After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. Tocheck, you roll it 48

times, recording the number of times each face appears. Do these results cast doubt on the die's fairness?

Face Count
1 9
2 11
3 6
4 6
5 9
6 7

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 testgoodness-of-fit, homogeneity, or independence?

c) State your hypotheses. Choose the correct answer below.

d) Check the conditions. Is the counted data conditionmet?

e) How many degrees of freedom are there?

f) Find chiχsquared2 and the P-value.