Suppose we wish to determine if an ordinary-looking six-sided die is fair, or balanced, meaning that every face has probability 1/6 of landing on top when the die is tossed. We could toss the die dozens, maybe hundreds, of times and compare the actual number of times each face landed on top to the expected number, which would be 1/6 of the total number of tosses. We wouldn't expect each number to be exactly 1/6 of the total, but it should be close. To be specific, suppose the die is tossedn = 60 times with the results summarized in Table 1.1 "Die Contigency Table". Question: Are the die fair or "loaded"? Assume an alpha of 0.1.

Table 1.1 Die Contingency Table

Die Value	Assumed Distribution	Observed Freq.	Expected Freq.
1	1/6	9
2	1/6	15
3	1/6	9
4	1/6	8
5	1/6	6
6	1/6	13

State the research/null hypotheses.

What test would you run?

Run the test! (make sure to fill in the expected frequency in table 1.1 to get started).

What is your calculated value, degrees of freedom, and cutoff value?

Based on your result, do you accept or reject the null hypothesis?