Question

find the critical value(s) and rejection region(s) for the indicated t - test, level of significance α, and sample size n.
right - tailed test, α = 0.005, n = 6
click the icon to view the t - distribution table.
the critical value(s) is/are 4.0322
(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 \(n = 6\), so \(df=6-1 = 5\).

Step2: Locate critical value in t - distribution table

For a right - tailed test with \(\alpha=0.005\) and \(df = 5\), looking up in the t - distribution table.
The critical value \(t_{\alpha,df}=t_{0.005,5}=4.032\) (rounded to the nearest thousandth).

Step3: Determine rejection region

For a right - tailed t - test, the rejection region is \(t>t_{\alpha,df}\). So the rejection region is \(t > 4.032\).

Answer:

The critical value is \(4.032\) and the rejection region is \(t>4.032\).