I am trying to figure out which participants who took a 18-item multiple choice test scored significantly above chance. Each item has 3 choices, so the probability of getting each question correct is 0.33. To know how many items correct a person would have to get in order to be significantly above chance, does it make sense to use a binomial probability calculator like this: https://stattrek.com/online-calculator/binomial.aspx and try different numbers of successes until the probability is < p=0.05 (assuming this is my significance criteria)?
For 18 items where the probability correct is 0.33, the probability of getting 9 correct is 0.061 and the probability of getting 10 correct is p=0.027, so does it make sense to use "10 items correct" as my criteria for "performed significantly above chance?"
