Please explain the difference between confidence interval and significance level and how they interact or "influence" each other.
Could you please give me a clear explanation with a simple example of these concepts.
Please see the attached files.
Confidence interval is associated with interval estimation and significance level is associated with testing of hypothesis. (Note that confidence interval is a random interval that contains the true parameter with a specified probability). Associated with a confidence interval there is a confidence level or confidence coefficient. It is to be noted that the interval estimation and testing of hypothesis are two parallel developments in Statistics. It is easy to see the following result.
Confidence level of a confidence interval = 1 - significance level of the associated test.
i.e. Confidence level of a confidence interval = 1- α, where α is the significance level of the associated test.
To make the concepts clear first, I will provide the procedure for finding a confidence interval and test construction:
Construction of a confidence interval for a parameter θ Construction of test associated with the parameter θ
Step 1: Fix the confidence level for the interval. Let it be 1-α
Step 2: Select a suitable statistic, say t, containing the parameter θ and identify its ...
The differences between confidence interval and significance levels are examined.