The Null hypothesis that given distribution is uniform and alternative hypothesis that distribution is not uniform.
we do not have supportive evidence to reject null hypothesis so, null hypothesis is accepted.
Therefore, distribution is uniform.
The null and alternate hypothesis are:
H₀ : Distribution is Uniform
Hₐ : Distribution is not Uniform
Expected values for each category = 150/3 = 50
Test statistic value = chi- square = ∑Eᵢ² = {(Oᵢ - Eᵢ)²{Eᵢ}= {(40-50)²}{50}+{(60-50)²{50}+{(50-50)²}{50}=4
Hence, test statistic value is 4
Degrees of freedom = k-1 = 3-1 = 2
The p-value is given by:
P( E²ₖ₋₁ > 4)=P( E²₂ >4) = 0.135335
Since p-value > alpha (0.05) , so at 5% level of significance, we do not have sufficient evidence to reject the null hypothesis H₀.
There is enough evidence to conclude that the distribution is uniform.
Thus we say that Distribution is uniform.
To learn more about Uniform distribution, refer:
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