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Suppose X1, · · · , Xn from a normal distribution N(µ, σ2 ) where µ...

Suppose X1, · · · , Xn from a normal distribution N(µ, σ2 ) where µ is unknown but σ is known. Consider the following hypothesis testing problem:

H0 : µ = µ0 vs. Ha : µ > µ0

Prove that the decision rule is that we reject H0 if

X¯ − µ0 σ/√ n > Z(1 − α),

where α is the significant level, and show that this is equivalent to rejecting H0 if µ0 is less than the 100(1 − α)% lower confidence bound for µ.

Math   Statistics-And-Probability   
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