Refer to the information in Exercise 18. (a) Give a 95% confidence interval for the mean consumption among teenage boys in your county. (b) The confidence interval in (b) has a wide margin of error....

Refer to the information in Exercise 18.

(a) Give a 95% confidence interval for the mean consumption among teenage boys in your county.

(b) The confidence interval in (b) has a wide margin of error. What sample size would you suggest if you wanted a margin of error of only 75 kcal?

Exercise 18

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 2620 kcal. 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 2600 kcal? (That is, what is the power if μ = 2600?)