With reference to Example 2, Chapter 2, use the \(U\) statistic to test the null hypothesis of equality versus the alternative that the distribution of copper content from the first heat is stochastically larger than the distribution for the second heat. Following the approach in Exercise 14.22, it can be shown that the exact distribution gives \(P\left(U_{i} \geq 19\right)=0.033\). Use this as the level of significance.

Data From Example 2

Data From Exercise 14.22

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EXAMPLE 2 A dot diagram for multiple samples reveals differences The vessels that contain the reactions at some nuclear power plants consist of two hemispherical components welded together. Copper in the welds could cause them to become brittle after years of service. Samples of welding material from one pro- duction run or "heat" used in one plant had the copper contents 0.27, 0.35, 0.37. Samples from the next heat had values 0.23, 0.15, 0.25, 0.24, 0.30, 0.33, 0.26. Draw a dot diagram that highlights possible differences in the two production runs (heats) of welding material. If the copper contents for the two runs are different, they should not be combined to form a single estimate.