Let mu denote the true average radioactivity level picocurie

Let mu 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 mu_o: mu = 5 versus H_a : mu = 5 or H_a: mu > 5 or H_0: mu = 5 versus H-a: mu

Solution

Option is 2

One should test H₀ : µ = 5 versus H_a : µ < 5, A type II error in this case involving deciding the water safe when it isn’t. this is 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 explicity controlled.