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You might introduce bias because of the wording of your survey. You could imagine a survey that says, do you consider yourself lucky to get a math education that very few other people in the world have access to? Well, that might bias you to say, well, yeah, I guess I feel lucky. Well, if the wording was, do you like t... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
Well, if the wording was, do you like the fact that a disproportionate, more students at your school tend to fail algebra than our surrounding schools? Well, that might bias you negatively. So the wording really, really, really matters in surveys, and there's a lot that would go into this. And the other one is just peo... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And the other one is just people's, it's called response bias. And once again, this isn't about response bias. And this is just people not wanting to tell the truth or maybe not wanting to respond at all. Maybe they're afraid that somehow their response is gonna show up in front of their math teacher or the administrat... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
Maybe they're afraid that somehow their response is gonna show up in front of their math teacher or the administrators, or if they're too negative, it might be taken out on them in some way. And because of that, they might not be truthful. And so they might be overly positive or not fill it out at all. So anyway, this ... | Techniques for random sampling and avoiding bias Study design AP Statistics Khan Academy.mp3 |
And what I have here are five different statements. And I want you to look at these statements. Pause the video, look at these statements, and think about which of these, based on the information in the box and whiskers plot, which of these are for sure true, which of these are for sure false, and which of these we don... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
It could go either way. All right, so let's work through these. So the first statement is that all of the students are less than 17 years old. Well, we see right over here that the maximum age, that's the right end of this right whisker, is 16. So it is the case that all of the students are less than 17 years old. So t... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Well, we see right over here that the maximum age, that's the right end of this right whisker, is 16. So it is the case that all of the students are less than 17 years old. So this is definitely going to be true. The next statement, at least 75% of the students are 10 years old or older. So when you look at this, this ... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
The next statement, at least 75% of the students are 10 years old or older. So when you look at this, this feels right because 10 is the value, that is at the beginning of the second quartile. This is the second quartile right over there. And actually, let me do this in a different color. So this is the second quartile... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And actually, let me do this in a different color. So this is the second quartile. So 25% of the value of the numbers are in the second, or roughly, sometimes it's not exactly, so approximately, I'll say roughly, 25% are going to be in the second quartile. Approximately 25% are going to be in the third quartile. And ap... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Approximately 25% are going to be in the third quartile. And approximately 25% are going to be in the fourth quartile. So it seems reasonable for saying 10 years old or older that this is going to be true. In fact, you could even have a couple of values in the first quartile that are 10. But to make that a little bit m... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
In fact, you could even have a couple of values in the first quartile that are 10. But to make that a little bit more tangible, let's look at some, so I'm feeling good that this is true, but let's look at a few more examples to make this a little bit more concrete. So they don't know, we don't know, based on the inform... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
We'll have to construct some scenarios. So we could do a scenario. Let's see if we can do, we could do a scenario where, well, let's see, let's see if I can construct something where, let's see, the median is 13. We know that for sure. The median is 13. So if I have an odd number, I would have 13 in the middle, just li... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
We know that for sure. The median is 13. So if I have an odd number, I would have 13 in the middle, just like that. And maybe I have three on each side. And I'm just making that number up. I'm just trying to see what I can learn about the different types of data sets that could be described by this box and whiskers plo... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And maybe I have three on each side. And I'm just making that number up. I'm just trying to see what I can learn about the different types of data sets that could be described by this box and whiskers plot. So 10 is going to be the middle of the bottom half. So that's 10 right over there. And 15 is going to be the midd... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
So 10 is going to be the middle of the bottom half. So that's 10 right over there. And 15 is going to be the middle of the top half. That's what this box and whiskers plot is telling us. And they of course tell us what the minimum, the minimum is seven, and they tell us that the maximum is 16. So we know that's seven, ... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
That's what this box and whiskers plot is telling us. And they of course tell us what the minimum, the minimum is seven, and they tell us that the maximum is 16. So we know that's seven, and then that is 16. And then this right over here could be anything. It could be 10, it could be 11, it could be 12, it could be 13.... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And then this right over here could be anything. It could be 10, it could be 11, it could be 12, it could be 13. It wouldn't change what these medians are. It wouldn't change this box and whiskers plot. Similarly, this could be 13, it could be 14, it could be 15. And so any of those values wouldn't change it. And so 75... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
