For observations 0.13,0.12,0.78,0.51,test a Uniform(0,1) CDF against a general alternative with the two-sided Kolmogorov–Smirnov statistic D. Under H₀,P(D>0.669)=0.01. Let ψ=1 if H₀ is accepted at level .01,and 0 otherwise. Find observed D+ψ to two decimals.
Sort the sample:.12,.13,.51,.78. Compute D⁺=max(i/4−x_(i))=max(.13,.37,.24,.22)=.37 and D⁻=max(x_(i)−(i−1)/4)=max(.12,−.12,.01,.03)=.12. Thus D=.37<.669,and the null is not rejected (ψ=1 in the stated convention). D+ψ=**1.37**.
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