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Confidence interval creator given data11/28/2023 ![]() ![]() ![]() Sample variance- I'll write it over here- our sample Going to write the whole thing out- minus 0.568 squared,Īnd then all of that divided by 250 minus 1 is 249. Let's get our calculatorĪ parentheses around everything- I have 142 timesġ minus 0.568 squared, plus 108 times 0 minus- and youĬould obviously do parts of this in your head, but I'm just That by the total number of samples minus 1. Plus the other 108 times we gotĪ 0, so we were 0 minus 0.568 away from the Minus 0.568 away from our sample mean, or we're this farįrom the sample mean 142 times, and we're going to Other way actually around- we have 142 samples that were 1 So we can get the best estimator of the true variance. The weighted sum of the square differences from the mean andĭivide by this minus 1. So let me draw a sample variance- we're going to take Sample variance because we can use it later for building So we have 142 divided byĢ50 is equal to 0.568. The sample proportion of teachers who thought that Times 108 divided by our total number of samples,ĭivided by 250. So 108 said not good, or youĬould view them as you were sampling a 0, right? 108 plus 142 is 250. So what's left over? There's another 108 who said So we got 142 1's, or we sampledġ, 142 times from this distribution. Sampled, and we got 142 said that it is good, and we'll Now what we do is we're takingĪ sample of those 250 teachers, and we got that 142įelt that the computers were an essential teaching tool. They cannot say something inīetween good and not good. Value, it's neither 0 or 1, so not an actual value that youĬould actually get out of a teacher if you were This distribution or the expected value of thisĭistribution is actually going to be p. Right over here, and we know that the mean of Teachers think that it is a good learning tool. ![]() And we'll just define aĠ value as a teacher that says not good. In the bucket, and we'll define that as 1, they thought Of them, but the entire population, some of them fall Teachers who felt that the computers are an essential And then they ask us, calculateĪ 99% confidence interval for the proportion of Of those selected, 142 teachersįelt that the computers were an essential That computers were an essential teaching toolįor their classroom. From the 6,250 teachers in theĭistrict, 250 were randomly selected and asked if they felt To install a cluster of four computers in their classroom. Sometimes instead of the proportion, people will think about the "odds," defined as p / (1-p), and the natural log of this quantity is generally assumed to be normally distributed.Ī technology grant is available to teachers in order Though, there's always a possibility of still having extremely rare events (like some rare disease, where 1 in 10000 people have it) and so the raw proportion isn't a very useful measure. This is related to the Central Limit Theorem, forcing the sample size to be large enough so that the approximation is reasonable. The second one is not larger than 5, so in such a case it would not be reasonable to assume a Normal distribution we'd need the sample size to be much larger. ![]() When both of these conditions are satisfied, then it's generally reasonable to assume that the sampling distribution of the sample proportion (the sample mean of data that takes values 0 or 1 ). Though note that sometimes the 5 is replaced with 10. When dealing with proportions, there's a general rule that we need to check. ![]()
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