It wouldn't change this box and whiskers plot. Similarly, this could be 13, it could be 14, it could be 15. And so any of those values wouldn't change it. And so 75% are 10 or older. Well, this value, in this case, six out of seven are 10 years old or older. And we could try it out with other scenarios where let's try ... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And so 75% are 10 or older. Well, this value, in this case, six out of seven are 10 years old or older. And we could try it out with other scenarios where let's try to minimize the number of 10s given this data set. Well, we could do something like, let's say that we have eight. So let's see, one, two, three, four, fiv... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Well, we could do something like, let's say that we have eight. So let's see, one, two, three, four, five, six, seven, eight. And so here, we know that the minimum, we know that the minimum is seven, we know that the maximum is 16. We know that the mean of these middle two values, we have an even number now. So the med... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
We know that the mean of these middle two values, we have an even number now. So the median is going to be the mean of these two values. So it's going to be the mean of this and this is going to be 13. And we know that the mean of, we know that the mean of this and this is going to be 10, and that the mean of this and ... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And we know that the mean of, we know that the mean of this and this is going to be 10, and that the mean of this and this is going to be 15. So what could we construct? Well, actually, we don't even have to construct to answer this question. We know that this is going to have to be 10 or larger, and then all of these ... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
We know that this is going to have to be 10 or larger, and then all of these other things are going to be 10 or larger. So this is exactly 75%, exactly 75%, if we assume that this is less than 10, are going to be 10 years old or older. So feeling very good, very good, about this one right over here. And actually, just ... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And actually, just to make this concrete, I'll put in some values here. You know, this could be a nine and an 11. This could be a 12 and a 14. This could be a 14 and a 16. Or it could be a 15 and a 15. You could think about it in any of those ways. But feeling very good that this is definitely going to be true based on... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
This could be a 14 and a 16. Or it could be a 15 and a 15. You could think about it in any of those ways. But feeling very good that this is definitely going to be true based on the information given in this plot. Now they say there's only one seven-year-old at the party. One seven-year-old at the party. Well, this fir... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
But feeling very good that this is definitely going to be true based on the information given in this plot. Now they say there's only one seven-year-old at the party. One seven-year-old at the party. Well, this first possibility that we looked at, that was the case. There was only one seven-year-old at the party, and t... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Well, this first possibility that we looked at, that was the case. There was only one seven-year-old at the party, and there was one 16-year-old at the party. And actually, that was the next statement. There's only one 16-year-old at the party. So both of these seem like we can definitely construct data that's consiste... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
There's only one 16-year-old at the party. So both of these seem like we can definitely construct data that's consistent with this box plot, box and whiskers plot, where this is true. But could we construct one where it's not true? Well, sure. Let's imagine, let's see, we have our median at 13. Median at 13. And then w... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
Well, sure. Let's imagine, let's see, we have our median at 13. Median at 13. And then we have, let's see, one, two, three, four, five. This is going to be the 10, the median of this bottom half. This is going to be 15. This is going to be 7. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And then we have, let's see, one, two, three, four, five. This is going to be the 10, the median of this bottom half. This is going to be 15. This is going to be 7. This is going to be 16. Well, this could also be 7. It doesn't have to be. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
This is going to be 7. This is going to be 16. Well, this could also be 7. It doesn't have to be. It could be 7, 8, 9, or 10. This could also be 16. It doesn't have to be. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
It doesn't have to be. It could be 7, 8, 9, or 10. This could also be 16. It doesn't have to be. It could be 15 as well. But just like that, I've constructed a data set. And these could be 10, 11, 12, 13. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
It doesn't have to be. It could be 15 as well. But just like that, I've constructed a data set. And these could be 10, 11, 12, 13. This could be 10, 11, 12, 13. This could be 13, 14, 15. This one also could be 13, 14, 15. | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
And these could be 10, 11, 12, 13. This could be 10, 11, 12, 13. This could be 13, 14, 15. This one also could be 13, 14, 15. But the simple thing is, or the basic idea here, I can have a data set where I have multiple 7's and multiple 16's. Or I could have a data set where I only have one 7, or only one 16. So both of... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
