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Statistical power, definition and levers

A test of H0:μ=0H_0: \mu = 0 against H1:μ>0H_1: \mu > 0 fails to reject at the 5% level, and a colleague concludes the effect doesn't exist.

Define statistical power, compute it for a concrete example, n=25n = 25 observations, known σ\sigma, true mean μ=0.5σ\mu = 0.5\sigma, one-sided α=0.025\alpha = 0.025, and list the levers that increase it.

Show a hint

Power is a probability computed under the alternative. Write the rejection region in terms of Xˉ\bar{X}, then ask how likely Xˉ\bar{X} is to land there when μ=0.5σ\mu = 0.5\sigma.

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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