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 pcoffeee = the true proportion of customers who drink coffee and use their own cup. The P-value for this significance test is 0.033. Which of the following is the correct conclusion for this test of the hypotheses Ho PEspresso - Pcoffeee =0 and H, PEspresso-PCoffee < 0 at the a = 0.05 level? O The owner should reject the null hypothesis since 15 < 24. There is convincing evidence that the true proportion customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup. O The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup. O The owner should fail to reject the null hypothesis since 15 < 24. There is not convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 p_Espresso= the true proportion of customers who drink espresso and use their own cup and p_Coffeee= the true proportion of customers who drink coffee and use their own cup. The P-value for this significance test is 0.033. Which of the following is the correct conclusion for this test of the hypotheses

The owner should reject the null hypothesis since 15 < 24. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.

The owner should reject the null hypothesis since 0.033 < 0.05. There is convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.

The owner should fail to reject the null hypothesis since 15 < 24. There is not convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.

The owner should fail to reject the null hypothesis since 0.033 < 0.05. There is not convincing evidence that the true proportion of customers who drink espresso and use their own cup is significantly less than the true proportion of customers who drink coffee and use their own cup.