A local researcher into health nutrition has collected data on the average calories an adult in their 40's eats for breakfast. His concern is that the average adult in their 40's is consuming more than 600 calories for breakfast. From this data he obtains the following statistics:

x = 627 n = 35 s = 159

(a) Test his theory at 80% confidence. what assumptions did you have to make?

(b) Test his theory at 95% confidence. what assumptions did you have to make?

(c) Up to what confidence could he use this data to support his research?