In: Statistics and Probability
What is the relationship between hypothesis testing and statistical prediction intervals? How does the p-value serve as importance in this relationship?
A confidence interval is an range of values which likely to contain a unknown population parameters.
A hypothesis is nothing but the assumption which we have to test based on the sample data.
Confidence intervals and hypothesis tests are similar in that they are both inferential methods that rely on an approximated sampling distribution. Confidence intervals use data from a sample to estimate a population parameter. Hypothesis tests use data from a sample to test a specified hypothesis.
P value is the minimum level of significance.
You can use either P values or confidence intervals to determine whether your results are statistically significant. If a hypothesis test produces both, these results will agree.