STAT202 Lecture 12: ch14_17_Confidence Intervals
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Confidence interval for a normal population mean (three cases) If you picked different samples from a population, you would probably get different sample means ( x ) and virtually none of them would actually equal the true population mean, . If the population is n( , ), the sampling distribution is n( , / n). We take one random sample of size n, and rely on the known properties of the sampling distribution. When we take a random sample, we can compute the sample mean and an interval of size plus-or- minus 2 / n around the mean. Based on the ~68-95-99. 7% rule, we can expect that: ~95% of all intervals computed with this method capture the parameter . A confidence interval is a range of values with an associated probability, or confidence level, c. this probability quantifies the chance that the interval contains the unknown population parameter. We have confidence c that falls within the interval computed.
