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So that's that our mean, the true population mean, is less than 128 fluid ounces. And so this is a situation where we are not in compliance, not in compliance, compliance in the alternative hypothesis. Now, if you're going to do a significance test, you need to set a significance level. So let's do that over here. Sign... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So let's do that over here. Significance level. And if you haven't noticed, I'm doing, I'm trying to do in this video what would be expected of you on a test. And this is an actual question from an AP exam. So our significance level here, I'll just pick it to be 0.05 because, well, that's a fairly typical one. And sinc... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And this is an actual question from an AP exam. So our significance level here, I'll just pick it to be 0.05 because, well, that's a fairly typical one. And since they didn't give it one to us, it's important to set one ahead of time. And now we wanna check our conditions for inference. So let me do that over here. Con... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And now we wanna check our conditions for inference. So let me do that over here. Conditions, conditions for inference. And this is to feel good that the sample that we're using to make our inference, to do our significance test, that it's a reasonable one to make inferences from. And so the first one is the random con... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And this is to feel good that the sample that we're using to make our inference, to do our significance test, that it's a reasonable one to make inferences from. And so the first one is the random condition. And do we meet that? Well, they tell us here it's a random sample of 12 containers of milk. If I was doing this ... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
Well, they tell us here it's a random sample of 12 containers of milk. If I was doing this on the AP exam, I would write it out here. So I would say in the passage or in question, in the question, they say, they say a random, a random sample of 12. And then they go on to say more things. And so I would say that meets c... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And then they go on to say more things. And so I would say that meets condition, meets condition. Now the next one we wanna care about is our normal condition and this is to feel good that our sampling distribution is roughly normal. Now there's a couple of ways that we could do that. One is if our sample size is great... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
Now there's a couple of ways that we could do that. One is if our sample size is greater than 30 or greater than or equal to 30, then we say, okay, our sampling distribution is going to be roughly normal. But in this situation, our sample size n, so sample size, sample size is less than 30, but, but there's another way... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And they actually say it right over here. Variability in the filling process causes the actual contents of milk to be normally distributed. So we could say in passage, in passage says, and let's see, I could quote part of this. So actual contents, actual contents, and then dot, dot, dot, normally distributed, normally ... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So actual contents, actual contents, and then dot, dot, dot, normally distributed, normally distributed. So that meets condition, meets condition. And then the last condition we wanna think about is the independence condition, independence. And this is to feel good that the observations, the individual observations in ... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And this is to feel good that the observations, the individual observations in our sample can be considered to be roughly independent. Now one way is if they were sampling with replacement, which they're not doing here. It looks like they took all 12 containers at once. But another way is if this is less than 10% of th... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
But another way is if this is less than 10% of the overall population, then you could say, okay, they're gonna, you can view them as roughly independent. And so you can say didn't, didn't sample with replacement, with replacement, but, but assume, assume that 12 is less than 10% of the population. And in that case, you... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So it looks like we are, we've met these three conditions that we need to make for inference, or we can assume we've done it. They haven't given us any information to the contrary. And so now what we can do is calculate a t-statistic, and then from that, calculate our p-value, compare our p-value to our significance le... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And so our t-statistic, right over here, and once again, if at any point you're inspired, and if you haven't done so already, try to do it on your own. Our t-statistic is going to be our sample mean minus the assumed mean from the null hypothesis. And let me, since I'm introducing this notation, this little sub zero, I... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So I'll do that, and then I'll divide. Ideally, if I was doing a z-statistic, I would divide by the standard deviation of the sampling distribution of the sample mean, which is often known as the standard error of the mean. But the whole reason why I'm doing a t-statistic is, well, I don't know exactly what that is, bu... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
If you're using standard notation, people might assume what they are, but if you have time on these tests, you can always explain more of what these actual variables are. But in this case, this is going to be 127.2, that is our sample mean, minus our assumed mean from our null hypothesis, minus 128, all of that over, o... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
