Identifying statistics and parameters

0:00- [Instructor] We're told a hospital reviews records from every emergency room visit in a month, to compute the average wait time for that month. They find that the mean wait time is 37 minutes. Does this mean represent a sample statistic or population parameter?

0:18Pause this video. Have a go at that. Okay, so let's just remind ourselves what a population parameter is, and what a sample statistic is. If we look at the entire population, and then based on that, we calculate something, say, a mean of the whole population, it's a parameter.

0:36If we're trying to estimate a population parameter by sampling a representative sample of them, usually that means a very random sample of them, then that estimate of the population parameter is a sample statistic. Now, in this situation, the hospital reviews records from every emergency room visit in a month.

0:58So, they're not just sampling. They looked at every emergency room visit in a month and they computed the average wait time for that month using all the data points. They didn't just say, "Hey, we're gonna sample 100 out of 1,000 visits." They said, "We're gonna look at everyone and take the average."

1:14Which, if people just say average, they're usually talking about mean. They tell us later. They find that the mean is 37 minutes. So, we know that this one right over here is a population parameter. Every data point in that population was used to calculate this mean.

1:31Let's do another example. Warren, a community center director, wants to estimate the average number of classes attended each year by the center's members. He selects 135 members at random to ask about their yearly class attendance, and calculates an average. He says, "Because I surveyed only some of the members, my result is a sample statistic."

1:54Is the director's reasoning correct? And there's actually several choices here. So, pause this video, have a go at that. Well, if he was looking at every person who attended classes that year, then he would be probably looking at a parameter. But they tell us he selects 135 members at random.

2:17So that's not all of them. And it's clear that he's estimating the average. If he actually talked to everyone, he could actually calculate the average. That would be a parameter. But when he's estimating the average with a sample, especially a random sample like this, that's representative, hopefully, then we are dealing with a sample statistic.

2:35So, his logic is correct. So let's see, one of these. Yes. "Yes, because he collected data from a subset of all members." Yeah, that's right. "Yes, because 135 is a large enough sample to represent the population." Well, we don't know how large of a population this is.

2:55I mean, in many cases, 135 is a nice sample set, even of a very large population if you do it truly randomly. But that's not why. Maybe 15 would've been enough. You don't necessarily have to do 135. We don't have enough information to know what a minimum sample set would be to get a reasonable estimate.

3:16And then no is isn't right. "No, because he needed to survey all members to calculate a sample statistic." No, it would've been all members for a population parameter. "No, because class attendance data cannot form a sample statistic." No, of course it can. If you're sampling something representatively of anything, and you do things like calculate a mean, of almost anything, you could create a sample statistic.

3:40So, I definitely like choice A.