In a herd of dairy cows the narrow-sense heritability for milk protein content is 0.76, and for milk butterfat it is 0.82. The correlation coefficient between milk protein content and butterfat is 0.91. If the farmer selects for cows producing more butterfat in their milk, what will be the most likely effect on milk protein content in the next generation?

Video transcript

Hi everyone, welcome back. Here's our next problem. It says the narrow sense heritability of egg yolk and egg white and the eggs of a poultry farm is 0.45 and 0. respectively, identify what, identify what you will calculate to investigate whether there is a relationship between these two. Well, this kind of problem is why it's always a good idea to look over your answer choices first, because by looking over them we see that we don't actually need those numbers that are provided, we're not calculating anything or solving a problem. Instead, the problem is asking us, what is it you need to calculate to investigate whether there's a relationship between the value of the egg yolk and the egg white. And when we look over our answer choices, we have choice a standard deviation choice B variants, choice C correlation coefficient and choice D standard error. Even if we didn't remember the meanings of these things. When we look at choice c correlation coefficient, correlation means the relatedness of two things. Do they depend on each other? Um How related are they? So that helps lead us to our correct answer choice C correlation coefficient. And that is what you would calculate to see whether there's a relationship between these two, because it tells us how much two variables are related. If this value is positive and high, that would indicate that when one of these variables increases the other increases that they're closely related and vice versa. Now let's look at our other answer choices to understand why they're not correct first of all, when we look at choice a standard deviation and choice B variants, those two are somewhat related items. So I'm gonna start actually with choice B variants, um, variance is the degree to which the values in a set diverge from the mean, but when you calculate that with an equation, the units of this variance are going to be squared. So that takes us to standard deviation. If you want to express that notion of how the values diverged from the mean, and you want to express in the original units, you'd use standard deviation. So the standard deviation comes from the square root of the variants. So it kind of expresses that notion of divergence for the mean in original units. So that kind of can make it more useful in terms of actually understanding its size when compared to the units of whatever you're looking at. But neither of those tells you whether there's a relationship between two different variables, so that's why neither a nor B is your correct answer. And finally, choice do you have standard error? And that says how different is your populations mean? Likely to be from your particular sample from the means, or from the mean of the entire population, your samples drawn from? So that's just kind of a measure of the accuracy of the way you picked your sample and how reflective it is of the larger population is drawn from. So it'd be how different that sample mean is from the population mean? But again, doesn't tell us whether there's a relationship between 22 things like egg yolk and egg white, so that's why twisty is not our correct answer. So again, when you're looking at egg yolk and egg white and the heritability in the eggs, what do you calculate to investigate where there's a relationship between these two, and the answer is choice C correlation coefficient. See you in the next video.