Briefly explain the relationship between confidence interval and hypothesis testing.

There is a close relationship between confidence intervals and hypothesis testing. When a 95% confidence interval is constructed, all values within that interval are considered plausible estimates for the parameter. Values outside this range are treated as implausible.

The connection operates as follows: "If the value of the parameter specified by the null hypotheses is contained in the 95% interval, then the null hypothesis cannot be rejected at the level of 0.05 levels." Conversely, if the null hypothesis value falls outside the interval, it can be rejected at the 0.05 significance level.

This relationship scales with confidence levels — a 99% confidence interval corresponds to rejecting values at the 0.01 significance level. Essentially, confidence intervals and hypothesis tests provide complementary approaches to statistical inference: confidence intervals show which parameter values are plausible, while hypothesis tests determine whether specific values can be rejected based on the same underlying probability principles.