Foran = 0.05-levellikelihood-ratiotestof H0: = 0 using thelikelihoodfunctionvalues () and 0 = (0), explainwhythecorresponding95%confidenceintervalfor

Foran α = 0.05-levellikelihood-ratiotestof H0: θ = θ0 using thelikelihoodfunctionvalues

ℓ(ˆθ) and ℓ0 = ℓ(θ0), explainwhythecorresponding95%confidenceintervalfor θ is thesetof

θ0 for which ℓ(ˆθ)~ℓ(θ0) ≤ exp(3.84~2) = 6.8, where3.84isthe0.95quantileforachi-squared distribution with df = 1. Illustratebyfindingthisratiofortheendpointsofthelikelihood-based confidence intervalshownfortheclimatechangeexamplein Section 5.7.2.