What is the relationship between q and p? Suppose you want to find out how many people support Policy X. A standard polling approach is to just ask Nmany people whether or not they support Policy X, and take the fraction of people who say yes as an estimate ofthe probability that any one person supports the policy. Suppose that the probability someone supports the policyis p, which you do not know. Let îy be the number of people polled who supported the policy, divided by the totalnumber of people polled N.However, a problem with polling is whether or not people are willing to answer honestly. If a question might beviewed as shameful or embarrassing (about politics, sexual activity, or whatever people are sensitive about), theymay be reluctant to answer honestly.A potential solution to this is the following: suppose that 'YES' is the embarrassing or socially shameful answer; givethe people you are polling the following instructions: flip a coin privately, and if it comes up heads answer honestly,but if it comes up tails answer 'YES' regardless of what the truth is. This gives people plausible deniability aboutwhy they answered yes, if pressed. Again, let pN be the fraction of people who said 'YES'. Let p be the probabilitythat a randomly selected person says 'yes'; let q be the probability that a person's true answer is 'yes'. Note again,we have that the expected value of pN is p, but we are actually interested in measuring q.

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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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