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 ( 1-alpha ) and the degrees of freedom, d.f. ( =n ). b. identify the level of significance ( \frac{alpha}{2} ) and the degrees of freedom, d.f. ( =n - 1 ). c. identify the level of significance ( alpha ) and the degrees of freedom, d.f. ( =n - 1 ). d. identify the level of significance ( \frac{1-alpha}{2} ) 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 with a t - distribution:

• The significance level for each tail is \(\frac{\alpha}{2}\). So, we use the "Two tails, \(\alpha\)" column in the t - distribution table.
• The t - distribution is symmetric about \(t = 0\). For the left - hand critical value (negative side), we take the value from the table as it is (with a negative sign). For the right - hand critical value (positive side), we take the value from the table as it is (with a positive sign).

Answer:

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