CSCI 3022 Lecture Notes - Lecture 14: Standard Deviation, Random Variable, Confidence Interval
6 Apr 2019
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Goal: want to extract properties of an underlying population by analyzing sampled data. The clt tells that as the sample size n increases, the sample mean of x is close to normally distributed with expected value and standard deviation. Standardizing the sample mean by first subtracting the expected value and dividing by the standard deviation yields a standard normal random variable. Q: how large does the sample need to be if. We saw a while ago that 95% of the area under the standard normal curve falls between -1. 96 and +1. 96, so we know that. P(-1. 96 (cid:15457) z (cid:15457) 1. 96) = 0. 95 where z~n(0,1) So: the 95% confidence interval is given by the values of x that satisfy that question! How do we find these? the 95% confidence interval for the mean is given by . The ci varies sample to sample, so the ci is really a random interval itself.
