Question

use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses sample sizes ( n_1 ) and ( n_2 ). assume that the samples are random and independent, and the pop distributed. complete parts (a) and (b).
( h_a: mu_1 > mu_2, alpha = 0.05, n_1 = 14, n_2 = 13 )
click the icon to view the t-distribution table.
(a) find the critical value(s) assuming that the population variances are equal.
(type an integer or decimal rounded to three decimal places as needed. use a comma to

Explanation:

Step1: Calculate degrees of freedom

For equal variances, \( df = n_1 + n_2 - 2 = 14 + 13 - 2 = 25 \).

Step2: Determine critical value

The alternative hypothesis is \( H_a: \mu_1 > \mu_2 \), so it's a right - tailed test with \( \alpha = 0.05 \) and \( df = 25 \). Using the t - distribution table, the critical value \( t_{\alpha, df} \) for \( \alpha = 0.05 \) and \( df = 25 \) is 1.708.

Answer:

1.708