Question

Let μ denote the true average radioactivity level(picocuries per liter). The value 5 pCi/L is considered thedividing line between safe and unsafe water. Would yourecommend testing H₀: μ = 5 versusH_a: μ > 5 or H₀: μ =5 versus H_a: μ < 5? Explain yourreasoning.

 

Answer 1

Ans:

Option (a) H0 : µ = 5 versus Ha : µ > 5; or

Option (b) H0 : µ = 5 versus Ha : µ < 5

If we choose (a) and make a type-I error, then we are declaring unsafe water safe.

If we choose (b) and make a type-I error, then we are declaring safe water unsafe. Since we can control type-I error, and not type-II, we need to opt for the less dangerous of the two; i.e., (b).

A type I error would involve deciding that the water is safe (rejecting 0H) when it isn’t (0His in fact true). (Note that this would be a very serious error, so we may want to use a very small significance level ?to make sure that we are highly unlikely to commit this error)