The owner of a popular coffee shop believes that customers who drink espresso are less likely to use their own cup compared to customers who drink coffee. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all espresso purchases and 50 receipts from all coffee purchases. For espresso purchases, 15 receipts showed that the customer used their own cup. For coffee purchases, 24 receipts showed the customer used their own cup. Let Pₑₛₚᵣₑₛₛₒ= the true proportion of customers who drink espresso and use their own cup and PCₒₑₑ = the true proportion of customers who drink coffee and use their own cup. Which of the following are the correct hypotheses to test the owner's claim?
a. H0: Pₑₛₚᵣₑₛₛₒ - PCₒₑₑ = 0; Hα: Pₑₛₚᵣₑₛₛₒ - PCₒₑₑ > 0
b. Hα: Pₑₛₚᵣₑₛₛₒ - PCₒₑₑ = 0; Hα: Pₑₛₚᵣₑₛₛₒ - PCₒₑₑ < 0
c. H0: Pₑₛₚᵣₑₛₛₒ - PCₒₑₑ = 0; Hα: Pₑₛₚᵣₑₛₛₒ - PCₒₑₑ ≠ 0
d. H0: Pₑₛₚᵣₑₛₛₒ - PCₒₑₑ = 0; Hα: Pₑₛₚᵣₑₛₛₒ - PCₒₑₑ < 0