Question

A die is rolled 1200 times with the following results :
No. that comes up : 1 2 3 4 5 6
Frequency : 195 289 202 242 163 109
Test, if the die. is unbiased at 5% level of significance. (Given that x 0.05 (5) = 11.07)

Answer 1

Step 1 :

Null hypothesis : (H0) The die is unbiased
Alternative Hypothesis (HA): The die is not unbiased.

Step 2 : Test Statistics

On the hypothesis that the die is unbiased we should expect the frequency of each number to be 132/6 =22

∴Xcal2=∑(O−E)2E=198/22=8.91
Step 3:

L.O.S (∝) = 0.05

Degree of freedom = n-1 = 6-1 =5

Step 4 :

∴ Critical value (X∝)2=11.0705
Step 5 : Decision

Since Xcal2< (X∝)2

HO is accepted.

∴ The die is unbiased.