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Sep 8, 2016 · The article uses the SAS DATA step and Base SAS procedures to estimate the coverage probability of the confidence interval for the mean of normally distributed data. This discussion is based on Section 5.2 (p. 74–77) of Simulating Data with SAS.
Coverage probability is a way to evaluate the performance of a confidence interval estimator; ideally, your CI should have the highest possible coverage probability [2]. The usual way to choose a coverage probability is by convention or your best judgment, with 90%, 95%, and 99% being typical choices [3].
Coverage probability is a fundamental concept in statistics, particularly in the context of confidence intervals and hypothesis testing. It refers to the proportion of times that a statistical method will produce an interval that contains the true parameter value across many repeated samples.
In statistical estimation theory, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will include the true value (parameter) of interest.
These are conservative procedures for constructing confidence intervals: the probability that the intervals they produce cover the true population mean is greater than the probability they claim, 1−1/k 2 (the nominal coverage probability).
Jul 10, 2022 · This short simulation study examines the coverage probability of 95% confidence intervals of the Horvitz-Thompson estimator of the population mean under simple random sampling without replacement.
For large random samples, a confidence interval for a population mean is given by \[\text{sample mean} \pm z^* \frac{s}{\sqrt{n}}\] where z* is a multiplier number that comes from the normal curve and determines the level of confidence (see Table 9.1 in section 9.2).
