I want to know the answer and detail step by step **Understanding Hypotheses Testing for Radioactivity Levels**Let $ \mu $ denote the true average radioactivity level measured in picocuries per liter (pCi/L). The threshold of 5 pCi/L is considered as the dividing line between safe and unsafe water. As a regulator, the decision on which hypothesis to test is critical for ensuring public safety.You have two potential hypotheses to consider:1. **Hypothesis Set A:** - Null Hypothesis ($ H_0 $): $ \mu = 5 $ - Alternative Hypothesis ($ H_a $): $ \mu > 5 $2. **Hypothesis Set B:** - Null Hypothesis ($ H_0 $): $ \mu = 5 $ - Alternative Hypothesis ($ H_a $): $ \mu < 5 $**Task:**- Choose the appropriate set of hypotheses to test.- Justify your choice with reasoning.The correct hypothesis set will help determine whether the average radioactivity level is safe or if regulatory actions need to be taken to protect the public.

Introduction: In this question we have to select correct pair of hypotheses for the given scenario. Given: μ = True average radioactivity level and, μ = 5 is dividing line between safe and unsafe water. Below 5 it is safe and above 5 it is unsafe.Explanation: We can choose the correct pair of hypotheses by checking the consequences of type - I errors for both the pairs of hypotheses. For, H0: μ = 5 Vs Ha: μ > 5. Type - I error: It is an error where the null hypothesis, H0 is rejected when it is true. We know type I error can be controlled, so here if we make a type - I error, then we are declaring unsafe water to be safe. _______(1) For, H0: μ = 5 Vs Ha: μ < 5. Type - I error: It is an error where the null hypothesis, H0 is rejected when it is true. We know type I error can be controlled, so safer option which is to test H0: μ = 5 vs Ha: μ < 5. If we choose second option and make a type-I error, then we are declaring safe water unsafe. _______(2) From (1) and (2), It is clear that the second option is less dangerous. So the correct pair of hypotheses should be, H0: μ = 5 vs Ha: μ < 5.