Explain how confidence intervals work over repeated sampling.

Question

Quizplus · Accepted Answer

The Answer is Confidence intervals work over repeated sampling by providing a range of values within which we can be confident that the true population parameter lies. When we take multiple samples from the same population and calculate confidence intervals for each sample, we will find that the true population parameter (such as the population mean or proportion) will fall within the confidence interval a certain percentage of the time, which is determined by the confidence level (e.g., 95% confidence level).

For example, if we calculate a 95% confidence interval for the population mean from multiple samples, we would expect that in the long run, 95% of these intervals will contain the true population mean. This means that if we were to take 100 different samples and calculate a 95% confidence interval for each sample, we would expect that 95 of these intervals would contain the true population mean, and 5 would not.

In essence, confidence intervals work over repeated sampling by providing a way to quantify the uncertainty in our estimates and by giving us a sense of how often our intervals will contain the true population parameter. This allows us to make inferences about the population based on our sample data and to understand the variability that comes from taking multiple samples from the same population.

Explain How Confidence Intervals Work Over Repeated Sampling