What is a Chi Square?

Explanation and History of the Chi Square

A Chi Square analysis is used to find out during an experiment whether or not the results expected are the same or if they are different purely by chance. In other words, the Chi Square takes the expected results and compares them with the actual results to determine if they are different due to a flaw in the experiment, or both the expected and actual results are different purely by chance. 

A null hypothesis is a prediction that something is missing from the experiment, that a specific treatment will not affect the outcome, or that there isn't a difference at all between the treatment (procedure) and the control (expected results) group. The null hypothesis for any Chi Square analysis is ALWAYS the same: Any difference between the observed and expected data is due to CHANCE!

Accepting or rejecting the null hypothesis all depends on what your results are. It also depends on the degrees of freedom which is the number of possible categories (in this case, number of m&m colors -1)  The reason why is because  when there are more categories, the more likely the experiment is to have a flaw. The Chi Square equation,  when solved, will be either greater than or lower then the specific degree of freedom and if it is lower, you'll accept the null hypothesis because the difference is small. If the Chi Square value is higher than the specific degree of freedom given, then the difference is too great to be chance; you reject the null hypothesis.

Accepting or Rejecting the Null Hypothesis