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<v Instructor>Hello students, this is problem 2e.</v>

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And this actually is not in our text,

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but it has been added because we want to show you guys

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how to determine if two factors are independent or not.

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So we are continuing to use the same example,

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and we want to know now

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if the child's hyperlipidemic status

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is independent of the parent's status.

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So conceptually, this means that the probability

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that the child is hyperlipidemic should be the same

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regardless of the parent's hyperlipidemia status,

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and that will demonstrate independence.

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So mathematically, what we want to do here is

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look at this probability,

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and I'm going to start.

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And again, here I am abbreviating hyperlipidemia as HL,

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and we are going to use

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the both parents being hyperlipidemic,

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but we could use the other columns as well.

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Okay, let me write a little smaller,

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so that they will fit here.

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So now, what are these numbers?

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So for this one,

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and we have gone through this calculation before,

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the numerator is going to be 45 plus 42 plus six

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because again, the child's hyperlipidemia status

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was given in the rows and the parents in the column.

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And then we are going to divide this by 223,

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which is our entire cohort.

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On this side,

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it's going to be 45 divided by 45 plus 13.

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Again, I like to put the parentheses around

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because it helps me remember

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that I have to do the addition before I do the division.

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So now what I'm gonna do is go and get a different color,

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so I can show you where each of these are coming from.

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So this is where we are getting

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the child status from, right.

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Okay, this row,

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and that's exactly what we have there.

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And then this is our denominator

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for the left hand side.

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And now, for the right hand side,

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I'm going to show you where 45 is coming from.

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Of course, it's coming from here,

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and the parent status is coming from here, okay.

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So,

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this is basically what is going on,

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and this is how we are doing our calculation.

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So now, let's go back,

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let me get the black ink,

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and I'm going to start doing the calculation.

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And when we do the calculation what we see is

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from this side, we get 0.42,

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and from this side, what we get is 0.78.

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So what?

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0.78, so basically we can say that they are not equal.

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So since they are not equal,

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now we can say that they are not independent.

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So not equal here means

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not independent.

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Let me see if I can write this a little more nicely.

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So not equal,

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not independent.

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Okay.