Type II Error
A Type II Error is also known as a False Negative or Beta Error. This happens when you accept the Null Hypothesis when you should in fact reject it. The Null Hypothesis is simply a statement that is the opposite of your hypothesis. For example, you think that dog owners are friendlier than cat owners. Your null hypothesis would be: "Dog owners are as friendly as cat owners."
You will make a Type II Error if dog owners are actually friendlier than cat owners, and yet you conclude that both kinds of pet owners have the same level of friendliness. In this case, you should reject the null hypothesis since there is a real difference in friendliness between the two groups. If you accept the null hypothesis and say that both types of pet owners are equally friendly, then you are making a Type II Error.
See also: Type I Error