Q. Answer Frequency

A 8

B 8

C 3

D 7

At the 10% significance level, is there evidence that the distribution of the correct answers was not uniform (that is, the answers each had the same likelihood)?

Q. A new casino game involves rolling 3 dice. The winnings are directly proportional to the total number of sixes rolled. Suppose a gambler plays the game 100 times, with the following observed counts:

Number of Sixes Number of Rolls

0 48

1 35

2 15

3 3

Q. The casino becomes suspicious of the gambler and wishes to determine whether the dice are fair. At the 5% significance level, is there evidence that the dice are not fair? Note: the classical probability of each outcome is given below for your convenience.

Number of Sixes Number of Rolls

0 0.58

1 0.34

2 0.07

3 0.01