Non-parametric Statistics · Rank and Sign Tests · 2 marks · Numerical answer
Five iid observations have Laplace density f(x;θ)=exp(−|x−θ|)/2. Test θ=0 against θ<0 using Yi=1 if Xi>0,0 otherwise. Reject ifΣYi≤2. Find test size(one decimal).
Under the symmetric continuous null, P(Xi>0)=1/2 independently. The sign count is Binomial(5,1/2). Its probability of being≤2 is[1+5+10]/32=16/32=0.5. By binomial symmetry the lower three counts form exactly half the null probability.
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