You roll a die 48 times with the following results. Number 1 2 3 4 5...

You roll a die 48 times with the following results.

Number	1	2	3	4	5	6
Frequency	3	1	15	13	4	12

Use a significance level of 0.05 to test the claim that the die is fair.

(PLEASE SHOW ALL YOUR WORK)

Solutions

Expert Solution

SOLUTION:

From given data,

Doing an observed/expected value table,

O	E	(O-E)² / E
3	8	(3-8)² / 8 = 3.125
1	8	(1-8)² / 8 = 6.125
15	8	(15-8)² / 8 = 6.125
13	8	(13-8)² / 8 = 3.125
4	8	(4-8)² / 8 = 2
12	8	(12-8)² / 8 = 2

Using ,

= 3.125+6.125+6.125+3.125+2+2

= 22.5

Degree of freedom

= 6

df = -1 = 6-1 = 5

significance level = = 0.05

Critical value

= 11.07049769

Also, the p value is

p = 0.000421

Thus, comparing and [or, p and significance level], we REJECT THE NULL HYPOTHESIS.

There is significant evidence at 0.05 level that the die is not fair.

orchestra answered 1 year ago

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