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Part CCSIR NET June 2025the-shifted-up-sample-is-the-x-one-so-large-mu-drags-the-y-ranks-down

The shifted up sample is the x one so large mu drags the y ranks down

Let and be two independent random samples from the continuous distribution functions and , respectively, where and are all unknown. Further, let be the unique median of and be the unique median of . Let be the rank of in the combined sample, i = 1, 2, …, 9. For testing against , the test statistic is proposed. Then, which of the following statements are true?

  1. A.The maximum possible value of T is 115
  2. B.Right-tailed test based on T is appropriate for testing against
  3. C.Under
  4. D.Under

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, and why this one tests what the inference means.

See pricing

50 are analysed free — try those first.

The trap it tests

What the inference means

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

Drill statements like this

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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