Phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. She takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. A simple random sample of 104 seniors reveals that 78 of them bring a bag lunch.

a. Do these data give convincing evidence to support Phoebe’s hunch at the α = 0.05 significance level?

b. Interpret the P-value from part (a) in the context of this study.