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Video transcript

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 promised 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 entire 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 a hundred thousand Ducks in the shipment he wants to figure out what percentage of them are defective he can't he can't look at all 100,000 Ducks it's not practical so he samples ten of them one two three four five six seven eight nine ten and he finds that one out of those ten are defective ten percent of the ten 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 hundred thousand duckies that are actually defective now the next question is is what kind of a conclusion can you make you know Roy since he got the shipment he and he took a sample and he found that ten percent of the sample was defective he might you know be all up in arms and say oh this this toy shipment from the factory you know they violated this this promise that the percentage of defective toys won't exceed five percent because I sampled ten toys and ten percent of those ten toys were defective well that isn't a reasonable conclusion because this is a small sample this is a small sample think about it he could have sampled five duckies and if he just happened to get one of the defective ones he was said oh maybe twenty percent 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 probability that your estimate is close to the actual parameter for the population and 10 on 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 whether your sample seems sufficient but for this one for what Roy did I don't think 10 Ducky's is enough if he sampled maybe a hundred 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