Data inferences — Basic example

- [Instructor] In a survey of a random sample of 1,500 residents aged 25 years or older from a particular country, 399 residents has a bachelor's degree or higher. If the entire county had 635,000 residents aged 25 years or older, approximately how many county residents could be expected to have a bachelor's degree or higher? All right, so we have this random sample. We randomly sampled 1,500 folks aged 25 years or older. We find out that 399 of them have a bachelor's degree or higher. So of our sample, 399/1500ths have a bachelor's degree. Now the entire county has 635,000 residents aged 25 years or older. So when they're saying approximately, so we're gonna estimate here, how many residents could be expected? Well, since this was a random sample, you would expect that the same fraction of the random sample, that that would be approximately the same fraction of the general population aged 25 years or older that would have a bachelor's degree or higher. So we could just take this fraction and multiply it times the entire population to have a good estimate of, or good expectation, for the total number of folks with a bachelor's degree or higher. So we could just multiply this. Now there's two things going on. We really just want to get an approximation, and the good is, we have multiple choices right over here, and these are fairly spread out, so we could round some of these numbers here to simplify this a little bit. So this is going to be approximately the same thing. 399 is awfully close to 400. So it's gonna be approximately 400 over 1500 times 635,000, 635,000, and that's approximately the same thing as, let's see, four over 15. If I divide the numerator and denominator by 100, times 635,000, 635,000. Let's see, I could multiply all of this out if I want, but this quantity right over here, that's gonna be, so this is what we're, if I could just, we could figure what that is, but once again, we're just approximating. So this is gonna be greater than, if I just made this a 600,000, and I'm just gonna do that, just 'cause it's kind of close to 635,000, and 15 goes into 600,000 nicely. So whatever quantity this is, this is going to be greater than four times 600,000 over 15. And once again, I went to 600,000, just to make my math a little bit easier, and because 15 goes into 600,000, nice and easy 'cause 15 goes into 60 four times. So if you divide the numerator and the denominator by 15, this becomes a one, and then this becomes 4,000. I'm sorry, 40,000. Instead of 600,000, you're at 40,000. So this boils down to, maybe I'll cross out this, this is 40,000. So it's gonna be four times 40,000, which is 160,000. So our approximation is gonna be greater than 160,000, and there's only one choice here that is greater 160,000. And if you were multiply this out, you would get even closer to 169,000.