Question

E) Another pair are called missers. They are supposed to roll 3 & 7 more often than fair dice Below is the data from 16 rolls.

{ 10, 3, 5, 7, 3, 7, 8, 10, 6, 7, 7, 11, 3, 8, 2, 11 }

Can we say to a 10% that these dice do not roll 3 & 7 the way that fair dice are supposed to?

Remember there is a chance that the guy from gamblingcollectibles.com charged me $100 for a regular pair of dice.

Answer 1

Number of rolls = 16

Number of times 3 and 7 have occured = 7

p_dice = 7/16 = 0.4375

For a pair of fair dice, all the possible outcomes:

1	2	3	4	5	6
1	(1, 1)	(1, 2)	(1, 3)	(1, 4)	(1, 5)	(1, 6)
2	(2, 1)	(2, 2)	(2, 3)	(2, 4)	(2, 5)	(2, 6)
3	(3, 1)	(3, 2)	(3, 3)	(3, 4)	(3, 5)	(3, 6)
4	(4, 1)	(4, 2)	(4, 3)	(4, 4)	(4, 5)	(4, 6)
5	(5, 1)	(5, 2)	(5, 3)	(5, 4)	(5, 5)	(5, 6)
6	(6, 1)	(6, 2)	(6, 3)	(6, 4)	(6, 5)	(6, 6)

Number of times 3 and 7 occur in a roll of pair of fair dice = 2 + 6 = 8

In a fair dice 8 out of 36 rolls provide a sum of 3 or 7

p = 8/36 = 0.22, q = 0.78, standard deviation = sqrt(p*q/n) = sqrt(0.22*0.78/36) = 0.069

z-value for 90% confidence interval = 1.64

Upper range of the 90% confidence interval:

x_upper = z*standard deviation + p

x_upper = 1.64*0.069 + 0.22 = 0.333

Since, 0.4375 is greater than 0.333, we can say to a 10% that these dice do not roll 3 & 7 the way that fair dice are supposed to.