Question

using the t - distribution table, find the critical value(s) for the t test for a two - tailed test with ( n = 28 ) and ( alpha=0.01 ). enter the answers separated by a comma if needed. critical value(s) =

Explanation:

Step1: Calculate degrees of freedom

Degrees of freedom \(df=n - 1\). Given \(n = 28\), so \(df=28-1=27\).

Step2: Locate critical value in t - distribution table

For a two - tailed test with \(\alpha = 0.01\) and \(df = 27\), looking up the t - distribution table. The critical values are \(\pm t_{\alpha/2,df}\). Here \(\alpha/2=0.01/2 = 0.005\). From the t - distribution table, \(t_{0.005,27}=2.771\). So the critical values are \(\pm 2.771\).

Answer:

\(\pm 2.771\)