A hypothesis tests that two population means are equal A sam

A hypothesis tests that two population means are equal. A sample of 9 with a standard deviation of 4 is selected from the first population and a sample of 25 with a standard deviation of 4 from the second population. Testing the claim at the 0.01 level, what is the critical value? Assume unequal standard deviations.

Solution

S1 = 4

n1= 9

s2= 4

n2=25

DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

      = ( 16/9 + 16/25)2/{ [ (16/9)2/9] + [ (16/25)2/24] } = 14.184 = 14

For t- distribution with 14 dof,

0.01 level two sided critical value = 2.977

Answer is D