The concept of Null Hypothesis is a key concept of statistics. When you analyze some data (e.g. looking for a possible correlation between two variables) you usually must formulate two opposite hypotheses:

• The Null Hypothesis H(0) is the idea that "there is NO relationship which exists between the two variables". It is this statement which is usually tested by statistical tools
  
• The hypothesis H(1) is the opposite statement, usually stating that there is a high degree of certainty (typically 95% certainty) that "some relationship exists between two variables"

Before you undertake a complex statistical calculation, you should always formulate the Null Hypothesis H(0). Your calculations will then lead you to one of three possible conclusions:

• The Null Hypothesis H(0) can be rejected in favor of H(1) with high degree of certainty (e.g. 95% certainty): this means that a relationship exists between the two variables, and that there is a 95% chance this result did not occur by accident
  
• The Null Hypothesis H(0) must be accepted: this means that there is NO relationship between the two variables
  
• The degree of certainty is not met: this means the calculations are inconclusive, and that more information is required (e.g. a different sample)
  

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Examples:

• Testing the idea that people with high income also tend to have high college degrees will lead you to reject the Null Hypothesis H(0) and accept H(1): there is a correlation between the two factors
  
• Testing the idea that people with high income also tend to be taller will lead you to accept the Null Hypothesis H(0) and reject H(1): there is NO correlation between the two factors
• Testing the idea that people with high income also tend to come from a particular neighborhood might lead to inconclusive results, for example if your sample is too small