There is an extremely close relationship between confidence intervals and hypothesis testing. When a 95% confidence interval is constructed, all values in the interval are considered plausible values for the parameter being estimated. Values outside the interval are rejected as relatively implausible. If the value of the parameter specified by the null hypothesis is contained in the 95% interval then the null hypothesis cannot be rejected at the 0.05 level. If the value specified by the null hypothesis is not in the interval then the null hypothesis can be rejected at the 0.05 level. If a 99% confidence interval is constructed, then values outside the interval are rejected at the 0.01 level.

Imagine a researcher wishing to test the null hypothesis that the mean time to respond to an auditory signal is the same as the mean time to respond to a visual signal. The null hypothesis therefore is:

μ

Ten subjects were tested in the visual condition and their scores (in milliseconds) were: 355, 421, 299, 460, 600, 580, 474, 511, 550, and 586.