Use the t-distribution table to find the critical value(s) for the indicated alt

Question

Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance alpha, and sample sizes n_1 and n_2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b). H_a: mu_1 > mu_2, alpha = 0.10, n_1 = 6, n_2 = 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.)

Explanation / Answer

a) The population variances are equal then degrees of freedom is n1 + n2 - 2 = 6 + 8 - 2 = 12

Level of significance = 0.10

Our test is one tail test because the alternative hypothesis has greater than sign.

So critical value is 1.356 ( Using t table)

b) The population variances are not equal then degrees of freedom is min( n1 - 1 , n2 - 1 ) = min(6 - 1 , 8 - 1) = 5

Level of significance = 0.10

Our test is one tail test because the alternative hypothesis has greater than sign.

So critical value is 1.476 ( Using t table)

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