Are Two Group Means Really Different?
The problem is that if you calculate two sample means and they are different, there are two possible reasons for the difference:

• Each group comes from a different population and the sample means represent two different population means. When this happens, you reject the Null Hypothesis.
  
  
• The groups come from the same population and the means vary by chance. You just happened to pick two groups with means that are far apart. The groups aren't really from different populations. When this happens, you fail to reject the Null Hypothesis.