Introduction:

A confidence interval is a range of values, derived from sample data, that likely contains the true population parameter (like the mean) with a specified level of confidence. It's a key concept in statistics for making inferences about a population based on a sample.



Understanding Confidence Intervals:



The confidence interval provides an estimated range believed to contain the population parameter.

It's expressed as (lower limit, upper limit) and includes a confidence level, typically 90%, 95%, or 99%.

Calculating the Confidence Interval:



To calculate a confidence interval, you need the sample mean, the standard deviation, and the sample size.

Then, use a statistical formula or a calculator to determine the interval.

Example Using Provided Data:



With the sample [234, 223, 210, 203, 258, 299, 281, 208, 278, 252, 295, 245, 280, 235, 219, 297, 214, 267, 212, 256, 232, 221] and a 99% confidence level, the confidence interval is calculated as (263.31, 229.33).

This means we are 99% confident that the true mean of the population from which the sample was drawn falls within this range.

Interpreting the Confidence Interval:



A wider interval provides more certainty about containing the population mean but is less precise.

The chosen confidence level reflects how sure we are that the interval includes the population mean.

Key Points to Remember:



Confidence intervals are used to estimate population parameters based on sample data.

They are not absolute but provide a range where the parameter is likely to be found with a certain level of confidence.