Question

explain how to find the critical values for a t - distribution. click the icon to view the t - distribution table. give the first step. choose the correct answer below. a. identify the level of significance $\frac{\alpha}{2}$ and the degrees of freedom, d.f. $=n - 1$. b. identify the level of significance $\alpha$ and the degrees of freedom, d.f. $=n - 1$. c. identify the level of significance $\frac{1 - \alpha}{2}$ and the degrees of freedom, d.f. $=n$. d. identify the level of significance $1 - \alpha$ and the degrees of freedom, d.f. $=n$. find the critical value(s) using the given t - distribution table in the row with the correct degrees of freedom. if the hypothesis test is left - tailed, use the column with a sign.

Explanation:

To find the critical values for a t - distribution:

• The first step is to identify the level of significance \(\alpha\) (which represents the probability of making a Type I error) and the degrees of freedom \(d.f.=n - 1\) (where \(n\) is the sample size).
• For a left - tailed test, in the t - distribution table, we use the column corresponding to the level of significance \(\alpha\) (since the area in the left tail is \(\alpha\)) and the row with the correct degrees of freedom. And the critical value will have a negative sign because it is in the left tail of the distribution.

Answer:

B. Identify the level of significance \(\alpha\) and the degrees of freedom, \(d.f.=n - 1\).
If the hypothesis test is left - tailed, use the \(\alpha\) column with a negative sign.