Type I and Type II errors
While data can give us a good idea of the characteristics of a distribution, it is possible for a hypothesis test to result in an error. Errors can occur because we are taking a random sample from a population. While randomization makes it less likely that a sample contains sampling bias, there is no guarantee that a random sample will be representative of the population. There are two possible errors that could occur as a result of a hypothesis test:
- Type I error: Rejecting the null hypothesis when it is actually true
- Type II error: Failure to reject the null hypothesis when it is actually false
Type I errors
A type I error occurs when a hypothesis test results in rejecting the null hypothesis, but the null hypothesis is actually true. For example, say we have a distribution of data with a population mean of 30. We state our null hypothesis as H 0 : _ x = 30. We take a random sample for our test, but the random...