Elementary Statistics and Computer Application

Sampling from variable

In sampling for variables, the test are as follows

1. Test for single Mean
2. Test for single Standard Deviation
3. Test for equality of two Means
4. Test for equality of two Standard Deviation

Test for single Mean

• In a sample of large size n, we examine whether the sample would have come from a population having a specified mean

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., µ=µo


2. Alternative Hypothesis(H1)

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

3. Test statistic



When population variance is not known, it may be replaced by its estimate






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.