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Is this true?

The Cramér–Rao bound is attained by the UMVUE

No — it is false.

The counterexample

This one comes with the Notes pack.

See pricing

85 counterexamples are free — including most of the ones Part C leans on hardest.

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
statistics

Others that fail the same way

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

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