Question

question 20
what is the critical value for a two - tail t - test with a significance level of.05
and two groups with 8 samples each?
○ t_cv = 2.12
○ t_cv = 2.13
○ t_cv = 2.14
○ t_cv = 2.15

Explanation:

Step1: Calculate degrees of freedom

For a two - group t - test, degrees of freedom \(df=n_1 + n_2-2\). Given \(n_1 = n_2=8\), then \(df=8 + 8-2=14\).

Step2: Locate critical value

Using a t - distribution table for a two - tail test with \(\alpha = 0.05\) and \(df = 14\). Looking up the value in the t - table, the critical value \(t_{cv}\) is \(2.145\approx2.14\) (rounded to two decimal places).

Answer:

\(T_{cv}=2.14\)