Question

As a simple example for which one would expect not equal distributions equal counts of results consider 60 rolls of a six-sided die. In theory if a fair die were rolled 60 times, one would expect the following equal frequency distribution displayed in following Table.

Die Side	Results	Weight
1	49	10
2	46	30
3	65	20
4	46	10
5	39	20
6	55	10

Suppose this die was rolled 300 times and the results recorded as displayed above in Table with different weight. Of interest is whether the results of these 300 die rolls conform to expected results of approximately equal counts for each side of the die. If the observed counts differ from the expected counts of equal distribution for each die side, this may provide evidence that the die is not fair.

1. H0:__________________________       HA:__________________________

2. Find the Chi Square c2 test:

3. Decision:

4. Conclusion:

Answer 1

CALCULATION TABLE
	O	E	O-E	(O-E)2/E
	49	50	-1	0.02
	46	50	-4	0.32
	65	50	15	4.5
	46	50	-4	0.32
	39	50	-11	2.42
n=6	55	50	5	0.5
SUM	300	300	0	8.08
MEAN	50
df =n-1
df =5			O=OBSERVED
			E= EXPECTED	E=300/6=50
Ho:  Distribution is uniform or die is fair
H1: Distribution is not uniform or die is not fair
CHI SQUARE	TEST STATISTCS=	8.08
Chi SQUARE	critical at 5%for 5 df=	11.07
Conclusion:	8.08<	11.07
Hence fail to reject H0
so we conclude that Distribution is uniform or die is fair