Statistics Full Video Course - Confidence Intervals for the Mean, minimum sample size required when estimating μ - Statistics
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Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error. c) The statement, "the 95% confidence interval for the population mean is (350, 400)", is equivalent to the statement, "there is a 95% probability that the population mean is between 350 and 400". Thus in general for a 100(1−α)% confidence interval, E=zα/2(σ/√n), so the formula for the confidence interval is ˉx±zα/2(σ/√n). While sometimes the population standard deviation σ is known, typically it is not. If not, for n≥30 it is generally safe to approximate σ by the sample standard deviation s
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