Question

Find the critical value, t0, to test the claim that μ1 < μ2. Two samples are random, independent, and come from populations that are normal. The sample statistics are given below. Assume that σ21(variance 1)= σ22(variance 2). Use α = 0.05.

n1 = 15

n2 = 15

x1 = 22.97

x2 = 25.52

s1 = 2.9

s2 = 2.8

Answer 1

Solution:

Given:

n1 = 15

n2 = 15

x1 = 22.97

x2 = 25.52

s1 = 2.9

s2 = 2.8

α = 0.05.

σ21(variance 1)= σ22(variance 2).

We have to find the critical value, t0, to test the claim that μ1 < μ2.

Since claim is left tailed ( < type ) and population variances are equal, thus we look in t table for

df = n1 + n2 - 2 = 15+15-2=28

and one tail area = 0.05

and find corresponding t critical value.

thus t critical value = -1.701

this is negative , since claim is left tailed.