Did I type that in correctly? Yeah, that looks right. Click Enter. And so this is negative, I'll say it's approximately negative 1.32. So negative 1.32. And now we can figure out our p-value, our p-value, which is the same thing as the probability of getting a t-statistic this low or lower. So we could say t is less th... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And so this is negative, I'll say it's approximately negative 1.32. So negative 1.32. And now we can figure out our p-value, our p-value, which is the same thing as the probability of getting a t-statistic this low or lower. So we could say t is less than or equal to negative 1.32 is equal to, so I'll get my calculator... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So we could say t is less than or equal to negative 1.32 is equal to, so I'll get my calculator back out. And so here, what I would use is I would use the cumulative distribution function for t-statistic, so that's that right over there. And so I do care about the left tail, so I care about the area under the curve fro... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So let's do negative 1.32. And then my degrees of freedom, well, it's gonna be my sample size minus one. My sample size was 12, so that minus one is 11. And then I do paste. And so I have this tcdf from negative E99 to negative 1.32 comma 11. And actually, you'd wanna write this down on your exam if you were doing it, ... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And then I do paste. And so I have this tcdf from negative E99 to negative 1.32 comma 11. And actually, you'd wanna write this down on your exam if you were doing it, just so they know where you got that from. And so this is, this is equal to 0.107. So let me write it. This is approximately 0.107. And it's important to... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And so this is, this is equal to 0.107. So let me write it. This is approximately 0.107. And it's important to say how you calculated this. So used, used tcdf, and we went from negative one times 10 to the 99th power, and we went up to negative 1.32, and then we had 11 degrees of freedom to get this result right over h... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And it's important to say how you calculated this. So used, used tcdf, and we went from negative one times 10 to the 99th power, and we went up to negative 1.32, and then we had 11 degrees of freedom to get this result right over here. And it also might be good practice to draw your t-distribution right over here. So t... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So that's our t-distribution. That's the mean of our t-distribution. So we say that this is the area that we care about. So that is that right over there, just to make sure people know what we're talking about. And so here, now we're ready to make a conclusion. We can compare this to our significance level. And so we c... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So that is that right over there, just to make sure people know what we're talking about. And so here, now we're ready to make a conclusion. We can compare this to our significance level. And so we can say since, since 0.107 is greater than, our significance level is greater than 0.05, which is alpha, we fail, we fail ... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
And so we can say since, since 0.107 is greater than, our significance level is greater than 0.05, which is alpha, we fail, we fail to reject, reject the null hypothesis. And so let's just make sure we read their question right. Is there sufficient evidence to conclude that the packaging plant is not in compliance with... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
A group of four friends likes to bowl together, and each friend keeps track of his all-time highest score in a single game. Their high scores are all between 180 and 220, except for Adam, whose high score is 250. Adam then bowls a great game and has a new high score of 290. How will increasing Adam's high score affect ... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
How will increasing Adam's high score affect the mean and median? Now, like always, pause this video and see if you can figure this out yourself. All right, so let's just think about what they're saying. We have four friends, and they're each going to have, they each keep track of their all-time high score. So we're go... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
We have four friends, and they're each going to have, they each keep track of their all-time high score. So we're gonna have four data points, an all-time high score for each of the friends. So let's see, this is the lowest score of the friends. This is the second lowest, second to highest, and this is the highest scor... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
This is the second lowest, second to highest, and this is the highest scoring of the friends. So let's see. Their high scores are all between 100 and 220, except for Adam, whose high score is 250. So before Adam bowls this super awesome game, the scores look something like this. The lowest score is 180. Adam scores 250... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
So before Adam bowls this super awesome game, the scores look something like this. The lowest score is 180. Adam scores 250. And if you take Adam out of the picture, the highest score is a 220. And we actually don't know what this score right over there is. Now, after Adam bowls a great new game and has a new high scor... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
And if you take Adam out of the picture, the highest score is a 220. And we actually don't know what this score right over there is. Now, after Adam bowls a great new game and has a new high score of 290, what does the data set look like? Well, this guy's high score hasn't changed. This guy's high score hasn't changed.... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
Well, this guy's high score hasn't changed. This guy's high score hasn't changed. This guy's high score hasn't changed. But now Adam has a new high score. Instead of 250, it is now 290. So my question is, well, the first question is, does this change the median? Well, remember, the median is the middle number. | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
