Critical value hypothesis test

The critical value test involves constructing a rejection region based on a significance level $𝛼$ . The critical region will depend on whether $𝐻 1$ is two sided. In general

For one sided, we use a rejection region $[𝑧 𝛼, \infty)$ or $(\infty, - 𝑧 𝛼]$ , where $𝑧 𝛼 = 𝐹 - 1 𝑍 (1 - 𝛼)$ .
For two sided, we use a rejection region $(\infty, - 𝑧 𝛼 2] \cup [𝑧 𝛼 2, \infty)$

Steps

Identify the appropriate distribution of the underlying random variable $𝑋$
Formulate a null hypothesis $𝐻 0$ of our assumed parameterisation of the distribution; and an alternate hypothesis $𝐻 1$ of its negation, which may be either one-sided or two-sided.
Construct the distribution of the test statistic being used $𝑍$ under the assumptions of $𝐻 0$ .
Calculate the critical value and rejection region for significance level $𝛼$ .
State the conclusion: Reject $𝐻 0$ if the observed statistic is in the rejection region; otherwise we maintain $𝐻 0$ .
Interpret these results in the context of the problem.

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