A large national survey of American dietary habits showed a mean calorie consumption of 2700 kcal and a standard deviation of 450 kcal among teenage boys. You are studying dietary habits of children in your county to see if they differ from the national norm.

(a) In a sample of 36 teenage boys, you find a mean consumption of 2620kcal.

At α = 0.05, is this significant evidence that the mean in your county differs from the national mean? Assume that the standard deviation observed nationally can be used for σ .

(b) Using α = 0.05 and a sample of size 36, what is the probability that you will actually be able to detect a situation where your county has a mean of only 2600kcal? (That is, what is the power if μ = 2600?) LO.1