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Is this true?

A sufficient statistic is complete

No — it is false.

The counterexample

$X_{(n)} ($ or $(X_{(1)}, X_{(n)}))$ for Uniform $(- θ, θ)$

Sufficient but not complete: symmetry gives non-zero functions with zero expectation.

The kind of mistake this is

What the inference means

p-values, size, power and error types say specific things. This was not one of them.

Drill statements like this

Others that fail the same way

From Estimation › Sufficiency, completeness, UMVUE, Cramér–Rao

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