For a statistics project, I gave out a 20 question multiple choice quiz with each question containing five answers. I would like to run some hypothesis tests on the data by using a Chi squared goodness of fit test. However, I can not decide how many degrees of freedom to use.
When I gave the quiz, I didn't stipulate that the questions had to be answered. If I did, there would be 4 degrees of freedom. However, this also adds the additional option to leave a question blank and unanswered, which would give 5 degrees of freedom.
None of the participants omitted any of the questions though, so should I consider the option to omit a question? Also, if I do consider it, what should I use for my expected count of omitted questions when running the test, as I would expect 0, but that would force me to divide by zero?
