Question

Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance a, and sample sizes n, and ny. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). H:44 * 12. a *0.20, n = 6, n2 = 8 (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.) (b) Find the critical value(s) assuming that the population variances are not equal. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) Enter your answer in each of the answer boxes.

Answer 1

Note that there is no impact of variances on the critical value of two sample t test. Because due to variances only standard error to calculate the test statistic has been affected.

Then the critical value is given as follows:

$t_{1-\frac{\alpha}{2},~d.f.}$

Where degrees of freedom are $(n_1+n_2-2)$ . Hence d.f. = 12 . Thus we get using the t provability table.

$t_{1-\frac{\alpha}{2},~d.f.} = t_{1-\frac{0.20}{2},~12}=t_{0.90,~12}=1.345$

A) The critical value assuming that the population variances are equal,

1.345

B) The critical value assuming that the population variances are not equal.

1.345