Question

A hypothesis will test that two population means are equal. A sample of 10 with a standard deviation of 3 is selected from the first population and a sample of 15 with a standard deviation of 8 from the second population. The standard deviations are not equal. Testing the claim at the 0.01 level, what is the critical value? Assume unequal standard deviations.

Please explain and show your work.

Thank you!

Answer 1

Solution:

Given:

s₁ = 3

n₁ = 10

s₂ = 8

n₂ = 15

Since variances are unequal we need to find df = degrees of freedom by following formula:

Level of significance =Two tail area = 0.01

( This is two tailed test , since claim is non-directional)

Look in t table for df = 19 and two tail area = 0.01 and find t critical value

t critical value = 2.861