Question

use the t-distribution table to find the critical value(s) for the indicated alternative hy sample sizes n₁ and n₂. assume that the samples are random and independent, a distributed. complete parts (a) and (b). hₐ: μ₁ < μ₂, α = 0.005, n₁ = 12, n₂ = 10 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 co

Explanation:

Step1: Calculate degrees of freedom

For equal variances, \( df = n_1 + n_2 - 2 = 12 + 10 - 2 = 20 \).

Step2: Determine critical value

The alternative hypothesis is left - tailed (\( H_a:\mu_1<\mu_2 \)) with \( \alpha = 0.005 \) and \( df = 20 \). Using the t - distribution table, the critical value \( t_{\alpha, df}=-2.845 \) (we look for the value in the t - table corresponding to a one - tailed test with \( \alpha = 0.005 \) and \( df = 20 \), and since it's left - tailed, the value is negative).

Answer:

\(-2.845\)