The owner of a popular coffee shop wants to determine if there is a difference between the proportion of customers who use their own cups when they purchase a coffee beverage and the proportion of customers who use their own cups when they purchase an espresso beverage.

Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all coffee purchases and 50 receipts from all espresso purchases. For coffee purchases, 24 receipts showed that the customer used their own cup. For espresso purchases, 18 receipts showed the customer used their own cup.

The owner wants to construct a 95% confidence interval for the difference in the proportions of customers who use their own cups. Are the conditions for inference met?

A. Yes, the conditions for inference are met.
B. No, the 10% condition is not met.
C. No, the randomness condition is not met.
D. No, the Large Counts Condition is not met.

10% Condition: This condition requires that the sample size should be less than 10% of the population. Assuming the coffee and espresso purchases are large enough, this condition is likely met.

Large Counts Condition: We need to check if each sample has at least 10 successes and 10 failures:

For coffee: 24 used their own cups (successes) and 50 - 24 = 26 did not (failures). Both are greater than 10.

For espresso: 18 used their own cups (successes) and 50 - 18 = 32 did not (failures). Both are greater than 10.

Since all conditions are met (randomness, 10% condition, and large counts condition), we can proceed with constructing the confidence interval.