What is true about confidence intervals?

Confidence intervals and p-values are both fundamental concepts in statistics that help researchers understand the uncertainty surrounding their estimates. The close relationship between confidence intervals and p-values arises from the fact that they are both used to make inferences about population parameters based on sample data.

A confidence interval provides a range of values within which we expect the true population parameter (like the mean or proportion) to fall, with a certain level of confidence (commonly 95% or 99%). This means that if we were to repeat the study many times, the true parameter would lie within this interval in a specified proportion of the studies.

P-values, on the other hand, are used in hypothesis testing to assess whether the observed data are consistent with a null hypothesis. A p-value indicates the probability of observing data as extreme as what was collected, assuming the null hypothesis is true.

The connection comes into play when interpreting the results: a confidence interval that does not include the null hypothesis value (like zero in the case of testing the difference between means) corresponds to a p-value that is statistically significant (typically less than 0.05). Conversely, if the confidence interval includes the null value, the corresponding p-value would be greater than the significance level, indicating a non