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Unformatted text preview: 4/5/2010 1 Confidence Intervals - I The last topic in our Review of Statistics is Confidence Intervals . Recall that we have an estimate, Y , of Y . Again, Y will likely be fairly close to Y, , but it will generally not equal Y . Given our estimate Y , we might want to try to quantify the range that Y might be in. We can do this using Confidence Intervals. Confidence Intervals - II Given our estimate Y , a 95% confidence interval for Y is given by: Statistically, this interval will contain (or cover) the true population mean Y 95% of the time. Hence, we can say that we are 95% confident that Y is in this interval or region. Confidence intervals are a very useful and intuitive way of describing what we have learned statistically. 2 2 1.96 , 1.96 Y Y s s Y Y n n - + 4/5/2010 2 Confidence Intervals - III Example: Suppose Y= 84, s 2 Y is 100, and n = 25. A 95% confidence interval for Y is: We would conclude that we are 95% sure that Y is in this range. ( 29 ( 29 100 100 84 1.96 , 84 1.96 25 25 80.08 , 87.92- + = Confidence Intervals - IV Notes: 1) Confidence interval shrinks (i.e. one gets a more precise interval) as: n increases (all else equal) s 2 Y decreases (all else equal) 2) Can also do 90% or 99% confidence intervals: 90% CI: 99% CI: To be more confident that your interval covers Y , you need a bigger interval!...
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This note was uploaded on 06/17/2010 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.
- Spring '07