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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 pN be the number of people polled who supported the policy, divided by the total number of people polled N.

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 pN be the number of people polled who supported the policy, divided by the total number of people polled N.

A First Course in Probability (10th Edition)
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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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 \(\hat{p}_N\) be the number of people polled who supported the policy, divided by the total number of people polled \( N \).
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 \(\hat{p}_N\) be the number of people polled who supported the policy, divided by the total number of people polled \( N \).
Just because the *expected* error is small doesn't mean the *actual* error is small. How many people should I poll to guarantee that the actual error on \( \hat{p}_N \) is less than \( \varepsilon \) with 90% confidence?
Transcribed Image Text:Just because the *expected* error is small doesn't mean the *actual* error is small. How many people should I poll to guarantee that the actual error on \( \hat{p}_N \) is less than \( \varepsilon \) with 90% confidence?
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