Question

Use the​ t-distribution table to find the critical​ value(s) for the indicated alternative​ hypotheses, level of significance

alphaα​,and sample sizes 1n1 and 2n2. Assume that the samples are​ independent, normal, and random. Answer parts​ (a) and​ (b).

Ha​:u1 ≠ u2 alpha=0.20 n1=10​, n2=2

a-Find the critical​ value(s) assuming that the population variances are equal.

b-Find the critical​ value(s) assuming that the population variances are not equal.

Answer 1

a-Find the critical​ value(s) assuming that the population variances are equal.

We are given

n1 = 10

n2 = 2

df = n1 + n2 – 2 = 10 + 2 – 2 = 10

α = 0.20

Test is two tailed.

So, critical t value by using t-table or excel is given as below:

Critical values = - 1.3722 and 1.3722

b-Find the critical​ value(s) assuming that the population variances are not equal.

We are given

n1 = 10

n2 = 2

df = Min(n1 – 1, n2 – 1) = Min(10 – 1, 2 – 1) = Min(9, 1) = 1

α = 0.20

Test is two tailed.

So, critical t value by using t-table or excel is given as below:

Critical values = - 3.0777 and 3.0777