![]() We can think about the variance, so the variance of the Well, we have seen in a previous video when we talked aboutĭifferences of proportions. So the first thing I wanna think about is what is going to be the standard deviation of the difference in the Thinking about the sampling distribution of the difference between the sample proportionsĪssuming that null hypothesis. And so with that out of the way, let's assume the null hypothesis, and let's just start The entire population, and so I guess we will assume that there's at least 1,000 folks in District A and at least 1,000 folks in District B and that will allow us to meet Independence condition, and the Independence condition, you're either sampling with replacement or you need to feel good thatĮach of these sample sizes are no more than 10% of Indeed have at least 10 successes and at least 10įailures in each of those samples. Have at least 10 successes and failures in each of these samples, and we see that we do You would have your Normal condition, which is that you would To feel good that both of these samples are truly random. You have the Random condition, where you would need ![]() The null hypothesis, "which would suggest the alternative." Now before we go deeperĬonditions for inference, and we've seen these many times before. Less than our significance "level, then we reject Getting a difference between our "sample proportions this extreme or more? "And if that probability is The null hypothesis is true, "and assuming the null hypothesis is true, "what is the probability of And what we would do is, we would say, "All right, let's assume that Let's say we set it atĪ 5% significance level. Often times it might beĪ 10% significance level or a 5% significance level. And if we were doing anĪll out hypothesis test, we would set a significance level, which we usually denote with an alpha. And our alternative hypothesis is that the absolute difference between the proportions is not equal to zero. Or another way to think about it is that the difference would be equal to zero. The new law is equal to the proportion in Districtī that support the law. True proportion of folks in District A that support Hypothesis is the one that we would assume that And so this is askingįor a hypothesis test, and the way we would do that is we would set up our null hypothesis, and remember our null And we're asked, does this suggest a significant differenceīetween the two districts. And then here we have the combined data, including the combined proportion. And then we were able toĬalculate the proportion from that sample that supported the law. Whether they supported a new law or not, and from each district, we took a sample of 100 voters. Results from a recent poll that involved sampling voters from each of two neighboring districts,ĭistrict A and District B, and folks were asked To explore hypothesis testing where we're thinking about the difference between proportions of
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