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Consider a single observation X from a Cauchy distribution centered at θ. That is, the p.d.f. of X is
Suppose that we wish to test the hypotheses
H0: θ ≤ θ0,
H1: θ >θ0.
Let δc be the test that rejects H0 if X ≥ c.
a. Show that π(θ|δc) is an increasing function of θ.
b. Find c to make δc have size 0.05.
c. If X = x is observed, find a formula for the p-value. |
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