Question:

Five dice are found in a bag. We’re not sure if they are fair or not (i.e., whether each side is

equally likely to land up).

1. If we run a test of the null hypothesis that a given die is fair or not then are we running a
   Χ 2 test of independence, or of the distribution of a categorical variable?
2. Each die is rolled 5000 times. We then use the collected data to test each die to see if it is
   fair. We test each die with an alpha level of 0.05. Assuming each die is actually fair, what is
   the probability of getting exactly two false positives?
3. Instead of running a χ 2 test of whether a die is fair, we decide to run a test of the hypothesis

that for a given die rolling an even is just as likely as rolling an odd. We then roll each die

5000 times and test each die with this new hypothesis with an alpha level of 0.05. Assuming

each die is actually fair, what is the probability of getting exactly two false positives?

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