Simulating samples from populations example 1
About this video
A manager estimates employees' mean travel time by surveying the first 20 employees to arrive each day for 3 weeks. Sal explains that this is not a random sample, and the sample means (between 15 and 20 minutes) do not represent the true population mean of 25 minutes.
You'll be able to
- decide whether a sampling method is random.
- explain why a non-random sample may not represent a population.
- compare sample means with a known population mean.
Key words
- population
- The whole group you want to know about, here all of the company's employees.
- sample
- A smaller group picked from the population to learn about it.
- random sample
- A sample where every member of the population has a fair chance of being chosen.
- sample mean
- The average of the values in one sample.
- representative
- Similar to the whole population, so it gives a fair picture of it.
Transcript
- [Instructor] We're told a company manager wants to estimate the mean amount of time it takes the employees to travel to work. Here's what the manager did. 1. Survey the first 20 employees to arrive that day. 2. Note the amount of time for each employee. Add those times and divide by 20.
And then last but not least, repeat steps 1-3 every day for 3 weeks. Here are their results, where each dot represents a sample mean from step 3. All right. A survey of all employees revealed that the true mean travel time was 25 minutes. So the true mean, for the population when they surveyed all employees.
This is of course a sample and now they ask us some questions. So answer two questions. Did the manager select random samples from the population? Pause this video and think about that before I have a takeout on it. All right. So when the manager decided to sample every day, they surveyed the first 20 employees to arrive that day.
So that is not really a random representative sample of the population, especially if you're thinking about time to travel to work. The people who arrive there early, they might be coming at a time, maybe they have a shorter commute, maybe they have a longer commute.
Maybe they're coming at a time where there's less traffic or more traffic. So this is not going to be representative of the entire population of employees. So I would say no. The manager did not select random samples from the population. Were their sample means representative of the population?
Well, they actually told us what the population mean is. They said the true mean travel time was 25 minutes. And we can see that the mean of what the manager did was under is between 15 and 20 minutes right over here. So I would've assumed that it wouldn't have been representative just based on how they did the sampling.
But we also know what the true population mean is, and it's definitely not representative. This is much shorter travel time. So it's actually happening, it seems like the people are coming to work earlier, have less of a commute than the broader population. So is it representative of the broader population? No.
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