Lucy recently asked the servers at her restaurant to only give straws to customers who request them. She thinks that about half of the customers will ask for straws but hopes that the rate will be less than half. She randomly selects 100 customers and finds that 43 of them ask for a straw. To determine if these data provide convincing evidence that the proportion of customers who will ask for a straw is less than 50%, 150 trials of a simulation are conducted. Lucy is testing the hypotheses: H0: p = 50% and Ha: p < 50%, where p = the true proportion of customers who will ask for a straw. Based on the results of the simulation, the estimated P-value is 0.0733. Using a = 0.10, what conclusion should Lucy reach? Because the P-value of 0.0733 < a, Lucy should reject H0. There is convincing evidence that the proportion of customers who will ask for a straw is less than 50%. Because the P-value of 0.0733 < a, Lucy should reject Ha. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%. Because the P-value of 0.0733 < a, Lucy should fail to reject Ha. There is convincing evidence that the proportion of customers who will ask for a straw is less than 50%. Because the P-value of 0.0733 < a, Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

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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Lucy recently asked the servers at her restaurant to only give straws to customers who request them. She thinks that about half of the customers will ask for straws but hopes that the rate will be less than half. She randomly selects 100 customers and finds that 43 of them ask for a straw. To determine if these data provide convincing evidence that the proportion of customers who will ask for a straw is less than 50%, 150 trials of a simulation are conducted. Lucy is testing the hypotheses: H₀: p = 50% and H_a: p < 50%, where p = the true proportion of customers who will ask for a straw. Based on the results of the simulation, the estimated P-value is 0.0733. Using a = 0.10, what conclusion should Lucy reach?

Because the P-value of 0.0733 < a, Lucy should reject H₀. There is convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

Because the P-value of 0.0733 < a, Lucy should reject H_a. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

Because the P-value of 0.0733 < a, Lucy should fail to reject H_a. There is convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

Because the P-value of 0.0733 < a, Lucy should fail to reject H₀. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

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