example: The statistics teacher, Mr. Hinders, used his calculator to simulate rolling a die 96 times
and storing the results in a list L1 . He did this by entering MATH PRB randInt(1,6,96)
→(L1) . Next he sorted the list (STAT SortA(L1) ). He then counted the number of each face
value. The results were as follows (this is called a one-way table).
Does it appear that the teacher’s calculator is simulating a fair die? (That is, are the observations
consistent with what you would expect to get if the die were fair?)
solution:
I . Let p 1 , p 2 ,...,p 6 be the population proportion for each face of the die to appear on
repeated trials of a roll of a fair die.H (^) A : Not all of the proportions are equal to 1/6.
II . We will use a χ^2 goodness-of-fit test. If the die is fair, we would expect to get
of each face. Because all expected values are greater than 5, the conditions are met for this
test.