Let X1, , Xn be a random sample from a n(, 2) population (a) If is unknown and 2 is known, show that Z n( 0) is a Wald statistic for testing H0 0 (b) If 2 is unknown and is known, find a Wald statistic for testing H0 0

Question: Let X1,..., Xn be a random sample from a n(, 2) population. (a) If is unknown and 2 is known, show that Z =

Let X1,..., Xn be a random sample from a n(μ, σ2) population.
(a) If μ is unknown and σ2 is known, show that Z = √n( - μ0)/σ is a Wald statistic for testing H0: μ = μ0.
(b) If σ2 is unknown and μ is known, find a Wald statistic for testing H0: σ = σ0.

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