Question

use the t - distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance α, and sample sizes ( n_1 ) and ( n_2 ). assume that the samples are random and independent, and the populations are normally distributed. complete parts (a) and (b).
( h_a:mu_1>mu_2,alpha = 0.10,n_1 = 10,n_2 = 2 )
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 separate answers as needed.)

Explanation:

Step1: Calculate degrees of freedom

When population variances are equal, the degrees of freedom is \(df=n_1 + n_2-2\). Given \(n_1 = 10\) and \(n_2=2\), then \(df=10 + 2-2=10\).

Step2: Determine the critical value

The alternative hypothesis is \(H_a:\mu_1>\mu_2\), which is a right - tailed test. For a right - tailed test with \(\alpha = 0.10\) and \(df = 10\), looking up the t - distribution table.

Answer:

\(1.372\)