This one also could be 13, 14, 15. But the simple thing is, or the basic idea here, I can have a data set where I have multiple 7's and multiple 16's. Or I could have a data set where I only have one 7, or only one 16. So both of these statements, we just plain don't know. Now the next statement, exactly half the stude... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
So both of these statements, we just plain don't know. Now the next statement, exactly half the students are older than 13. Well, if you look at this possibility up here, we saw that 3 out of the 7 are older than 13. So that's not exactly half. 3 7's is not 1 half. But in this one over here, we did see that exactly hal... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
So that's not exactly half. 3 7's is not 1 half. But in this one over here, we did see that exactly half are older than 13. In fact, if you're saying exactly half, well, in this one, we're saying that exactly half are older than 13. We have an even number right over here. So it is exactly half. So it's possible that it... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
In fact, if you're saying exactly half, well, in this one, we're saying that exactly half are older than 13. We have an even number right over here. So it is exactly half. So it's possible that it's true. It's possible that it's not true based on the information given. We once again do not know. Anyway, hopefully you f... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
So it's possible that it's true. It's possible that it's not true based on the information given. We once again do not know. Anyway, hopefully you found this interesting. The whole point of me doing this is, when you look at statistics, sometimes it's easy to kind of say, OK, I think it roughly means that. And that's s... | Interpreting box plots Data and statistics 6th grade Khan Academy.mp3 |
We're told a company produces processing chips for cell phones. At one of its large factories, 2% of the chips produced are defective in some way. A quality check involves randomly selecting and testing 500 chips. What are the mean and standard deviation of the number of defective processing chips in these samples? So ... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
What are the mean and standard deviation of the number of defective processing chips in these samples? So like always, try to pause this video and have a go at it on your own, and then we will work through it together. All right, so let me define a random variable that we're gonna find the mean and standard deviation o... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
And I'm gonna make that random variable the number of defective processing chips in a 500-chip sample. So let's let X be equal to the number of defective chips in 500-chip sample. So the first thing to recognize is that this will be a binomial variable. This is binomial. How do we know it's binomial? Well, it's made up... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
This is binomial. How do we know it's binomial? Well, it's made up of 500, it's a finite number of trials right over here. The probability of getting a defective chip, you could view this as a probability of success. It's a little bit counterintuitive that a defective chip would be a success, but we're summing up the d... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
The probability of getting a defective chip, you could view this as a probability of success. It's a little bit counterintuitive that a defective chip would be a success, but we're summing up the defective chips. So we would view the probability of a defect, or I should say a defective chip, it is constant across these... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
You might be saying, hey, well, are we replacing the chips before or after? But we're assuming it's from a functionally infinite population, or if you wanna make it feel better, you could say, well, maybe you are replacing the chips. They're not really telling us that right over here. So we'll assume that each of these... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
So we'll assume that each of these trials are independent of each other, and that the probability of getting a defective chip stays constant here. And so this is a binomial random variable, or binomial variable, and we know the formulas for the mean and standard deviation of a binomial variable. So the mean, the mean o... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
Well, this is going to be equal to, we have 500 trials, and then the probability of success on each of these trials is 0.02. So it's 500 times 0.02. And what is this going to be? 500 times 2 hundredths is going to be, it's going to be equal to 10. So that is your expected value of the number of defective processing chi... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
500 times 2 hundredths is going to be, it's going to be equal to 10. So that is your expected value of the number of defective processing chips, or the mean. Now what about the standard deviation? So the standard deviation of our random variable, x, well that's just going to be equal to the square root of the variance ... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
So the standard deviation of our random variable, x, well that's just going to be equal to the square root of the variance of our random variable, x. So I could just write it, I'm just writing it all the different ways that you might see it, because sometimes the notation is the most confusing part in statistics. And s... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
Well, the variance of a binomial variable is going to be equal to the number of trials, times the probability of success in each trial, times one minus the probability of success in each trial. And so in this context, this is going to be equal to, you're gonna have the 500, 500, times 0.02, 0.02, times one minus 0.02 i... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
I didn't make that radical sign long enough. And so what is this going to be? Well, let's see, 500 times 0.02, we already said that this is going to be 10, 10 times 0.98, this is going to be equal to the square root of 9.8. So it's going to be, I don't know, three point something. If we want, we can get a calculator ou... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
