Simulating samples from populations example 1 | Grade 8 (TX) | Khan Academy

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.
3. Last but not least, repeat steps one to three every day for 3 weeks.

Here are their results where each dot represents a sample mean from step three.

All right, a survey of all employees revealed 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 take out 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 say the true mean travel time was 25 minutes, and we can see that the mean of what the manager did was under between 15 and 20 minutes right over here.

So, I would have 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 seems like the people who are coming to work earlier have less of a commute than the broader population. So, is it representative of the broader population? No.