##### Question

In: Statistics and Probability

# 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.

## 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.

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