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Part CCSIR NET June 2024a-smaller-statistic-has-a-larger-p-value

A smaller statistic has a larger p value

Observations on the shear strength of concrete from 5 randomly selected structures are given below — structure 1, 2, 3, 4, 5 with shear strength 1718.4, 1787.4, 2562.3, 2356.9, 2153.2 respectively. The null hypothesis H0H_{0} that the median shear strength is 2000 units is tested against the alternative hypothesis H1H_{1} that the median shear strength is greater than 2000 units at 5% level of significance. Which of the following statements are true?

  1. A.p-value of the sign test is 0.04
  2. B.H0H_{0} is NOT rejected at 5% level of significance by the sign test✓ Correct
  3. C.The observed value of Wilcoxon signed rank test statistic W⁺ is equal to 10✓ Correct
  4. D.If P(H0)(WP_(H_{0})(W⁺ ≥ 14) = 0.06, then H0H_{0} is rejected at 5% level of significance by the Wilcoxon signed rank test

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.

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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 Testing › Likelihood ratio and standard tests

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