So it's going to be, I don't know, three point something. If we want, we can get a calculator out to feel a little bit better about this value. So I'm gonna take 9.8, and then take the square root of it, and I get three point, if I round to the nearest hundredth, 3.13. So this is approximately 3.13 for the standard dev... | Finding the mean and standard deviation of a binomial random variable AP Statistics Khan Academy.mp3 |
What is the smallest sample size required to obtain the desired margin of error? So let's just remind ourselves what the confidence interval will look like and what part of it is the margin of error and then we can think about what is her sample size that she would need. So she wants to estimate the true population pro... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
She doesn't know what this is so she is going to take a sample size of size n and in fact this question is all about what n does she need in order to have the desired margin of error. Well whatever sample she takes there she's going to calculate a sample proportion and then the confidence interval that she's going to c... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
What z-star, what critical value would correspond to a 95% confidence level times and then you would have times the standard error of her statistic and so in this case it would be the square root. It would be the standard error of her sample proportion which is the sample proportion times one minus the sample proportio... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
So the margin of error is this part right over here. So this part right over there she wants to be no more than 2%. Has to be less than or equal to 2%. That green color is kind of too shocking. It's unpleasant. All right, less than or equal to 2% right over here. So how do we figure that out? | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
That green color is kind of too shocking. It's unpleasant. All right, less than or equal to 2% right over here. So how do we figure that out? Well the first thing, let's just make sure we incorporate the 95% confidence level. So we could look at a z-table. Remember, 95% confidence level, that means if we have a normal ... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
So how do we figure that out? Well the first thing, let's just make sure we incorporate the 95% confidence level. So we could look at a z-table. Remember, 95% confidence level, that means if we have a normal distribution here, if we have a normal distribution here, 95% confidence level means the number of standard devi... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
Remember, 95% confidence level, that means if we have a normal distribution here, if we have a normal distribution here, 95% confidence level means the number of standard deviations we need to go above and beyond this in order to capture 95% of the area right over here. So this would be 2.5% that is unshaded at the top... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
You would look up the percentage that would leave 2.5% unshaded at the top. So you would actually look up 97.5%. But it's good to know in general that at a 95% confidence level, you're looking at a critical value of 1.96. And that's just something good to know. We could of course look it up on a z-table. So this is 1.9... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
And that's just something good to know. We could of course look it up on a z-table. So this is 1.96. And so this is going to be 1.96 right over here. But what about p hat? We don't know what p hat is until we actually take the sample, but this whole question is, how large of a sample should we take? Well, remember, we ... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
And so this is going to be 1.96 right over here. But what about p hat? We don't know what p hat is until we actually take the sample, but this whole question is, how large of a sample should we take? Well, remember, we want this stuff right over here that I'm now circling or squaring in this less, less bright color, th... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
Well, remember, we want this stuff right over here that I'm now circling or squaring in this less, less bright color, this blue color. We want this thing to be less than or equal to 2%. This is our margin of error. And so what we could do is we could pick a sample proportion. We don't know if that's what it's going to ... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
And so what we could do is we could pick a sample proportion. We don't know if that's what it's going to be, that maximizes this right over here. Because if we maximize this, we know that we're essentially figuring out the largest thing that this could end up being, and then we'll be safe. So the p hat, the maximum p h... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
So the p hat, the maximum p hat. And so if you wanna maximize p hat times one minus p hat, you could do some trial and error here. This is a fairly simple quadratic. It's actually going to be p hat is 0.5. And I wanna emphasize, we don't know. She didn't even perform the sample yet. She didn't even take the random samp... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
It's actually going to be p hat is 0.5. And I wanna emphasize, we don't know. She didn't even perform the sample yet. She didn't even take the random sample and calculate the sample proportion. But we wanna figure out what n to take. And so to be safe, she says, okay, well, what sample proportion would maximize my marg... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
She didn't even take the random sample and calculate the sample proportion. But we wanna figure out what n to take. And so to be safe, she says, okay, well, what sample proportion would maximize my margin of error? And so let me just assume that, and then let me calculate n. So let me set up an inequality here. We want... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
And so let me just assume that, and then let me calculate n. So let me set up an inequality here. We want 1.96, that's our critical value, times the square root of, we're just going to assume 0.5 for our sample proportion, although, of course, we don't know what it is yet until we actually take the sample. So that's ou... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
That's one minus our sample proportion. All of that over n needs to be less than or equal to 2%. We don't want our margin of error to be any larger than 2%. And let me just write this as a decimal, 0.02. And now we just have to do a little bit of algebra to calculate this. So let's see how we could do this. So this cou... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
And let me just write this as a decimal, 0.02. And now we just have to do a little bit of algebra to calculate this. So let's see how we could do this. So this could be rewritten as, we could divide both sides by 1.96, 1.96, one over 1.96. And so this would be equal to, on the left-hand side, we'd have the square root ... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
So this could be rewritten as, we could divide both sides by 1.96, 1.96, one over 1.96. And so this would be equal to, on the left-hand side, we'd have the square root of all of this. But that's the same thing as the square root of 0.5 times 0.5, so that'd just be 0.5 over the square root of n. Needs to be less than or... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
This is the same thing as two over 100. So two over 100 times one over 1.96 needs to be less than or equal to two over 196. Let me scroll down a little bit. This is fancier algebra than we typically do in statistics, or at least in introductory statistics class. All right, so let's see. We could take the reciprocal of ... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
This is fancier algebra than we typically do in statistics, or at least in introductory statistics class. All right, so let's see. We could take the reciprocal of both sides. We could say the square root of n over 0.5 and 1.96 over two. And let's see, what's 196 divided by two? That is going to be 98. So this would be ... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
We could say the square root of n over 0.5 and 1.96 over two. And let's see, what's 196 divided by two? That is going to be 98. So this would be 98. And so if we take the reciprocal of both sides, then you're gonna swap the inequality, so it's gonna be greater than or equal to. Let's see, I can multiply both sides of t... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
So this would be 98. And so if we take the reciprocal of both sides, then you're gonna swap the inequality, so it's gonna be greater than or equal to. Let's see, I can multiply both sides of this by 0.5. So 0.5, that's what my, I said 0.5, but my fingers wrote down 0.4. Let's see, 0.5. And so there we get the square ro... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
So 0.5, that's what my, I said 0.5, but my fingers wrote down 0.4. Let's see, 0.5. And so there we get the square root of n needs to be greater than or equal to 49, or n needs to be greater than or equal to 49 squared. And what's 49 squared? Well, you know 50 squared is 2,500, so you know it's going to be close to that... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
And what's 49 squared? Well, you know 50 squared is 2,500, so you know it's going to be close to that, so you can already make a pretty good estimate that it's going to be d. But if you wanna multiply it out, we can. 49 times 49, nine times nine is 81. Nine times four is 36, plus eight is 44. Four times nine, 36. Four ... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
Nine times four is 36, plus eight is 44. Four times nine, 36. Four times four is 16 plus three, we have 19. And then you add all of that together, and you indeed do get, so that's 10. And so this is a 14. You do indeed get 2,401. So that's the minimum sample size that Della should take if she genuinely wanted her margi... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
And then you add all of that together, and you indeed do get, so that's 10. And so this is a 14. You do indeed get 2,401. So that's the minimum sample size that Della should take if she genuinely wanted her margin of error to be no more than 2%. Now, it might turn out that her margin of error, when she actually takes t... | Determining sample size based on confidence and margin of error AP Statistics Khan Academy.mp3 |
If the significance level was lowered to 1 hundredth, which of the following would be true? So pause this video and see if you can answer it on your own. Okay, now let's do this together. And let's see, they're talking about how the probability of a type two error or the power, and or the power would change. So before ... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
And let's see, they're talking about how the probability of a type two error or the power, and or the power would change. So before I even look at the choices, let's think about this. We have talked about in previous videos that if we increase our level of significance, that will increase our power. And power is the pr... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
And power is the probability of not making a type two error. So that would decrease the probability of making a type two error. But in this question, we're going the other way. We're decreasing the level of significance, which would lower the probability of making a type one error, but this would decrease the power. It... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
We're decreasing the level of significance, which would lower the probability of making a type one error, but this would decrease the power. It actually would increase, it actually would increase the probability of making a type two, a type two error. And so which of these choices are consistent with that? Well, choice... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
Well, choice A says that both the type two error and the power would decrease. Well, those don't, these two things don't move together. If one increases, the other decreases. So we rule that one out. Choice B also has these two things moving together, which can't be true. If one increases, the other decreases. Choice C... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
So we rule that one out. Choice B also has these two things moving together, which can't be true. If one increases, the other decreases. Choice C, the probability of a type two error would increase. That's consistent with what we have here. And the power of the test would decrease. Yep, that's consistent with what we h... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
Choice C, the probability of a type two error would increase. That's consistent with what we have here. And the power of the test would decrease. Yep, that's consistent with what we have here. So that looks good. And choice D is the opposite of that. The probability of a type two error would decrease. | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
Yep, that's consistent with what we have here. So that looks good. And choice D is the opposite of that. The probability of a type two error would decrease. So this is, they're talking about this scenario over here, and that would have happened if they increased our significance level, not decreased it. So we could rul... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
The probability of a type two error would decrease. So this is, they're talking about this scenario over here, and that would have happened if they increased our significance level, not decreased it. So we could rule that one out as well. Let's do another example. Asha owns a car wash and is trying to decide whether or... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
Let's do another example. Asha owns a car wash and is trying to decide whether or not to purchase a vending machine so that customers can buy coffee while they wait. She'll get the machine if she's convinced that more than 30% of her customers would buy coffee. She plans on taking a random sample of N customers and ask... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
She plans on taking a random sample of N customers and asking them whether or not they would buy coffee from the machine. And she'll then do a significance test using alpha equals 0.05 to see if the sample proportion who say yes is significantly greater than 30%. Which situation below would result in the highest power ... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
So again, pause this video and try to answer it. Well, before I even look at the choices, we could think about what her hypotheses would be. Her null hypothesis is, you could kind of view it as a status quo, no news here. And that would be that the true population proportion of people who want to buy coffee is 30%. And... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
And that would be that the true population proportion of people who want to buy coffee is 30%. And that her alternative hypothesis is that no, the true population proportion, the true population parameter there, is greater than, is greater than 30%. And so if we're talking about what would result in the highest power f... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
So a high power, a high power means the lowest probability of making a type two error. And in other videos, we've talked about it. It looks like she's dealing with the sample size and what is the true proportion of customers that would buy coffee. And the sample size is under her control. The true proportion isn't. Don... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
And the sample size is under her control. The true proportion isn't. Don't wanna make it seem like somehow you can change the true proportion in order to get a higher power. You can change the sample size. But the general principle is, the higher the sample size, the higher the power. So you want a highest possible sam... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
You can change the sample size. But the general principle is, the higher the sample size, the higher the power. So you want a highest possible sample size. And you're going to have a higher power if the true proportion is further from your hypothesis, your null hypothesis proportion. And so we want the highest possible... | Examples thinking about power in significance tests AP Statistics Khan Academy.mp3 |
The filling machines can be set to the labeled amount. Variability in the filling process causes the actual contents of milk containers to be normally distributed. A random sample of 12 containers of milk was drawn from the milk processing line in a plant, and the amount of milk in each container was recorded. The samp... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
The sample mean and standard deviation of this sample of 12 containers of milk were 127.2 ounces and 2.1 ounces, respectively. Is there sufficient evidence to conclude that the packaging plant is not in compliance with the regulations? Provide statistical justification for your answer. So pause this video and see if yo... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So pause this video and see if you can have a go at it. All right, now let's do this together. So first, let's say what we're talking about. So let me define mu, and this is going to be the mean amount amount of milk in population, population of containers, containers at the plant that we care about. And so then we can... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
So let me define mu, and this is going to be the mean amount amount of milk in population, population of containers, containers at the plant that we care about. And so then we can set up our hypotheses. Our null hypothesis over here is that we are in compliance. We could say that the mean for our population of containe... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
We could say that the mean for our population of containers is actually 128. That's our minimum we need to be in compliance. And that our alternative hypothesis is that we are not in compliance. 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... | Free response example Significance test for a mean AP Statistics Khan Academy (2).mp3 |
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