Question

How can a confidence interval be used to test a hypothesis typically addressed in a difference of means test (t-test)?

Answer 1

A confidence interval is a range of values that is likely to contain an unknown population parameter. If you draw a random sample many times, a certain percentage of the confidence intervals will contain the population mean. This percentage is the confidence level. Here we use the confidence interval to bound the difference in means.

If the confidence interval does contain the null hypothesis value (i.e 0 in the case of difference in means), we say that there is no difference between the means of two population, so the result is statistically insignificant.

If the confidence interval does not contain the null hypothesis value (i.e other that a 0 value), we say that there is a difference between the means of two population, so the result is statistically significant.