Phoebe has a theory that older students at her 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. letting p1= proportion of sophomores who bring a bag lunch, and p2= proportion of seniors who bring a bag lunch, phoebe tests the hypotheses