Confidence Intervals as Tests:
By using the confidence interval to execute a hypothesis test only works with two-tailed test.
A) When the hypothesized value of parameter lies in the confidence interval with 1-alpha level of confidence, then the decision at alpha level of significance is to fail to reject the null hypothesis.
B) When the hypothesized value of parameter lies outside the confidence interval with 1-alpha level of confidence, then decision at alpha level of significance is to reject the null hypothesis.
It sounds simple enough, right? It is..
Though, it has a couple of problems.
A) This works only with two-tail hypothesis tests.
B) This requires that you evaluate the confidence interval first. This includes taking a z-score or t-score and transforming it into an x-score that is much difficult than standardizing an x-score.
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