Homework Help is Here – Start Your Trial Now!
Math
Probability
How many people should I poll to guarantee the actual error on qn is less than e, with 90% confidence, if I don't know q?

How many people should I poll to guarantee the actual error on qn is less than e, with 90% confidence, if I don't know q?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
See similar textbooks
icon
Related questions
Question
How many people should I poll to guarantee the actual error on ĝn is less than e, with 90% confidence, if I don't know q?
Transcribed Image Text:How many people should I poll to guarantee the actual error on ĝn is less than e, with 90% confidence, if I don't know q?
Suppose you want to find out how many people support Policy X. A standard polling approach is to just ask N many people whether or not they support Policy X, and take the fraction of people who say yes as an estimate of the probability that any one person supports the policy. Suppose that the probability someone supports the policy is p, which you do not know. Let îy be the number of people polled who supported the policy, divided by the total number of people polled N. However, a problem with polling is whether or not people are willing to answer honestly. If a question might be viewed as shameful or embarrassing (about politics, sexual activity, or whatever people are sensitive about), they may be reluctant to answer honestly. A potential solution to this is the following: suppose that 'YES' is the embarrassing or socially shameful answer; give the 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 about why they answered yes, if pressed. Again, let pN be the fraction of people who said 'YES'. Let p be the probability that 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.
Transcribed Image Text:Suppose you want to find out how many people support Policy X. A standard polling approach is to just ask N many people whether or not they support Policy X, and take the fraction of people who say yes as an estimate of the probability that any one person supports the policy. Suppose that the probability someone supports the policy is p, which you do not know. Let îy be the number of people polled who supported the policy, divided by the total number of people polled N. However, a problem with polling is whether or not people are willing to answer honestly. If a question might be viewed as shameful or embarrassing (about politics, sexual activity, or whatever people are sensitive about), they may be reluctant to answer honestly. A potential solution to this is the following: suppose that 'YES' is the embarrassing or socially shameful answer; give the 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 about why they answered yes, if pressed. Again, let pN be the fraction of people who said 'YES'. Let p be the probability that 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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer