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(8) 3 points) Suppose we select & simple random sample from population and generate a QQ plot of it (given below)QQ plot1Theorelical QuanblesBased on this QQ pl...

Question

(8) 3 points) Suppose we select & simple random sample from population and generate a QQ plot of it (given below)QQ plot1Theorelical QuanblesBased on this QQ plot, what can you conclude about the underlying population?

(8) 3 points) Suppose we select & simple random sample from population and generate a QQ plot of it (given below) QQ plot 1 Theorelical Quanbles Based on this QQ plot, what can you conclude about the underlying population?



Answers

Which of the following normal quantile plots appear to represent data from a population having a normal distribution? Explain. (GRAPHS CAN'T COPY)

In this video, we're going to continue talking about normal probability plots and looking at examples and determining if in fact they are normal. Now, we can recall from our previous um problems that a normal probability plot is going to be representative representative of a normal data set. If our if our scatter plot is following a linear pattern and you can see in all these examples that the um you know, the sort of trend line there in the middle is given to you and you want your data points to stay between those kind of between those bounds um that you're that you're given on each side of that. Um And if you look at the one um for number three, you can see that it starts off um a good bit away from that trend line that we're sort of given and works. It's way up almost in a vertical pattern, not in a linear pattern, It is uh you know, increasing very, very quickly. And then it starts to level out, kind of stays in the right range here and then levels way off. So you've got some huge outliers here and you know here, you would expect the Z scores down here to be a lot closer to um to the trend line in order to represent a linear pattern. And over here you would not expect them to be off the charts, um increasing, you would expect them to stay more on that linear pattern as well. So again, really, what you're looking at there on the right is you're looking at a value that is an outlier. I mean you can just look along the X axis and you can tell that this X value is not like the other ones, it is a good bit further to the right. So um due to that and that pattern of increasing really quickly, there are in the beginning of our scatter plot. This one is not normally distributed based off of what we are given.

On this normal probability plot. You can see that the points um the where are expected Z scores and our actual Z scores um match up. Um They do follow a linear trend. There are some spots here at the end of the value at the end of the trend line. And even a bit at the beginning that do sort of um don't really follow the trend line exactly. Um So you might have kind of some some lengthy tales um things like that. Um You know you might have one tail be a little bit longer than the other. Um But overall it does match the linear trend. It does sort of stay in that line. Um So you can see there that are Z scores are increasing in a linear pattern. And that's really what we're looking for here. We're looking do our Z scores increase in um a linear in a linear pattern? And we know that if something is is normal then the Z scores will increase in the linear pattern. Because of the Z score formula is, you know, a linear formula. So um you know the percentage of data to the left of given observation um does sort of follow that linear pattern because the observed is pretty close to the expected, and therefore we would say that this one is approximately normal.

Alright, so again we're looking at our normal probability plots and determining if this could come from a normal data set. And what we're really looking for is does the scatter plot, given the normal probability plot follow a linear pattern? Does it follow a normal trend line? And um so basically, you know, if you think back to linear regression, what are the residuals? Like how far are the data points? My red data points from my blue trend line? Are they fairly close to it? Did they follow that linear pattern or are they a good bit often if they're a good bit off, that sort of leads you to think that maybe it's not um normal. And in this case we have one data point that really sticks out to me. Um The one over here all the way to the right. That um really makes me question the normal trend. It also does have a kind of a clear curved pattern. Um As as you work your way to the right, you know, it's under the curve and then it comes up above the curve and then curves back out and then you jump over here to the outlier on the right. So this one does not really seem to follow a linear pattern. Uh It definitely seems to have a different type of regression pattern, um Maybe a power function of some sort um or something to that nature. So in this case, since it does not best fit a linear regression model, uh we would say this one is not approximately normal, and also that outlier, we know that um normal data typically does not have outliers. So that one is one that is I'm a bit a bit troublesome, especially in a smaller data set, like what we're seeing here.

So we're again going to continue our discussion on normal probability plots. And in this particular example, um as always we're looking to see, does our scatter plot, given by our normal probability plot follow a linear trend pattern. Um Or does it follow some other type of pattern? Um And and this one right here, as you can see sketched up, um it kind of drastically curves, you know, drastically increasing up and then curves and flattens out. And then you got one point kind of over here to the right, which is not too much of a concern because it's not significantly to the right, but it is separated from the rest of them, but you do have a very drastic increase here. Um To me, I think this looks a lot more like maybe a log arrhythmic pattern or something like that, definitely not a linear pattern. Um If you remove the trend line and I want to ask what type of trend is this follow, we would definitely not say that it follows a linear trend. Um So due to the fact that it does follow maybe a more log arrhythmic pattern, not a linear pattern than this would not necessarily be described as approximately normal. This would definitely be one that is more skewed because you do have so much data um over here on the on the right, and this kind of drastic increase here instead of a constant increase in the point. Um That is kind of a huge sign that your data is skewed More one way or the other. Um So this particular data would not be approximately normal, it would be skewed. And so.


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