But now Adam has a new high score. Instead of 250, it is now 290. So my question is, well, the first question is, does this change the median? Well, remember, the median is the middle number. And if we're looking at four numbers here, the median is going to be the average of the middle two numbers. So we're going to ta... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
Well, remember, the median is the middle number. And if we're looking at four numbers here, the median is going to be the average of the middle two numbers. So we're going to take the average of whatever this question mark is in 220. That's going to be the median. Now, over here, after Adam has scored a new high score,... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
That's going to be the median. Now, over here, after Adam has scored a new high score, how would we calculate the median? Well, we still have four numbers, and the middle two are still the same two middle numbers, whatever this friend's high score was, and it hasn't changed. And so we're going to have the same median. ... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
And so we're going to have the same median. It's going to be 220 plus question mark divided by two. It's going to be halfway between question mark and 220. So our median won't change. So median no change. So let's think about the mean now. Well, the mean, you take the sum of all these numbers and then you divide by fou... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
So our median won't change. So median no change. So let's think about the mean now. Well, the mean, you take the sum of all these numbers and then you divide by four. And then you take the sum of all these numbers and divide by four. So which sum is going to be higher? Well, the first three numbers are the same, but in... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
Well, the mean, you take the sum of all these numbers and then you divide by four. And then you take the sum of all these numbers and divide by four. So which sum is going to be higher? Well, the first three numbers are the same, but in the second list, you have a higher number, 290. 290 is higher than 250. So if you t... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
Well, the first three numbers are the same, but in the second list, you have a higher number, 290. 290 is higher than 250. So if you take these four and divide by four, you're going to have a larger value than if you take these four and divide by four because their sum is going to be larger. And so the mean is going to... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
And so the mean is going to go up. The mean will increase. So median no change and mean increase. All right, so this says both increase. No, that's not right. The median will increase. No, median doesn't change. | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
All right, so this says both increase. No, that's not right. The median will increase. No, median doesn't change. The mean will increase, yep, and the median will stay the same. Yep, that's exactly what we're talking about. And if you want to make it a little bit more tangible, you could replace question mark with some... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
No, median doesn't change. The mean will increase, yep, and the median will stay the same. Yep, that's exactly what we're talking about. And if you want to make it a little bit more tangible, you could replace question mark with some number. You could replace it, maybe this question mark is 200. And if you try it out w... | Impact on median and mean when increasing highest value 6th grade Khan Academy.mp3 |
In this video I want to do some examples looking at distributions, in particular different features in distributions like clusters, gaps, and peaks. So over here I want to do some examples. Which of the following are accurate descriptions of the distribution below? Select all that apply. So the first statement is the d... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
Select all that apply. So the first statement is the distribution has an outlier. So an outlier is a data point that's way off of where the other data points are. It's way larger or way smaller than where all of the other data points seem to be clustered. And if we look over here, we have a lot of data points between z... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
It's way larger or way smaller than where all of the other data points seem to be clustered. And if we look over here, we have a lot of data points between zero and six. And just think about what they're measuring. This is shelf time for each apple at Gorge's Grocer. So for example, we see there's one, two, three, four... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
This is shelf time for each apple at Gorge's Grocer. So for example, we see there's one, two, three, four, five, six, seven apples that have a shelf life of zero days. So they're about to go bad. You see you have one, two, three, four, five, six, seven, eight apples that are gonna be good for another day. You have two ... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
You see you have one, two, three, four, five, six, seven, eight apples that are gonna be good for another day. You have two apples that are gonna be good for another six days. And you have one apple that's gonna be good for 10 days. And this is unusual. This is an outlier here. It has a way larger shelf life than all o... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
And this is unusual. This is an outlier here. It has a way larger shelf life than all of the other data. So I would say this definitely does have an outlier. We just have this one data point sitting all the way to the right. Way larger, way more shelf life than everything else. So it definitely has an outlier. | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
So I would say this definitely does have an outlier. We just have this one data point sitting all the way to the right. Way larger, way more shelf life than everything else. So it definitely has an outlier. And this one would be the outlier. The distribution has a cluster from four to six days. And we indeed do see a c... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
