What does a confidence interval provide?

What does a confidence interval provide?

• A. A precise estimate of the population mean
• B. A range that likely contains the population parameter with a specified level of confidence
• C. An exact value of a sample statistic
• D. A method to compare multiple populations

Answer: (B)

A confidence interval provides a range that likely contains the population parameter with a specified level of confidence. This means that based on the sample data, we can construct an interval estimate that gives us an idea of where the true population parameter (such as the mean) lies. The key aspect is the confidence level, which indicates the degree of certainty we have that this interval captures the true parameter. For instance, a 95% confidence interval suggests that if we were to take many samples and compute a confidence interval from each, around 95% of those intervals would contain the actual population mean. The other choices imply different concepts. A precise estimate of the population mean is not guaranteed because confidence intervals reflect uncertainty and variability within sample data. The statement about an exact value of a sample statistic misrepresents what a confidence interval is, as it involves a range rather than a single value. The method to compare multiple populations is outside the scope of what a confidence interval provides; while confidence intervals can be constructed for different populations, they are primarily used to estimate parameters within a single population context.

A confidence interval provides a range that likely contains the population parameter with a specified level of confidence. This means that based on the sample data, we can construct an interval estimate that gives us an idea of where the true population parameter (such as the mean) lies. The key aspect is the confidence level, which indicates the degree of certainty we have that this interval captures the true parameter. For instance, a 95% confidence interval suggests that if we were to take many samples and compute a confidence interval from each, around 95% of those intervals would contain the actual population mean.

The other choices imply different concepts. A precise estimate of the population mean is not guaranteed because confidence intervals reflect uncertainty and variability within sample data. The statement about an exact value of a sample statistic misrepresents what a confidence interval is, as it involves a range rather than a single value. The method to compare multiple populations is outside the scope of what a confidence interval provides; while confidence intervals can be constructed for different populations, they are primarily used to estimate parameters within a single population context.