Answer the following questions accordingly. Thanks in advance!

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 13PT
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Answer the following questions accordingly. Thanks in advance!
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,
etc.), they may be reluctant to answer honestly.
A potential solution to this is the following: let's 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, you must answer honestly. However, if it
comes up tails, you must answer 'YES’ regardless of what the truth is. This gives people
л
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
л
again, we have that the expected value of p,, is p, but we are actually interested in
N
measuring q.
Transcribed Image Text: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, etc.), they may be reluctant to answer honestly. A potential solution to this is the following: let's 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, you must answer honestly. However, if it comes up tails, you must answer 'YES’ regardless of what the truth is. This gives people л 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 л again, we have that the expected value of p,, is p, but we are actually interested in N measuring q.
C) IfI want my estimate to be accurate, I want the error of q, to be small. How many
N
people should I poll to guarantee that the expected squared error on q, is less than
E, when I don't know the value of q?
D) How many people should I poll to guarantee the actual error of q, is less than E,
N
with 90% confidence, if I don't know q?
Transcribed Image Text:C) IfI want my estimate to be accurate, I want the error of q, to be small. How many N people should I poll to guarantee that the expected squared error on q, is less than E, when I don't know the value of q? D) How many people should I poll to guarantee the actual error of q, is less than E, N with 90% confidence, if I don't know q?
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