Statistical hypothesis

Critical value hypothesis test

The critical value test involves constructing a rejection region based on a significance level . The critical region will depend on whether is two sided. In general

• For one sided, we use a rejection region or , where .
• For two sided, we use a rejection region

Steps

1. Identify the appropriate distribution of the underlying random variable
2. Formulate a null hypothesis of our assumed parameterisation of the distribution; and an alternate hypothesis of its negation, which may be either one-sided or two-sided.
3. Construct the distribution of the test statistic being used under the assumptions of .
4. Calculate the critical value and rejection region for significance level .
5. State the conclusion: Reject if the observed statistic is in the rejection region; otherwise we maintain .
6. Interpret these results in the context of the problem.

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