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## Problem solving and data analysis

# Data inferences — Basic example

## Video transcript

- [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.