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 py be the number of people polled who supported the policy, divided by the total number of people polled N. 1) What distribution of N * PN? 2) Show that the expected value of pN is p. 3) If I want my estimate to be accurate, I want the error of pN to be small. How many people should I poll to guarantee the expected squared error on py is less than e? 4) How many people should I poll to guarantee the expected squared error on py is less than e, if I don't know p? 5) 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 py is less than with 90% confidence? 6) How many people should I poll to guarantee the actual error on py is less than with 90% confidence, if I don't know p?
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 py be the number of people polled who supported the policy, divided by the total number of people polled N. 1) What distribution of N * PN? 2) Show that the expected value of pN is p. 3) If I want my estimate to be accurate, I want the error of pN to be small. How many people should I poll to guarantee the expected squared error on py is less than e? 4) How many people should I poll to guarantee the expected squared error on py is less than e, if I don't know p? 5) 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 py is less than with 90% confidence? 6) How many people should I poll to guarantee the actual error on py is less than with 90% confidence, if I don't know p?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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