Some people claim that they can tell the difference between a diet soda and a regular soda

in the first sip. A researcher wanting to test this claim randomly sampled 80 such people. He then filled 80

plain white cups with soda, half diet and half regular through random assignment, and asked each person

to take one sip from their cup and identify the soda as diet or regular. 51 participants correctly identified

the soda.

(a) Do these data provide strong evidence that these people are any better or worse than random guessing

at telling the difference between diet and regular soda?

(b) Interpret the p-value in this context.