Does Your Group Come From a Different Population Than the One Specified?
The problem is that if you calculate a sample mean and it is different from the one hypothesized, there are two possible reasons for the difference:

• Your sample comes from a different population and the sample mean represents a different population mean. When this happens, you reject the Null Hypothesis.
  
  
• The group comes from the same population and the mean varies by chance. You just happened to pick a sample group with a mean that misrepresents the population it came from. The group isn't really different. When this happens, you fail to reject the Null Hypothesis.