You are playing a game of dice in the back alley and you sus

You are playing a game of dice in the back alley and you suspect that your opponent is cheating with a loaded die. You take the die and roll it 100 times and count the number of time that each face comes up. The die rolls are: (16, 17, 12, 22, 21, 12) for sides one through six respectively. Conduct a Goodness of Fit test of the hypothesis that the die is fair. What is the Chi Square Statistic of the test?

Question 1 options:

5.23

5.95

5.06

5.48

5.19

5.58

Solution

For a fair die, the probability of each face is 1/6.

Thus, the expected value of each face shoud be

Expected = (16.667,16.667,16.667,16.667,16.667,16.667)

Thus, using

chi^2 = Sum[(O - E)^2 / E]

Then

chi^2 = 5.48 [ANSWER, OPTION 4]