Question

1)    A dice is tossed 120 times with the following results

No. turned up

1

2

3

4

5

6

Frequency

30

25

18

10

22

15

Test the hypothesis that the dice is unbiased (X² = 11.7). Calculate the frequency observed for Chi Square distribution.

Answer 1

Null Hypothesis $H_0:$ Set up the null hypothesis that the dice is unbiased. On the basis of hypothesis that the dice is unbiased, we expect each number to turn up,

$$\dfrac{30+25+18+10+22+15}{6}=20\ times$$

Applying $\chi^2-test$ (Chi square test)

Number of degrees of freedom = n-1 = 6 - 1= 5

For 5 degrees of freedom at 5% level of significance, the table value of $\chi^2$ is 11.7.

The calculated value of $\chi^2$ (12.9)is greater than the table value of $\chi^2$ (11.7)

Hence, we reject the null hypothesis that the dice is unbiased.

We conclude that the dice is biased.