Can someone please help me understand how confidence intervals fit within the broader context of inferential statistics

https://www.google.com/search?client=safari&rls=en&q=confidence+intervals+inferential+statistics&ie=UTF-8&oe=UTF-8

Certainly! Confidence intervals are a fundamental concept within inferential statistics, which involves making inferences or conclusions about a population based on sample data. Confidence intervals provide a range of values within which we believe the true population parameter lies.

To understand how confidence intervals fit within the broader context of inferential statistics, let's break it down into steps:

1. Data collection: The first step in inferential statistics is collecting a representative sample from the population of interest. This sample should ideally be random and unbiased, to ensure that the results can be generalized to the population.

2. Point estimation: Once the sample is collected, we use statistics to estimate the unknown parameter of interest. For example, if we want to estimate the mean salary of all employees in a company, we would calculate the sample mean. This point estimate is a single value that provides an estimate of the parameter.

3. Uncertainty and variability: Since we typically only have access to a sample, our estimate will not be exactly equal to the true population parameter. There is always some degree of uncertainty and variability involved in estimating population parameters based on sample data.

4. Confidence intervals: To account for this uncertainty, we use confidence intervals. A confidence interval is a range of values around the point estimate that, according to statistical theory, likely contains the true population parameter. For example, a 95% confidence interval for the mean salary would provide a lower bound and an upper bound within which we are 95% confident that the true population mean lies.

5. Confidence level: The confidence level represents the percentage of confidence intervals, computed from different samples, that would contain the true population parameter. In most cases, a 95% confidence level is used, indicating that if we were to repeatedly sample from the population, 95% of the resulting intervals would contain the true parameter.

6. Interpretation: When reporting the results, we do not claim that the parameter falls within a specific point estimate but rather state that it is likely to fall within the calculated confidence interval. The wider the interval, the less precise our estimate, and the more uncertainty there is surrounding the parameter's true value.

In summary, confidence intervals provide a way to quantify the uncertainty associated with estimating population parameters from sample data. They allow us to gauge the range of plausible values and provide valuable information for decision-making based on sample statistics.