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 $H_{0}$ that the median shear strength is 2000 units is tested against the alternative hypothesis $H_{1}$ that the median shear strength is greater than 2000 units at 5% level of significance. Which of the following statements are true?

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

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50 are analysed free — try those first.

A smaller statistic has a larger p value

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