Question

The owner of a popular coffee shop believes that customers who drink espresso are less likely to use their own cup compared with 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 pcoffee= the true proportion of customers who drink coffee and use their own cup. which of the following is a correct statement about the conditions for this test? the random condition is not met. the 10% condition is not met. the large counts condition is not met. all conditions for inference are met.

Answer 1

The conditions for conducting a hypothesis test on the proportions of espresso and coffee drinkers using their own cups are met. The samples are random, the 10% condition is likely met, and there are more than 10 successes and failures for each group.

Step-by-step explanation:

The question pertains to checking whether all conditions for conducting a hypothesis test on two proportions are satisfied. The three conditions generally required are the random condition, the 10% condition, and the large counts condition.

The random condition requires that the data comes from a random sample or randomized experiment. In this scenario, it is stated that the owner randomly selected the receipts, thus this condition is met.

The 10% condition ensures that the sample size is less than 10% of the population. This condition is likely met unless the coffee shop serves fewer than 500 customers for each type of drink (espresso and coffee) since 50 receipts were selected for each.

The large counts condition requires that both the number of successes and failures are at least 10 for each group. Here, for espresso (15 successes, 35 failures) and for coffee (24 successes, 26 failures), both conditions are met.

Therefore, the correct statement about the conditions for this test is that all conditions for inference are met.