So it definitely has an outlier. And this one would be the outlier. The distribution has a cluster from four to six days. And we indeed do see a cluster from four to six days. A cluster, you can imagine it's a grouping of data that's sitting there, or you have a grouping of apples that have a shelf life between four an... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
And we indeed do see a cluster from four to six days. A cluster, you can imagine it's a grouping of data that's sitting there, or you have a grouping of apples that have a shelf life between four and six days. And you definitely do see that cluster there. And since I already selected two things, I'm definitely not gonn... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
And since I already selected two things, I'm definitely not gonna select none of the above. So let me check my answer. Let me do a few more of these. Which of the following are accurate descriptions of the distribution below? And once again, we're going to select all that apply. So the distribution has an outlier. So l... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
Which of the following are accurate descriptions of the distribution below? And once again, we're going to select all that apply. So the distribution has an outlier. So let's see, this distribution, I do have a data point here that's at the high end, and I have another data point here that's at the low end. But I don't... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
So let's see, this distribution, I do have a data point here that's at the high end, and I have another data point here that's at the low end. But I don't have any data points that are sitting far above or far below the bulk of the data. If I had a data point that was out here, then yeah, I would say that was an outlie... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
If I had a data point way to the left off the screen over here, maybe that would be an outlier. But I don't really see any obvious outliers. All of the data, it's pretty clustered together. So I would not say that the distribution has an outlier. The distribution has a peak at 22 degrees. Yeah, it does indeed look like... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
So I would not say that the distribution has an outlier. The distribution has a peak at 22 degrees. Yeah, it does indeed look like we have, and let's just look at what we're actually measuring, high temperature each day in Edgton, Iowa in July. So it does indeed look like we have the most number of days that had a high... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
So it does indeed look like we have the most number of days that had a high temperature at 22, most number of days in July had a high temperature at 22 degrees Celsius. So that is a peak, and you can see it. If you imagine this is kind of a mountain, this is a peak right here. This is a high point. You have, at least l... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
This is a high point. You have, at least locally, you have the most number of days at 22 degrees Celsius. So I would say it definitely has a peak there. Since I selected something, I'm not gonna select none of the above. Let's do a couple more of these. Which of the following are accurate descriptions of the distributi... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
Since I selected something, I'm not gonna select none of the above. Let's do a couple more of these. Which of the following are accurate descriptions of the distribution below? So the first one, the distribution has an outlier. So let's see, this number of guests by day at Seth's Sandwich Shop. So let's see, the lowest... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
So the first one, the distribution has an outlier. So let's see, this number of guests by day at Seth's Sandwich Shop. So let's see, the lowest, they have, so they have no days, no days where he had between zero and 19 guests. No days where he had between 20 and 39 guests. Looks like there's about nine days where he ha... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
No days where he had between 20 and 39 guests. Looks like there's about nine days where he had between 40 and 59 guests. Looks like 20 days where he had between 60 and 79 guests. All the way, it looks like this is maybe eight days that he had between 180 and 199 guests. But the question of outliers, there doesn't seem ... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
All the way, it looks like this is maybe eight days that he had between 180 and 199 guests. But the question of outliers, there doesn't seem to be any day where he had an unusual number of guests. There's not a day that's way out here where he had like 500 guests. So I would say this distribution does not have an outli... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
So I would say this distribution does not have an outlier. The distribution has a cluster from zero to 39 guests. So zero to 39 guests is right over here, zero to 39 guests. And there's no days where he had between zero and 39 guests, either zero to 19 or 20 to 39. So there's definitely not a cluster there. I would say... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
And there's no days where he had between zero and 39 guests, either zero to 19 or 20 to 39. So there's definitely not a cluster there. I would say that the cluster would be between, were days that had between 40 and 199 guests. Definitely not zero and 39. There was no days that were between zero and 39 guests. So I wou... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
Definitely not zero and 39. There was no days that were between zero and 39 guests. So I would say none of the above, very confidently. Let's do one more of these. Which of the following are accurate descriptions of the distribution below? All right. The distribution has a peak from 12 to 13 points. | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
Let's do one more of these. Which of the following are accurate descriptions of the distribution below? All right. The distribution has a peak from 12 to 13 points. Let me see what this is measuring or what this data is about. Test scores by student in Ms. Friend's class. | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
