A product analyst knows whether the proportion of people in her state who prefer hot dogs to hamburgers varies from state to state. She samples 50 random people from Idaho and 50 random people from Oklahoma for their cookout preferences and finds that 18% of the people in Idaho prefer hot dogs, while 22% of the people in Oklahoma prefer hot dogs. Are the conditions for performing a z-test for the difference between population proportions satisfied. Select all that apply

a. The samples are random.
b. The samples are independent.
c. The values of n1p1, n1q1, n2p2 and n2q2, are all at least 5.
d. None the conditions are satisfied.