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Part BCSIR NET December 2024randomise-at-the-boundary-to-hit-the-size

Randomise at the boundary to hit the size

Let be a random sample of size 5 from an absolutely continuous distribution having median M. Let S denote the number of greater than 0. For testing against , let if if S = c, and 0 if S < c be a test of size , where and c ∈ {−1, 0, …, 5} are fixed constants. Then equals

  1. A.11/25
  2. B.49/6
  3. C.103/25
  4. D.53/6

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: Any interval of the form [X̄ − (S/√n)t, ∞) with a 90% quantile t is a 90% confidence interval

More on this topic

The chapter behind this: Standard tests and confidence intervals — free to read

From Hypothesis TestingLikelihood ratio and standard tests

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