STATS 250 Lecture Notes - Lecture 3: Simple Random Sample, Confidence Interval, Bias Of An Estimator
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Definition: a sample of size n drawn from population of size n is a simple random sample if every possible sample of size n is equally likely. Implication: each element in population has the same probability of selection. Probability of being included in the sample is n/n. Use theory that assumes the distribution of the sample mean is approximately normal, thus a confidence interval can be constructed. If sampling distribution of the unbiased estimator theta-hat for parameter theta is approximately normal, then in approximately 95% of samples theta is contained in the interval defined by the respective confidence interval. Proportion is the mean that arises when the characteristic being measured is binary: yi is either 0 or 1. Population proportion: sum up all yi and divide it over n. Begin by specifying the desired bound on the error of estimation. Use the formula 2, where n is sample size, b is desired bound, v is variance.
