Elementary Statistics and Computer Application

Test for equality of two Means

• Given two sets of sample data of large size n1 and n2 from variables. We may examine whether the two samples come from the populations having the same mean. We may proceed as follows

1. Null Hypothesis (Ho)

• Ho: There is no significance difference between the sample mean ie., µ=µo
or

• The given sample would have come from a population having a specified mean
ie., µ1=µ2


2. Alternative Hypothesis(H1)

• H1 : There is significance difference between the sample mean ie., µ=µo
• ie., µ1≠µ2 or µ1<µ2 or µ1>µ2

3.Test statistic
When the population variances are known and unequal (i.e)



When,




where

• The equality of variances can be tested by using F test.
• When population variance is unknown, they may be replaced by their estimates s1^₂ and s2²
when s12≠ s22
when s12 = s22



where

4. Level of Significance

• The level may be fixed at either 5% or 1%

5.Expected vale

• The expected value is given by





6. Inference

• If the observed value of the test statistic Z exceeds the table value Ze we may reject the Null Hypothesis Ho otherwise accept it