Answer
Step 1:
$H_0$ : The proportions of adults’ opinion on genetically modified are as follows: 35% felt it was safe , 52%felt it was not safe, 13% had no opinion
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.01, and the degrees of freedom are 3-1=2 , the critical value is 9.210.
Step 3:
Expected Value:
0.35 * 120 = 42
0.52 * 120 = 62.4
0.13 * 120 = 15.6
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(40-42)^{2}}{142}$ + $\frac{(60-62.4)^{2}}{62.4}$ + $\frac{(20-15.6)^{2}}{15.6}$
=0.095+0.092+1.241
=1.429
Step 4:
Since 1.429 < 9.210, the decision is not to reject the null hypothesis.
Step 5:
There is no enough evidence to reject the claim that the distribution is 35% felt it was safe, 52% felt it was not safe, 13% had no opinion.
