Answered: 3. A coffee chain owner is concerned…

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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Question

3. A coffee chain owner is concerned with the proportion of people who would rather order a coffee from another store. The corporate office tells her that from a separate large-scale study, they found the true proportion to be p = 0.6. As she wants to estimate this proportion herself, she asks 20 people in line whether they would switch and records a ‘1’ if they said “Yes” and records a ‘0’ otherwise. (a) Based on this study, what is the approximate distribution of the sample proportion pˆ? State all parameters and assumptions required for your answer. (b) The store owner wants to determine the cutoff point for the sample proportion for which the probability of observing a larger sample proportion is 0.50. That is, find the value ‘a’ such that P(ˆp > a) = 0.50. Show all your work. Explain how you could have found your answer immediately without using the Normal probability table and using a property about the Normal distribution.

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