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 \one tail, $\alpha$\ column with a negative sign. if the hypothesis test is right - tailed, use the \one tail, $\alpha$\ column with a positive sign. if the hypothesis test is two - tailed, use the column with a sign.

Explanation:

For a two - tailed hypothesis test in the t - distribution:

• The significance level for each tail is \(\frac{\alpha}{2}\). So, we use the "Two tails, \(\alpha\)" column.
• The t - distribution is symmetric about \(t = 0\). For a two - tailed test, we have both a negative and a positive critical value.

Answer:

If the hypothesis test is two - tailed, use the "Two tails, \(\alpha\)" column with a "both negative and positive" sign.