Confidence Level

Statistics · Axiom Academy

Understanding what confidence means in statistical inference When we estimate a population parameter from a sample, we use a confidence interval to express our uncertainty. But what does the confidence level really mean? This lesson explores the frequentist interpretation of confidence and common confidence levels used in practice. A confidence level is a probability that describes how often our confidence interval procedure will capture the true population parameter if we repeat the sampling process many times. 2 The Frequentist Interpretation The frequentist interpretation focuses on repeated sampling : If we construct many 95% confidence intervals from different samples of the same population, approximately 95% of those intervals will contain the true parameter , and about 5% will not. In practice, researchers use several standard confidence levels. Each level corresponds to a specific critical value (z*) from the standard normal distribution: Higher confidence levels create wider intervals (more conservative), while lower confidence levels create narrower intervals (less conservative). The confidence level is related to the significance level α (alpha): The critical value z* cuts off the extreme α/2 in each tail of the standard normal distribution. This is because we create a two-tailed interval. For a population mean with known standard deviation, the confidence interval formula is: z* is the critical value for your confidence level σ is the population standard deviation

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