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 random sample of sophomores and a random sample of seniors and determines the proportion of each sample that brings a bag lunch. Let p1 = proportion of all sophomores who bring a bag lunch, and p2 = proportion of all seniors who bring a bag lunch. Which answers make a pair of hypotheses that are appropriate to test Phoebe's theory?

a) Ho: = 0.5; Ha: > 0.5

b) Ho: p1 = p2; Ha: p1 < p2

c) Ho: p1 = p2; Ha: p1 < p2

d) Ho: p =0.5; Ha: p 0.5

e) Ho: p = 0.5; Ha: p 0.5

f) Ho: p1 = p2; Ha: p1 > p2

g) Ho: p,1 = p2; Ha: p1, > p2

h) Ho: p1 = p2; Ha : p1 p2