Question

find the critical value(s) and rejection region(s) for the indicated t - test, level of significance α, and sample size n.
two - tailed test, α = 0.02, n = 17
click the icon to view the t - distribution table.
the critical value(s) is/are - 2.583, 2.583. (round to the nearest thousandth as needed. use a comma to separate answers as needed.)
determine the rejection region(s). select the correct choice below and fill in the answer box(es) within your choice. (round to the nearest thousandth as needed.)
○ a. t > □
○ b. t < □ and t > □
○ c. □ < t < □
○ d. t < □

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \( df=n - 1\). Given \(n = 17\), so \(df=17-1 = 16\).

Step2: Find the critical values for a two - tailed test

For a two - tailed \(t\) - test with \(\alpha=0.02\) and \(df = 16\), we divide \(\alpha\) by 2 (\(\frac{\alpha}{2}=0.01\)). Looking up in the \(t\) - distribution table, the critical values are \(t_{1 - \frac{\alpha}{2},df}\) and \(t_{\frac{\alpha}{2},df}\). The critical values are \(t=- 2.583\) and \(t = 2.583\) (from the \(t\) - distribution table for \(df = 16\) and \(\alpha/2=0.01\)).

Step3: Determine the rejection regions

For a two - tailed \(t\) - test, the rejection regions are \(tt_{1-\frac{\alpha}{2},df}\). Substituting the values, the rejection regions are \(t < - 2.583\) and \(t>2.583\).

Answer:

B. \(t < - 2.583\) and \(t>2.583\)