front of you out of convenience, but they might not be a true random sample. Now, there's other reasons why you might ... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
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