stat400lec26 - Statistics 400 Section 7.2 Confidence...

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Statistics 400 Section 7.2 Confidence intervals for means The Statistical End Goal: draw conclusions about the data we have collected and analyzed. Every time we estimate μ using statistic X , we will never get the same answer. Due to sampling variability Need to provide intervals around the estimated statistics. For example: Draw a random sample of size n from N( μ , σ 2 ). Estimate μ using statistic X . Repeat your experiment to make sure you get similar results each time. Note, however, that each time you will end up with different answers that are very close to each other. You want to provide a range of values where we think X will occur. In addition to providing a range of values, you want to attach some level of confidence to the range you calculate. Recall: Density Curves: Used to represent a distribution of random variables. Density of X : Ping Ma Lecture 26 Fall 2005 - 1 -

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Interpretation: Confidence Intervals: Form: estimate ± margin of error Estimate: Whatever statistic we are estimating:
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stat400lec26 - Statistics 400 Section 7.2 Confidence...

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