Record the results of rolling your die 500 times into the table on the row labeled "Observed Results":
 

	1	2	3	4	5	6
Observed Results (O)	.	.	.	.	.	.
Expected Results (E)	.	.	.	.	.	.
Difference (O-E)	.	.	.	.	.	.

2. If your dice was fair, then with 500 rolls of the dice you would expect to see each face to show approximately  one sixth of the time.  Divde 500 by 6.  What is this value? ___________   Enter this value into each cell on the row labeled “Expected Results”.

3. Calculate the difference between the Observed Results and Expected Results.  Enter these values into the last row.  Suppose your dice was fair, you would expect to see little difference between the observed and expected values.  Do you think your dice was fair?     Y     N

4. Is 500 rolls of the dice a sufficient number of rolls to make a good judgement about the fairness of the dice?  Y   N

5. The test to show if the dice is fair is called the “Goodness of Fit” test.  It is measured by a unit called the chi-square statistic.  Refer to p. 630 in the IPS text,  and find the formula for calculating the chi-square statistic.
 

6. Calculate the value of the chi-square statistic for your data.
 
 

7. Which of the roll(s) of the die contributed the most to the total value of the chi-square statistic?
 

8. Your table of observed values was sized 1 x 6, (in general: 1 x n).  Find the degrees of freedom for your data.
df = ________.
 

9. Set up a hypothesis test for your claim that your dice is fair.  Write it as a sentence, not a formula.

Ho:

Ha:

10. Check the assumptions that must be satisfied to use the chi-square hypothesis test.  Write them here.
 

11.  Consult a chi-square  table (p. T-20 in the back of IPS).  Look up the P-value for your data.
P-value = _____________

12. Is your die fair?  Write a sentence, stating your conclusion which accepts or rejects the null hypothesis in context of the problem.