The distribution has a peak from 12 to 13 points. Let me see what this is measuring or what this data is about. Test scores by student in Ms. Friend's class. So you had one student who got between a zero and a one on the 20 point scale. So got between, I guess you may be out of 20 questions, got between zero and one po... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
Friend's class. So you had one student who got between a zero and a one on the 20 point scale. So got between, I guess you may be out of 20 questions, got between zero and one points. And then you see that those students got between two and three or four and five or six and seven. Then we have another student who got b... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
And then you see that those students got between two and three or four and five or six and seven. Then we have another student who got between eight and nine. Looks like three students got between 10 and 11. And then we keep increasing. This looks like it's about 12 students got either a 16 or a 17 or something in betw... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
And then we keep increasing. This looks like it's about 12 students got either a 16 or a 17 or something in between, maybe if you could get decimal points on that test. And then it looks like 10 students got from 18 to 19. All right, so this says the distribution has a peak from 12 to 13 points. 12 to 13 points. There ... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
All right, so this says the distribution has a peak from 12 to 13 points. 12 to 13 points. There were five students, but this isn't a peak. If you just go to 14 to 15 points, you have more students. So this is definitely not a peak. If you were looking at this as a mountain of some kind, you definitely wouldn't describ... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
If you just go to 14 to 15 points, you have more students. So this is definitely not a peak. If you were looking at this as a mountain of some kind, you definitely wouldn't describe this point as a peak. You would say this distribution has a peak, has the most number of students who got between 16 and 17 points. So tha... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
You would say this distribution has a peak, has the most number of students who got between 16 and 17 points. So that's the peak right there, not 12 to 13 points. So I would not select that first choice. The distribution has an outlier. Well, yeah, look at this. You have this outlier. Most of the students scored betwee... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
The distribution has an outlier. Well, yeah, look at this. You have this outlier. Most of the students scored between eight and 19 points. And then you have this one student who got between zero and one. It's really an outlier. You even see this, when you look at it visually, it's not even connected to the rest of the ... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
Most of the students scored between eight and 19 points. And then you have this one student who got between zero and one. It's really an outlier. You even see this, when you look at it visually, it's not even connected to the rest of the distribution. It's way to the left. If something's way to the left or way to the r... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
You even see this, when you look at it visually, it's not even connected to the rest of the distribution. It's way to the left. If something's way to the left or way to the right, that's an outlier. If it's unusually low or unusually high. So I would say this distribution definitely does have an outlier. And I'm not go... | Examples analyzing clusters, gaps, peaks and outliers for distributions 6h grade Khan Academy.mp3 |
And so the idea of statistical inference is new to you, or hypothesis testing, once again, watch those videos as well. But let's say we think there's a positive association between shoe size and height. And so what we might wanna do is, we could, here on the horizontal axis, that is shoe size, our sizes could go size o... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
And then on this height, on this axis, our y-axis, this would be height. So one foot, two feet, three feet, four feet, five feet, six feet, seven feet. And then you could, to see if there's an association, you might take a sample, let's say you take a random sample of 20 people from the population, and in future videos... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
Well, let's say those 20 people are these 20 data points. So there's a young child, then maybe there's a grown adult with bigger feet, and who's taller, and then three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, and so you have these 20 data points, and then what you're likely to d... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
And the computer could try to fit a regression line. And there's many techniques for doing it, but one typical technique is to try to overall minimize the square distance between these points and that line. And this regression line will have an equation as any line would have, and we tend to show that as saying y hat, ... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
So this right over here would be a. Now to be clear, if you took another sample, you might get different results here. In fact, let's call this y sub one for our first sample, a sub one, b sub one, and this is a sub one. If you were to take another sample of 20 folks, so let's do that, maybe you get one, two, three, fo... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
If you were to take another sample of 20 folks, so let's do that, maybe you get one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, and then you tried to fit a line to that, that line might look something like this. It might have a slightly different y-intercept and a sligh... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
Remember, statistics are things that we can get from samples and we're trying to estimate true population parameters. Well, what would be the true population parameters we're trying to estimate? Well, imagine a world, imagine a world here that you're able to find out the true linear relationship, or maybe there is some... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
