Worked example identifying sample study

Let's look, let's take a look at some statistical studies and see if we can figure out what type they are. So this first one, Roy's toys received a shipment of 100,000 rubber duckies from the factory. The factory couldn't promise that all rubber duckies are in perfect form, but they promised that the percentage of defective toys won't exceed 5%. Let me underline that: they promise that the percentage of defective toys won't exceed 5%.

Roy wanted to get an estimation of the percentage of defective toys, and since he couldn't go over the hire 100,000 duckies, he took a random sample of 10 duckies. He found that 10% of them were defective. So what's going on here? Roy gets a shipment; there's 100,000 ducks in the shipment. He wants to figure out what percentage of them are defective. He can't look at all 100,000 ducks; it's not practical. So he samples 10 of them: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and he finds that one out of those 10 are defective—10% of the 10.

So first of all, this is clearly a sample study. This is a sample study. How do we know that? Well, he is taking a sample from a broader population in order to estimate a parameter. The parameter is the percentage of those 100,000 duckies that are actually defective.

Now the next question is: what kind of conclusion can you make? You know, Roy, since he got the shipment and he took a sample, and he found that 10% of the sample was defective, he might, you know, be all up in arms and say, "Oh, this toy shipment from the factory, you know, they violated this promise that the percentage of defective toys won't exceed 5% because I sampled 10 toys and 10% of those 10 toys were defective."

Well, that isn't a reasonable conclusion, because this is a small sample. This is a small sample. Think about it. If he could have sampled five duckies and if he just happened to get one of the defective ones, he would have said, "Oh, maybe 20% are defective."

What he's really got to do is sample, take a larger sample. And once again, whenever you're sampling, there's always a probability that your estimate is going to be not close or definitely not the same as the parameter for the population. But the larger your sample, the higher the probability that your estimate is close to the actual parameter for the population.

And ten, in this is just too low. In future videos, we'll talk about how you can estimate the probability or how you can figure out whether your sample seems sufficient. But for this one, for what Roy did, I don't think 10 duckies is enough. If he sampled maybe 100 duckies or more than that and he found that 10% of them were defective, well, that seems less likely to happen just purely due to chance.

Let's do a few more of these, and actually, I'll do those in the next videos.