Sampling with and without replacement

0:00- [Instructor] A quality control specialist at a cannery selects a can from the day's production, inspects its seal, and sets the can aside. She repeats this until she has inspected 12 cans. Is the inspector sampling with replacement or without replacement? Pause this video and have a go at that.

0:20Okay, so let's see what's happening. If she's doing it with replacement, she will select a can from the day's production, inspect its seal, and then put it back in the batch from which she could potentially sample. But that's not what she's doing. She is setting the can aside.

0:38So she is doing this without replacement. Another way to think about it, if you're sampling with replacement, you could in theory sample the same can multiple times. But the way that she's doing it, that's actually impossible because every time she samples a can, she's putting it aside.

0:53So the next can she samples can't be that one. So this is definitely without replacement. And let's see, so it's either C or D. Without replacement because each inspected can is set aside and cannot be selected again. Yep, I like that choice. Let's just read what this one is.

1:07Because she inspects only 12 of the cans produced that day. No, that has nothing to do with replacement or not. Let's do another example. So here we're told a librarian numbers the 340 chairs in a reading room from 1 to 340. She uses a random number generator to produce a number in that range, inspects the matching chair, and then generates another number.

1:32She repeats this 20 times inspecting whichever chair each number names. Is a librarian sampling with replacement or without replacement? So in this scenario, a random number generator, we assume that a random number generator, let's say it picks two the first time, and then she goes and inspects chair number two.

1:53The second time, it could still produce two. Random number generators don't say, oh, I just picked a two. I can't pick a two again. They can pick the same chair again. So another way to think about it, this is with replacement. You might say, well, what are you replacing?

2:07Well, you're replacing, the number two isn't taking out. Every time you are able to get a number out of the random number generator, it's not taken out. It can be selected again. The way that she's doing this, this is completely like, hey, she picked one out of the 340 chairs at random, inspected it, and then picked another and then put it back.

2:28That's the replacement. And then she did that again. So in theory, she could select the same chair. So this is with replacement. Let's see which choice. With replacement because she inspects the chairs rather than removing them from the room. That's not exactly right.

2:44With replacement because the generator can produce the same number more than once, so a chair can be inspected again. Yes, that is correct. Because there is a world where you could inspect the chair, not remove it from the room, but whatever selection criteria, you're not able to pick that chair again and that would not be replacement.

3:03But this one is because she literally has, she can pick that chair, that chair is just as equal. Even if a chair is picked, it's just as equal as the other chairs to be picked again in any of the successive rounds.