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
(round to the nearest thousandth as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Calculate degrees of freedom

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

Step2: Find critical values for two - tailed test

For a two - tailed \(t\) - test with \(\alpha=0.02\), the area in each tail is \(\frac{\alpha}{2}=\frac{0.02}{2}=0.01\).
Looking up in the \(t\) - distribution table with \(df = 16\) and tail area \(0.01\), the critical values are \(t_{16,0.01}\) and \(-t_{16,0.01}\).
From the \(t\) - distribution table, \(t_{16,0.01}=2.583\).

Answer:

\(- 2.583,2.583\)