For the following alternative hypotheses, give the appropriate null hypothesis.

a. Pygmy mammoths and continental mammoths differ in their mean femur lengths.

b. Patients who take phentermine and topiramate lose weight at a different rate than control patients without these drugs.

c. Patients who take phentermine and topiramate have different proportions of their babies born with cleft palates than do patients not taking these drugs.

d. Shoppers on average buy different amounts of candy when Christmas music is playing in the shop compared to when the usual type of music is playing.

e. Male white-collared manakins (a tropical bird) dance more often when females are present than when they are absent.