Simulating samples from populations example 2
About this video
Students each estimate the percent of a school's 100 computers that work by numbering them, using a random number generator to pick 20, and converting the working count to a percent. Sal explains that this is a random sample, and the class's sample percents centre on 75%, matching the true percentage, so they are representative.
You'll be able to
- recognise a random sampling method.
- turn a sample count into a sample percent.
- judge whether sample results represent the population.
Key words
- random number generator
- A tool that picks numbers by chance so each one is equally likely.
- sample percent
- The percent of items in a sample that have a feature, such as working properly.
- population
- The whole group being studied, here all 100 computers.
- representative
- Giving a fair picture of the whole population.
Transcript
- [Instructor] We're told a teacher asked each student in their class to estimate what percent of the a hundred computers at the school were working properly following these steps? One, assign each computer a different number from one to a hundred. Two, use a random number generator to select a sample of 20 computers.
All right? Three, count how many of those computers are working properly? Four, divide that count by 20 and multiply by a hundred to convert to a percent. Here are their results where each dot represents a single student's sample percent from step four. All right?
The teacher revealed that the true percentage of computers working properly was 75%. So I guess the teacher actually went to all hundred and knew what the population statistic here is for the entire population of a hundred computers. So they're asking us two questions here.
The first one is, did the students select random samples from the population? Pause this video and think about it. And actually, let me scroll up so you can see the methodology to think about whether it's truly a random and representative sample. Well, what we're doing here is we literally are using a random number generator to sample the 20 computers out of a hundred.
So I would say that this is truly a random sample. So this is looking good and it would be representative. Well, let's see. That's the next question. Were their sample percents representative of the population? Well, when we look at the class average over here, we got to, it looks like 75%.
And the teacher said that the true population percentage that is working properly is 75%. So it actually is very representative, and that's typically going to be the case when you're taking a nice random sample that it is representative of the population.
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