Part CCSIR NET December 2024the-stated-theta-values-are-built-to-give-round-probabilities

The stated theta values are built to give round probabilities

The life (in hours) of an electrical component is exponentially distributed with mean $θ > 0$ . For testing $H_{0} : θ = 5/ (ln (10) - ln (9))$ against $H_{1} : θ = 5/ ln (2)$ , three such components are chosen at random. Suppose that we reject the null hypothesis $H_{0}$ if and only if two or more of these three components survive for less than five hours. Then, which of the following statements are true?

A.The size of the test is 0.01.
B.The power of the test is 0.5.✓
C.The test is unbiased at level $α = 0.05$ .✓
D.If all of these three components survive for less than five hours, then the p-value of the test is 0.001.✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Related counterexample: A UMP test exists for every testing problem

The stated theta values are built to give round probabilities

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