Fifty percent of the coffee brewed at a particular coffeeshop will stay fresh for 30 minutes. The owners of the coffeeshop are considering trying a different brand of coffee bean because they have heard that it will keep brewed coffee stay fresh for more than 30 minutes. To check this out, they brew 20 pots of coffee with the new bean and decide that they will conclude that the new bean is better if 15 or more of these pots of coffee still taste fresh after 30 minutes a) What is the probability that the coffeeshop owners will conclude that the new bean is better even if, in fact, it is no better than the beans they have always used in the past? b) In a second test, the coffeeshop owners brew 25 pots of coffee with the new bean and test the same hypotheses as in part 'a' using an alpha of 01. Suppose that the new bean would actually allow 80% of these pots of coffee to stay fresh longer than 30 minutes: what is the power of the coffeeshop owners' experiment?

Fifty percent of the coffee brewed at a particular coffeeshop will stay fresh for 30 minutes. The owners of the coffeeshop are considering trying a different brand of coffee bean because they have heard that it will keep brewed coffee stay fresh for more than 30 minutes. To check this out, they brew 20 pots of coffee with the new bean and decide that they will conclude that the new bean is better if 15 or more of these pots of coffee still taste fresh after 30 minutes a) What is the probability that the coffeeshop owners will conclude that the new bean is better even if, in fact, it is no better than the beans they have always used in the past? b) In a second test, the coffeeshop owners brew 25 pots of coffee with the new bean and test the same hypotheses as in part 'a' using an alpha of 01. Suppose that the new bean would actually allow 80% of these pots of coffee to stay fresh longer than 30 minutes: what is the power of the coffeeshop owners' experiment?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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