After getting trounced by your little brother in a children’s game, you suspect that the die he gave you is unfair. To check, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die’s fairness?

Face Count

1 .........11

2 ......... 7

3 ......... 9

4 .........15

5 .........12

6 ......... 6

a) If the die is fair, how many times would you expect each face to show?

b) To see if these results are unusual, will you test goodness-of-fit, homogeneity, or independence?

c) State your hypotheses.

d) Check the conditions.

e) How many degrees of freedom are there?

f) Find x2 and the P-value.