Question

In 120 throws of a single dice, following distribution of faces was observed. FACES 1 2 3 4 5 6 TOTAL F0 30 25 18 10 22 15 120 From the given data, verify that the hypothesis “dice is biased” is acceptable or not.

Answer 1

the die is baised.as it has even number of faces(6).

Answer 2

PROOF:

H0: The die is unbiased

Ha:The die is biased

If the die were unbiased, each number has a probability of 1/6 in a single throw.

In 120 throws, one would expect (120)(1/6) = 20 throws for each numbers 1 - 6.  

     O     E  

1    30   20

2   25   20

3   18    20

4   10    20

5   22   20

6   15    20

O - observed

E - expected

Chi-squared = Σ(O-E)^2 /E

Chi-squared = (30-20)^2/20 +(25-20)^2/20 +(18 -20)^2/20+(10-20)^2/20+(22-20)^2/20+...

= 12.9

The critical chi-squared with 5 degrees of freedom with significance level 0.05 is 11.07

Calculated chi-squared exceeds critical value,

so reject H0.

We conclude that the die is biased.