In a recent poll, 450 people were asked if they liked dogs, and 65% said they did. Find the Margin of Error for this poll, at the 90% confidence level. Give your answer to four decimal places if possible. Submit Question

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter4: Equations Of Linear Functions
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In a recent poll, 450 people were asked if they liked dogs, and 65% said they did. Find the Margin of Error
for this poll, at the 90% confidence level. Give your answer to four decimal places if possible.
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Transcribed Image Text:Question 7 > In a recent poll, 450 people were asked if they liked dogs, and 65% said they did. Find the Margin of Error for this poll, at the 90% confidence level. Give your answer to four decimal places if possible. Submit Question
Expert Solution
Step 1

The margin of error provides the percentage difference between a true population value and the estimated value.

The margin of error defines as

MOEγ=zγ σn,σ is the standard deviation,n is the sample size,zγ is the quantile,γ is the confidence level.

Step 2

Suppose, p be the proportion of people like dogs.

Given that 65% of people like dogs. 

p=0.65

450 samples are taken,

then n=450.

 

The standard deviation is 

σ=np1-p=450×0.65×1-0.65=102.375=10.1181

 

From the z table 

zγ=z0.90=1.646

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