Question

Let μ denote the true average radioactivity level (picocuries per liter). The value 5 pCi/L is considered the dividing line between safe and unsafe water. Would you recommend testing

H₀: μ = 5 versus H_a: μ > 5 or H₀: μ = 5 versus H_a: μ < 5?

Explain your reasoning. [Hint: Think about the consequences of a type I and type II error for each possibility.]

---One should test H₀: μ = 5 versus H_a: μ < 5.A type II error in this case involves deciding the water is safe when it isn't. This is a very serious error, so a test which ensures that this error is highly unlikely is desirable. We prefer that the most serious error be a type II error because it can be explicitly controlled.

---One should test H₀: μ = 5 versus H_a: μ > 5. A type II error in this case involves deciding the water is safe when it isn't. This is a very serious error, so a test which ensures that this error is highly unlikely is desirable. We prefer that the most serious error be a type II error because it can be explicitly controlled.

--- One should test H₀: μ = 5 versus H_a: μ < 5. A type I error in this case involves deciding the water is safe when it isn't. This is a very serious error, so a test which ensures that this error is highly unlikely is desirable. We prefer that the most serious error be a type I error because it can be explicitly controlled.

---One should test H₀: μ = 5 versus H_a: μ > 5. A type I error in this case involves deciding the water is safe when it isn't. This is a very serious error, so a test which ensures that this error is highly unlikely is desirable. We prefer that the most serious error be a type I error because it can be explicitly controlled.

Answer 1