You could get it if, theoretically, you could measure every human being on the planet and depending what you define as the population, it could be all living people or all people who'll ever live. This isn't practical, but let's just say that you actually could. You would have billions of data points here for the true ... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
And so that would be y hat is equal to, and to make it clear that here, the y-intercept and the slope, this would be the true population parameters. Instead of saying a, we say alpha, and instead of saying b, we say beta times x. But it's very hard to come up exactly with what alpha and beta are, and so that's why we e... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
Now, what's interesting with this in mind is we can start to make inferences based on our sample. So we know that, for example, b sub two is unlikely to be exactly beta, but how confident can we be that there is at least a positive linear relationship or a non-zero linear relationship? Or can we create a confidence int... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
And the simple answer is yes. And to do so, we'll use the same exact ideas that we did when we made inferences based on proportions or based on means. The way that you can make an inference, for example, for your true population slope of your regression line, you say, okay, I took a sample. I got this slope right over ... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
I got this slope right over here, so I'll just call that b two, and then I could create a confidence interval around that. And so that confidence interval is going to be based on some critical value times ideally the standard deviation of the sampling distribution of your sample statistic. In this case, it would be the... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
But because we don't know exactly what this is, we can't figure out precisely what this is going to be from a sample, we are going to estimate it with what's known as the standard error of the statistic, and we'll go into more depth in this in future videos. And since we're estimating here, we're going to use a critica... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
And from our sample, we can figure this out, and we can figure this out, and then we would have constructed a confidence interval. We'll also see that you could do hypothesis testing here. You could say, hey, let's set up a null hypothesis, and the null hypothesis is going to be that there's no non-zero linear relation... | Introduction to inference about slope in linear regression AP Statistics Khan Academy.mp3 |
So let's say the probability of scoring, score, you know, free throw, is equal to, is going to be, let's say 70%. If we want to write it as a percent, or we could write it as 0.7 if we write it as a decimal. And let's say the probability of missing a free throw then, and this is just gonna come straight out of what we ... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
So the probability of missing, of missing a free throw is just going to be 100% minus this. You're either gonna make or miss, you're either gonna score or miss. I don't wanna use make and miss because they both start with M. So this is going to be a 30% probability, or if we write it as a decimal, 0.3. One minus 0.7. T... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
One minus 0.7. These are the only two possibilities, so they have to add up to 100%, or they have to add up to one. Now let's say that you are going to take six attempts. And what we're curious about, what we're curious about is the probability of exactly, exactly two scores, two scores in six attempts. In six, in six ... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
And what we're curious about, what we're curious about is the probability of exactly, exactly two scores, two scores in six attempts. In six, in six attempts. So let's think about what that is. And I encourage you, if you get inspired at any point in this video, you should pause it and you should try to work through wh... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
And I encourage you, if you get inspired at any point in this video, you should pause it and you should try to work through what we're asking right now. So this is what we wanna figure out. The probability of exactly two scores in six attempts. So let's think about the way, let's think about the particular ways of gett... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
So let's think about the way, let's think about the particular ways of getting two scores in six attempts, and think about the probability for any one of those particular ways, and then we can think about, well how many ways can we get two scores in six attempts? So for example, you could get, you could make the first ... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
So what's the probability of this exact thing happening, this exact thing? Well you have a 0.7 chance of making, of scoring on the first one. Then you have a 0.7 chance of scoring on the second one. And then you have a 0.3 chance of missing the next four. So the probability of this exact circumstance is going to be wha... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
And then you have a 0.3 chance of missing the next four. So the probability of this exact circumstance is going to be what I'm writing down. And hopefully you don't get the multiplication symbols confused with the decimals. I'm trying to write them a little bit higher. So times 0.3. And what is this going to be equal t... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
I'm trying to write them a little bit higher. So times 0.3. And what is this going to be equal to? Well this is going to be equal to, this is going to be 0.7 squared times 0.3, times 0.3 to the one, two, three, fourth, to the fourth power. Now is this the only way to get two scores in six attempts? No, there's many way... | Probability of making 2 shots in 6 attempts Probability and Statistics Khan Academy.mp3 |
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