Question

find the critical value(s) and rejection region(s) for the indicated t - test, level of significance α, and sample size n.
left - tailed test, α = 0.01, n = 26
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 \(n = 26\), so \(df=26-1 = 25\).

Step2: Find critical value from t - distribution table

For a left - tailed test with \(\alpha=0.01\) and \(df = 25\), looking up the t - distribution table, the critical value \(t_{0}\) is such that \(P(T<t_{0})=\alpha\). The critical value \(t_{0}=- 2.485\) (using t - distribution table where for \(df = 25\) and one - tailed \(\alpha = 0.01\)).

Step3: Determine rejection region

The rejection region for a left - tailed t - test is \(t

Answer:

The critical value is \(-2.485\) and the rejection region is \(t < - 2.485\)