How does hypothesis testing related to confidence intervals?
The “confidence interval” tells you the relative degree to which your hypothesis fits the observations.
First, a “hypothesis test” is a binary, either-or condition. It often will not provide a complete answer to a more complex question, but it may focus future data collection. The various calculations applied to a set of data to determine how well the data conform to the expectations of a hypothesis only provide a particular value in the whole range of possibilities. The determined value is NOT some absolute fact in the sense of algebraic equations. It is only an indicator of where your existing data are with respect to a larger population of data.
The “confidence interval” is a calculation applied to the particular distribution of population values that defines the “range” of data that fit a particular (arbitrary) level of confidence that the results are accurate. It is VERY important to recognize that ANY combination of confidence levels and intervals does NOT generate an “absolute” value! Even a value well within a confidence interval at a confidence level of 99% STILL means that the reality COULD be different – that 1%.
It remains with the individual and their personal “risk tolerance” to make a decision based on the data and the statistics. Someone may decide that anything within an 80% confidence interval is satisfactory for one decision, and another may decide to not make the same decision even at a 95% confidence interval compliance.
ALL statistics can only help a person make a more informed decision about risks. None of them can guarantee against a particular risk.